A trajectory planning method for a variant near space vehicle and related apparatus

Abstract

The application discloses a trajectory planning method of a variant near-space vehicle and a related device, relates to the technical field of aerospace guidance control, and comprises the following steps: constructing a three-dimensional mass center kinematics and dynamics model; a state vector of the model comprises a voyage, a lateral position, a height, a speed, a ballistic inclination angle and a ballistic deflection angle, and a control vector comprises an attack angle, a roll angle and a variable configuration ratio; based on the three-dimensional mass center kinematics and dynamics model, the obtained initial state vector and terminal state vector, a heuristic optimization algorithm and a gradient descent method are used for flight time optimization to obtain a final optimal flight time; the initial state vector, the terminal state vector and the final optimal flight time are input into a neural network model to obtain an initial control history guess sequence; based on the initial control history guess sequence, homotopy and Gauss pseudospectrum methods are used for trajectory planning solution to obtain an optimal trajectory. The application significantly improves the planning precision and calculation efficiency of a flight trajectory.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aerospace guidance and control, in particular to a trajectory planning method for a morphing near space vehicle and a related device. BACKGROUND

[0002] As a flight platform with high attack precision, strong attack capability and high cost, the morphing near space vehicle is usually used to attack targets with important strategic or tactical value. In the flight process of this type of vehicle, the main concern in the midcourse guidance phase is how to ensure that the vehicle can accurately reach the mid- and terminal guidance handover area. However, existing guidance methods often ignore the control of the mid- and terminal guidance handover point speed, which is a key parameter affecting the terminal attack effect. If the terminal speed is too small, the attack kinetic energy of the vehicle will be weakened; if the terminal speed is too large, the performance of the infrared seeker may be reduced, thereby affecting the attack precision. Since this type of vehicle does not rely on thrust during the midcourse guidance phase, its trajectory planning needs to control multiple state variables such as terminal range, altitude, lateral position, speed, ballistic inclination angle and ballistic deflection angle through control variables such as attack angle, roll angle and variable configuration ratio, thereby forming a typical under-actuated guidance problem.

[0003] For the above-mentioned under-actuated trajectory planning problem, existing technologies usually use trajectory planning methods for solution, but there are still some limitations in actual application. First, most aerospace trajectory planning methods assume that the flight time is a fixed value, but in fact the vehicle is not sensitive to time constraints. If the flight time can be reasonably optimized, the overall flight performance and stability can be improved, so it is of great value to determine the optimal flight time. Second, under the condition of limited computing resources, it is often difficult for the vehicle to quickly obtain effective trajectory initial values. Poor initial values can easily lead to slow convergence or even divergence in the planning process, so an intelligent mapping mechanism from initial and terminal state constraints to initial value guessing is needed to quickly generate high-quality initial values. In addition, although direct trajectory planning methods have a wide convergence range, due to the strong nonlinearity of the model, the trajectory may not converge or diverge. Therefore, how to stably and accurately solve high-complexity trajectory planning problems has become a technical difficulty that needs to be broken through. SUMMARY

[0004] The purpose of the present application is to provide a trajectory planning method for a morphing near space vehicle and a related device, which can significantly improve the planning accuracy and computational efficiency of the flight trajectory.

[0005] To achieve the above-mentioned purpose, the present application provides the following solutions:

[0006] In a first aspect, the present application provides a trajectory planning method for a morphing near space vehicle, comprising:

[0007] constructing a three-dimensional mass center kinematics and dynamics model of the variant near space vehicle, a state vector of the three-dimensional mass center kinematics and dynamics model comprising a range, a lateral position, an altitude, a velocity, a ballistic inclination angle and a ballistic declination angle, and a control vector of the three-dimensional mass center kinematics and dynamics model comprising an angle of attack, a roll angle and a variable configuration ratio;

[0008] obtaining an initial state vector and a terminal state vector of the variant near space vehicle, and based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, optimizing a flight time of the variant near space vehicle by using a heuristic optimization algorithm and a gradient descent method to obtain a final optimal flight time;

[0009] inputting the initial state vector, the terminal state vector and the final optimal flight time into the neural network model to obtain an initial control history guess sequence;

[0010] based on the initial control history guess sequence, solving the three-dimensional mass center kinematics and dynamics model by using a homotopy method and a Gauss pseudospectral method to obtain an optimal trajectory.

[0011] In a second aspect, the present application provides a computer device, comprising: a memory, a processor, a computer program stored on the memory and executable on the processor, and the processor executes the computer program to implement the trajectory planning method of the variant near space vehicle according to any one of the above.

[0012] In a third aspect, the present application provides a computer readable storage medium having a computer program stored thereon, and the computer program is executed by a processor to implement the trajectory planning method of the variant near space vehicle according to any one of the above.

[0013] In a fourth aspect, the present application provides a computer program product comprising a computer program, and the computer program is executed by a processor to implement the trajectory planning method of the variant near space vehicle according to any one of the above.

[0014] According to the embodiments provided in the present application, the present application has the following technical effects:

[0015] The application provides a trajectory planning method of a variant near-space vehicle and a related device, wherein a heuristic optimization algorithm and a gradient descent method are fused, the performance index in the flight process is improved, the final optimal flight time is obtained, and therefore the smoothness of the control curve can be further improved. Meanwhile, the optimal flight time and the state vector are input into a neural network model, an initial control history guess sequence is obtained through network learning, the convergence can be ensured under the same condition, the iteration divergence or non-convergence is further avoided, and accurate initial control information is provided for subsequent trajectory planning. Moreover, the homotopy method and the Gauss pseudospectrum method are used to accurately solve the three-dimensional centroid kinematics and dynamics model, the reference solution output by the simple trajectory planning problem is used as a good input of the complex trajectory planning problem, and the optimal solution of the complex, fast time-varying and nonlinear planning problem can be obtained under the condition of a small convergence radius, so that the optimal trajectory planning of the vehicle from the initial state to the terminal state is realized. Through optimization of the flight time, neural network prediction control sequence and efficient trajectory solving method, the calculation efficiency and precision of the trajectory planning of the vehicle are significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor based on these drawings.

[0017] Figure 1 An application environment diagram of a trajectory planning method of a variant near-space vehicle according to an embodiment of the present application;

[0018] Figure 2 A flowchart of a trajectory planning method of a variant near-space vehicle provided by an embodiment of the present application;

[0019] Figure 3 A framework diagram of a trajectory planning method of a variant near-space vehicle provided by an embodiment of the present application;

[0020] Figure 4 A coordinate system diagram of a variant near-space vehicle provided by an embodiment of the present application;

[0021] Figure 5 A structure diagram of a back propagation neural network provided by an embodiment of the present application;

[0022] Figure 6 A simulation diagram of a trajectory curve of a variant near-space vehicle provided by an embodiment of the present application;

[0023] Figure 7 A simulation schematic diagram of a time-attack angle curve provided by an embodiment of the present application is shown in FIG. 6;

[0024] Figure 8 A simulation schematic diagram of a time-tilt angle curve provided by an embodiment of the present application is shown in FIG. 7;

[0025] Figure 9 A simulation schematic diagram of a time-deformation ratio curve provided by an embodiment of the present application is shown in FIG. 8;

[0026] Figure 10 A simulation schematic diagram of a time-velocity curve provided by an embodiment of the present application is shown in FIG. 9;

[0027] Figure 11 A simulation schematic diagram of a time-trajectory inclination angle curve provided by an embodiment of the present application is shown in FIG. 10;

[0028] Figure 12 A simulation schematic diagram of a time-trajectory deflection angle curve provided by an embodiment of the present application is shown in FIG. 11;

[0029] Figure 13 A structural schematic diagram of a computer device provided by an embodiment of the present application is shown in FIG. 12. DETAILED DESCRIPTION

[0030] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by those of ordinary skill in the art without any creative work fall within the protection scope of the present application.

[0031] The above-mentioned purposes, features and advantages of the present application can be more obvious and easy to understand. The present application will be described in further detail below with reference to the drawings and specific embodiments.

[0032] The trajectory planning method of the variant near-space vehicle provided by the embodiments of the present application can be applied to, for example, Figure 1The application environment shown. Among them, the terminal 102 communicates with the server 104 through the network. The data storage system can store the data required by the server 104 to process. The data storage system can be set up separately, or integrated on the server 104, or placed on the cloud or other servers. The terminal 102 can send the initial state vector and the terminal state vector of the aircraft to the server 104, and the server 104 optimizes the flight time of the variable near space aircraft based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, using the heuristic optimization algorithm and the gradient descent method, to obtain the final optimal flight time; input the initial state vector, the terminal state vector and the final optimal flight time into the neural network model to obtain the initial control history guess sequence; based on the initial control history guess sequence, the homotopy method and the Gauss pseudospectral method are used to solve the trajectory planning to obtain the optimal trajectory. The server 104 can feed back the optimal trajectory obtained to the terminal 102.

[0033] Among them, the terminal 102 can be but not limited to various desktop computers, notebook computers and Internet of Things devices and portable wearable devices. The server 104 can be implemented by an independent server or a server cluster composed of multiple servers, and can also be a cloud server.

[0034] In an exemplary embodiment, as Figures 2-3 shown, a trajectory planning method of a variable near space aircraft is provided, which is executed by a computer device, specifically can be executed by a terminal or a server and the like computer device alone, or can be executed by a terminal and a server together, in the embodiment of the application, taking the server 104 in Figure 1 the application environment as an example, the method includes the following steps 201 to 204. Among them:

[0035] Step 201, a three-dimensional mass center kinematics and dynamics model of a variable near space aircraft is constructed, the state vector of the three-dimensional mass center kinematics and dynamics model includes range, lateral position, height, velocity, ballistic inclination angle and ballistic deflection angle, and the control vector of the three-dimensional mass center kinematics and dynamics model includes angle of attack, angle of roll and variable configuration ratio.

[0036] Step 202, the initial state vector and the terminal state vector of the variable near space aircraft are obtained, and the flight time of the variable near space aircraft is optimized based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, using the heuristic optimization algorithm and the gradient descent method, to obtain the final optimal flight time.

[0037] Step 203, input the initial state vector, the terminal state vector and the final optimal flight time into the neural network model to obtain the initial control history guess sequence.

[0038] At step 204, based on the initial control history guess sequence, the trajectory planning of the three-dimensional centroid kinematics and dynamics model is solved by using the homotopy method and the Gauss pseudospectrum method to obtain an optimal trajectory.

[0039] By implementing the above steps 201 to 204, the present application improves the performance index in the flight process by fusing the heuristic optimization algorithm and the gradient descent method, and obtains the final optimal flight time, so as to further improve the smoothness of the control curve. At the same time, the optimal flight time and the state vector are input into the neural network model, and the initial control history guess sequence is obtained through network learning, so as to ensure that the convergence can be quickly achieved under the same conditions, and further avoid the iteration divergence or non-convergence, thereby providing accurate initial control information for subsequent trajectory planning. Moreover, the three-dimensional centroid kinematics and dynamics model is accurately solved by using the homotopy method and the Gauss pseudospectrum method, the reference solution output by the simple trajectory planning problem is used as a good input of the complex trajectory planning problem, and it is ensured that the optimal solution of the complex, fast time-varying and nonlinear planning problem can be obtained under the condition of small convergence radius, so as to realize the optimal trajectory planning of the aircraft from the initial state to the terminal state. Through optimizing the flight time, the neural network prediction control sequence and the efficient trajectory solving method, the calculation efficiency and accuracy of the aircraft trajectory planning are significantly improved.

[0040] Further, in step 201, the trajectory curve of the variable near-space vehicle is researched only for the three-degree-of-freedom centroid model, without considering the attitude motion. Therefore, the motion model only needs to research the three-dimensional centroid kinematics and dynamics model. Without considering the earth rotation and curvature, the trajectory coordinate system of the variable near-space vehicle is as shown in FIG. 1, wherein the x-axis points to the north, the z-axis points upward, and the y-axis points to the east according to the right-hand screw rule. Figure 4 Therefore, the three-dimensional centroid kinematics and dynamics model is specifically as follows:

[0041] (1);

[0042] wherein, denotes the change rate of the range; denotes the change rate of the lateral position; denotes the change rate of the height; denotes the change rate of the velocity; denotes the change rate of the ballistic inclination angle; denotes the change rate of the ballistic deflection angle; denotes the velocity; denotes the ballistic inclination angle; denotes the ballistic deflection angle; denotes the roll angle; denotes the mass; denotes the gravitational acceleration; denotes the lift. Indicates resistance.

[0043] In formula (1), L and D represent lift and drag, respectively, and their expressions are as follows:

[0044] (2);

[0045] in, Indicates the reference area; The density of the atmosphere is expressed as follows:

[0046] (3);

[0047] in, Indicates reference atmospheric density; Indicates atmospheric elevation.

[0048] and These represent the lift coefficient and drag coefficient, respectively:

[0049] (4);

[0050] in, Represents the Mach number; The angle of attack is defined as the angle between the projection of the velocity vector onto the longitudinal plane of symmetry and the longitudinal axis of the aircraft, with the pitch-up direction being positive. and These represent terms related to the drag coefficient; , , , , These represent terms related to the lift coefficient, which are calculated from aerodynamic simulation or wind tunnel testing. This represents the deformation ratio, ranging from [0.8, 1.2]. It should be noted that... It is immutable, but the aircraft used in this application has a variable configuration. It can be dynamically adjusted.

[0051] The state vector consisting of six states is , For the voyage, It is a lateral position. For height, Indicates speed, Indicates the trajectory inclination angle, The ballistic deflection angle is represented by the three control variables (i.e., guidance commands). The control vector consists of these three variables. , Indicates angle of attack. Indicates the tilt angle. The variable configuration ratio is represented. Therefore, the trajectory planning problem needs to achieve accurate control of the six terminal states through three control variables.

[0052] Further, in the aerospace trajectory planning problem, the terminal flight time is usually insensitive, and the performance index is sensitive. Therefore, the performance index is further improved by optimizing the flight time. The terminal flight time optimization is realized by combining the heuristic optimization algorithm and the gradient descent method, wherein the ibis optimization algorithm is an improved heuristic algorithm, aiming to search for a near-optimal suboptimal solution (i.e. an approximate optimal flight time); the gradient descent method aims to search for an optimal solution (i.e. the final optimal flight time) in a small range.

[0053] In step 202, based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, the flight time of the morphing near-space vehicle is optimized by using the heuristic optimization algorithm and the gradient descent method to obtain the final optimal flight time, which specifically includes:

[0054] In step a1, based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, the heuristic optimization algorithm is used to perform global search in a preset flight time range to obtain an approximate optimal flight time.

[0055] In step a2, the approximate optimal flight time is determined as an initial time value, and based on the initial time value, the adaptive gradient descent method is used to perform local fine search to obtain the final optimal flight time.

[0056] Further, inspired by the existing heuristic algorithm, the ibis optimization algorithm aims to simulate the foraging behavior of the ibis group by computer, i.e. the heuristic optimization algorithm is the ibis optimization algorithm. This algorithm simulates the natural foraging behavior of the ibis group, searches for the optimal flight time in a one-dimensional space by a group of ibis individuals, interacts information, and constantly updates the position, speed and acceleration of itself, and finally obtains the optimal solution. Each ibis has an independent position, speed and acceleration array in a one-dimensional search space, and updates its own position according to the individual optimal position and the group optimal position. Based on swarm intelligence, the optimal solution is finally obtained. The ibis optimization algorithm requires fewer parameters to be set, the theory is intuitive, and is suitable for solving the optimal flight time estimation problem of the morphing near-space vehicle. In order to meet various different constraints, considering that the trajectory planning problem of the near-space vehicle has fewer feasible solutions, the estimation accuracy of the optimal flight time is required to be higher. Therefore, in step a1, the ibis optimization algorithm is used to perform global search in a preset flight time range to obtain an approximate optimal flight time, which specifically includes:

[0057] In step b1, the positions, speeds and accelerations of all individuals are initialized.

[0058] Step b2, obtaining the performance index of each individual at the current iteration number based on the position of each individual at the current iteration number, the initial state vector and the terminal state vector; when the current iteration number is 1, the position of each individual is each candidate flight time in the preset flight time range.

[0059] Step b3, selecting the minimum performance index of all performance indexes of each individual to determine the optimal position of each individual at the current iteration number based on the current performance index set of each individual (i.e. all performance indexes of each individual obtained until the current iteration number), and selecting the minimum performance index of all performance indexes of all individuals at the current iteration number to determine the optimal position of the population at the current iteration number based on the performance indexes of all individuals at the current iteration number.

[0060] Step b4, determining whether the current iteration number reaches the maximum iteration number; if yes, outputting the optimal position of the population at the current iteration number, and determining the optimal flight time as the approximate optimal flight time; if no, calculating the position, velocity and acceleration of each individual at the next iteration number based on the optimal position of each individual at the current iteration number, the optimal position of the population, the velocity and acceleration of each individual, and the dynamics model of the Crested Ibis optimization algorithm, updating the optimal position, velocity and acceleration of each individual at the current iteration number to the position, velocity and acceleration of each individual at the next iteration number, increasing the current iteration number by 1, considering that the discrete time interval is 1 (i.e. the step is 1), and returning to the step "obtaining the performance index of each individual at the current iteration number based on the position of each individual at the current iteration number, the initial state vector and the terminal state vector".

[0061] The dynamics model of the Crested Ibis optimization algorithm comprises a velocity update formula, an acceleration update formula and a position update formula.

[0062] The velocity update formula is:

[0063] (5);

[0064] The acceleration update formula is:

[0065] (6);

[0066] The position update formula is:

[0067] (7);

[0068] wherein, represents the current iteration number velocity of the individual at the current iteration number next iteration number velocity of the individual at the current iteration number velocity memory term and weighting coefficients, respectively random number optimal position of the individual next iteration number position of the individual at the current iteration number next iteration number position of the individual at the current iteration number optimal position of the population acceleration memory term next iteration number acceleration of the individual at the current iteration number next iteration number acceleration of the individual at the current iteration number and weighting coefficients, respectively

[0069] Further, the above red-crowned crane optimization algorithm realizes the approximate suboptimal estimation of the optimal flight time, but in order to ensure a higher precision estimation, an adaptive gradient descent method is used to determine the final optimal flight time, and the iteration formula of the adaptive gradient descent method in step a2 is specifically:

[0070] (8)

[0071] wherein, final optimal flight time approximate optimal flight time adaptive learning rate, calculated by adaptive theory gradient value

[0072] Further, whether it is a direct trajectory planning method or an indirect trajectory planning method, there is a problem of small convergence radius, initial value sensitivity leading to direct divergence of the trajectory. Whether the trajectory converges in the iteration process depends on two major influencing factors: the goodness of the initial value (i.e. the initial control history guess sequence) and the goodness of the trajectory planning method design. Therefore, in order to better serve the subsequent trajectory planning method, the present application outputs a good initial value sequence based on the trained back propagation neural network (BP neural network) architecture.

[0073] The BP neural network is a multi-layer feedforward neural network architecture based on the error back propagation method, which is composed of an input layer, a hidden layer and an output layer. The core of the method is to back propagate the gradient error to realize the dynamic adjustment of the weight parameters, so it is easy to solve the fast initial value generation problem of the nonlinear strong coupling complex trajectory planning. Specifically, the neural network model in the embodiment is a trained back propagation neural network as shown in Figure 5 ; the trained back propagation neural network includes an output layer, a first hidden layer (containing 64 neurons), a second hidden layer (containing 256 neurons) and an output layer; the first hidden layer and the second hidden layer each include a hyperbolic tangent function; a multi-step recursive prediction method is used to predict the actions at multiple future time points (discrete points) through historical data. The discrete points are established in an equidistant manner within the optimal flight time. The determination process of the trained back propagation neural network is as follows:

[0074] Step c1, a sample state vector set is obtained, and the sample state vectors are processed by Monte Carlo targeting simulation to obtain a sample control vector set.

[0075] Step c2, the sample state vector set and the sample control vector set are preprocessed to obtain a preprocessed sample state vector set and a preprocessed sample control vector set; the preprocessing includes data cleaning and normalization.

[0076] Step c3, the preprocessed sample state vector set and the preprocessed sample control vector set are used to train the back propagation neural network to determine a trained back propagation neural network. Thus, the control actions at each discrete point are obtained by using the trained back propagation neural network, and an initial control history guess sequence is obtained.

[0077] Further, the activation function is selected as a hyperbolic tangent function, and the expression is:

[0078] (9);

[0079] wherein, represents a hyperbolic tangent function; represents a hyperbolic sine function; represents a hyperbolic cosine function; the function represents a natural exponential function exp( x ), that is, an exponential function with a natural constant e ( e ≈2.71828) as the base; the function represents exp(- x ).

[0080] Further, the trajectory planning problem is solved based on the Gauss pseudospectral method and the nonlinear programming method. However, the existing method has the problems of non-convergence and even direct divergence when solving the complex strong nonlinear trajectory planning problem. Therefore, the homotopy method is used to improve the above problems.

[0081] The homotopy method, also known as the homotopy extension method or the homotopy continuation method, is a numerical technique for solving complex optimization problems in the field of variable configuration near space vehicle guidance and control. It connects the original complex strong nonlinear trajectory planning problem and an easily solvable simple weak nonlinear programming problem by constructing a path of interrelated functions. In other words, a simple weak nonlinear trajectory planning problem is gradually transformed into an original complex strong nonlinear trajectory planning problem by gradually changing the homotopy parameter in the trajectory planning problem. Therefore, by controlling the change of the homotopy parameter, a relatively easy parameter optimization problem can be found in each iteration, and the solution of the previous iteration is used as the initial guess to gradually approach the optimal solution of the original problem.

[0082] In short, the process of solving the trajectory planning problem by the homotopy method is as follows:

[0083] (1) Define the homotopy function vector ;

[0084] (2) Select an auxiliary function ;

[0085] (3) When s = 0, solve the simple weak nonlinear trajectory planning problem;

[0086] (4) When s gradually changes from 0 to 1, solve the homotopy function vector by using the solution output in the last iteration as the initial guess. When s equals 1, the original complex strong nonlinear trajectory planning problem is solved.

[0087] Based on the above homotopy idea, the Gauss pseudospectral method is used to solve the above nonlinear trajectory planning problem. The Gauss pseudospectral method constructs a very sparse Jacobian matrix by interpolation instead of integration. This method can be regarded as a real-time online trajectory solving method.

[0088] Specifically, in step 204, based on the initial control history guess sequence, the homotopy method and the Gauss pseudospectral method are used to solve the trajectory planning of the three-dimensional mass center kinematics and dynamics model to obtain the optimal trajectory, which specifically includes:

[0089] Step d1, constructing homotopy function; the homotopy function is used to combine the complex strong nonlinear trajectory planning problem with the simple weak nonlinear trajectory planning problem, and control the transformation degree between the complex strong nonlinear trajectory planning problem and the simple weak nonlinear trajectory planning problem through the homotopy parameter; the expression of the homotopy function is:

[0090] (10);

[0091] wherein, represents the function vector reconstructed by the homotopy method; represents the state vector; represents the homotopy parameter, ranging from 0 to 1; represents the complex strong nonlinear trajectory planning problem which needs to be solved finally; represents the simple weak nonlinear trajectory planning problem which is constructed initially.

[0092] Step d2, according to the homotopy parameter of the current step, the trajectory planning problem defined by the homotopy function which needs to be solved currently is determined.

[0093] Step d3, the continuous trajectory planning problem defined by the homotopy function which needs to be solved currently is discretized into the nonlinear programming problem which needs to be solved currently by using the Gauss pseudospectrum method; the discretization process includes transforming the time interval to the standard interval, discretizing the state vector and the control vector on the collocation point, and converting the dynamic differential equation constraint in the three-dimensional mass center kinematics and dynamics model into algebraic constraint, which is specifically:

[0094] The performance index of the nonlinear trajectory planning problem is designed as:

[0095] (11);

[0096] wherein, represents the performance index; represents the initial time; represents the deformation ratio; represents the penalty coefficient about the deformation ratio.

[0097] The dynamic differential equation constraint in the three-dimensional mass center kinematics and dynamics model can be expressed as:

[0098] (12);

[0099] wherein, represents the derivative of the state vector, ; is the function in formula (11) ; is the control vector.

[0100] The expression of the initial state vector constraint and the terminal state vector constraint is:

[0101] (13);

[0102] wherein, denotes the initial state vector value; denotes the desired terminal state vector value.

[0103] The Gauss pseudospectral method converts the continuous time into the standard interval , and the conversion relationship is:

[0104] (14);

[0105] wherein, denotes the normalized time.

[0106] In the optimal control problem, the Gauss pseudospectral method can be approximately expressed as:

[0107] (15);

[0108] wherein, denotes the state vector under continuous time; denotes the state vector under discrete time; the subscript denotes the th collocation point; denotes the last collocation point; denotes the interpolation basis function, and the expression is:

[0109] (16);

[0110] wherein, denotes the function related to the interpolation point; the subscript denotes the th collocation point.

[0111] The numerical integration problem is calculated by weight summation, which ensures that the pseudospectral method has high computational efficiency, and the numerical integration equation is:

[0112] (17);

[0113] wherein, and denote the lower limit and the upper limit of the integral interval, respectively; denotes the integral weight matrix; denotes the function value of the homotopy function at the normalized time τ ; and denotes the function value of the homotopy function at the normalized time denotes the time at the normalized discrete point i

[0114] In the Gauss pseudospectral method, the dynamic constraint equation of the terminal state can be rewritten according to formula (10) as:

[0115] (18);

[0116] wherein, and denote the first and last discrete points, respectively; denotes the terminal state vector; denotes the initial state vector; denotes the state vector at a certain discrete point; denotes the control vector at a certain discrete point.

[0117] Based on formula (17), formula (18) can be rewritten as:

[0118] (19);

[0119] wherein, denotes the discretized terminal state vector; denotes the discretized initial state vector; denotes the last discrete point; denotes the time i corresponding to the discrete point.

[0120] The dynamic equation constraint can be derived by differentiating formula (15) as:

[0121] (20);

[0122] wherein, denotes the normalized time corresponding to the state vector derivative; denotes the discretized form of the normalized time corresponding to the state vector derivative; denotes the discretized form of the normalized time corresponding to the interpolation basis function; the subscript denotes the th node; denotes the differential matrix.

[0123] (21);

[0124] wherein, the function denotes the Legendre interpolation polynomial; ​​denotes the normalized time the discrete form of the corresponding Legendre interpolating polynomial; denotes the normalized time the derivative of the discrete form of the corresponding Legendre interpolating polynomial; denotes the normalized time the derivative of the discrete form of the corresponding Legendre interpolating polynomial.

[0125] Therefore, according to the weighted residual rule, the formula (20) dynamics constraint can be rewritten as an algebraic constraint:

[0126] (22);

[0127] wherein, denotes the algebraic constraint.

[0128] Step d4, based on the previous guess, the nonlinear trajectory planning solver is used to solve the nonlinear programming problem to be solved at present, and the current guess is obtained; the current guess is the state vector and control vector under the homotopy parameter of the current step; when the homotopy parameter of the current step is 0, the current guess is the initial control history guess sequence;

[0129] Step d5, judge whether the homotopy parameter of the current step is 1; if yes, output the current guess, and determine the current guess as the optimal trajectory; if not, based on the homotopy parameter of the current step and the preset value, the homotopy parameter of the next step is calculated, and the homotopy parameter of the current step is updated to the homotopy parameter of the next step, and return to the step of “determining the trajectory planning problem defined by the homotopy function to be solved according to the homotopy parameter of the current step”.

[0130] In an exemplary embodiment, in order to verify the effectiveness and feasibility of the variational near space vehicle homotopy trajectory planning method based on the optimization estimation of the optimal flight time of the red crane, the present application is oriented to the simulation verification of the middle guidance of the variational near space vehicle. The initial state and the expected terminal state constraint of the vehicle are shown in Table 1.

[0131] Table 1 Initial state and expected terminal state of variational near space vehicle

[0132]

[0133] The flight trajectory of the variational near space vehicle is shown in Figure 6 The control amount attack angle, roll angle, variable configuration ratio (referred to as deformation ratio) curve is shown in Figures 7-9 The speed curve is shown in Figure 10 The ballistic inclination angle and ballistic deflection angle curve is shown in Figures 11-12The terminal state control error is shown in the table. The range error is -0.5810 meters; the height error is 1.3592 meters; the lateral position error is -23.0420 meters; the velocity error is 0.0123 meters / second; the ballistic angle error is -0.0011 degrees; and the ballistic deflection angle error is -0.0037 degrees.

[0134] The error statistics and Figure 6 It is shown that the homotopy trajectory optimization method based on the Zhu He optimization estimation of the optimal flight time of the variant near-space vehicle under the limited computing resources achieves high-precision control of the terminal state. Compared with the flight range of more than 56 kilometers, the lateral position error is more than 20 meters, but it can still be considered as small and negligible. In addition, the terminal guidance segment has strong robustness and dynamic error correction capability, and can fully meet the accuracy requirements of terminal attack. Figures 7-8 It is shown that the attack angle and tilt angle curves are relatively smooth, and there is no phenomenon of large amplitude or high frequency jitter, which is beneficial to the attitude tracking control system. Figure 9 It is shown that although the third control variable (deformation ratio) has a small overall amplitude, it can achieve the guidance task through configuration fine-tuning. Affected by the configuration change, Figure 11 It is shown that the ballistic angle curve appears a slight disturbance at about 3 seconds. The disturbance amplitude is small, and it has little effect on the actual flight performance of the vehicle. Figure 12 It is shown that the ballistic angle curve changes smoothly and has high terminal control accuracy.

[0135] In an exemplary embodiment, a computer device, which can be a server or a terminal, has an internal structure diagram as shown in the figure. Figure 13 The computer device includes a processor, a memory, an input / output interface (I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store processing data. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals through network connection. The computer program is executed by the processor to implement a trajectory planning method for a variant near-space vehicle.

[0136] Those skilled in the art can understand, Figure 13The structure shown in the figure is only a block diagram of part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. The specific computer device can include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components. In an exemplary embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps in the above method embodiments.

[0137] In an exemplary embodiment, a computer readable storage medium is provided, storing a computer program, which is executed by a processor to implement the steps in the above method embodiments.

[0138] In an exemplary embodiment, a computer program product is provided, including a computer program, which is executed by a processor to implement the steps in the above method embodiments.

[0139] 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 for analysis, stored data, displayed data, etc.) involved in the present application are all information and data authorized by the user or authorized by all parties, and the collection, use and processing of related data need to comply with relevant regulations.

[0140] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer readable storage medium, and when the computer program is executed, the processes of the above-mentioned embodiments of the methods can be included. Any reference to memory, databases or other media used in the embodiments provided in the present 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 storage, high-density embedded non-volatile memory, resistive memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration but not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0141] The database involved in the embodiments provided in the present application can include at least one of a relational database and a non-relational database. The non-relational database can include a distributed database based on a blockchain, etc., without being limited thereto. The processor involved in the embodiments provided in the present application can be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., without being limited thereto.

[0142] The technical features of the above embodiments can be combined in any manner. To make the description concise, not all possible combinations of the technical features in the above embodiments are described, but as long as the combinations of the technical features do not exist contradictions, they should be considered as the scope of the present application.

[0143] The principles and implementation modes of the present application are described by applying specific examples in the present application. The above-mentioned embodiments are only used to help understand the method and its core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed. In conclusion, the content of the present application should not be understood as a limitation.

Claims

1. A method for trajectory planning of a variant near space vehicle, characterized by, The trajectory planning method of the variant near-space vehicle comprises the following steps: A three-dimensional mass center kinematics and dynamics model of the variant near-space vehicle is constructed; a state vector of the three-dimensional mass center kinematics and dynamics model comprises a range, a lateral position, an altitude, a velocity, a ballistic inclination angle and a ballistic declination angle, and a control vector of the three-dimensional mass center kinematics and dynamics model comprises an angle of attack, a roll angle and a variable configuration ratio; An initial state vector and a terminal state vector of the variant near-space vehicle are obtained, and a heuristic optimization algorithm and a gradient descent method are used to optimize a flight time of the variant near-space vehicle based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, so as to obtain a final optimal flight time; The initial state vector, the terminal state vector and the final optimal flight time are input into a neural network model to obtain an initial control history guess sequence; Based on the initial control history guess sequence, a homotopy method and a Gauss pseudospectral method are used to solve the three-dimensional mass center kinematics and dynamics model to obtain an optimal trajectory, specifically comprising the following steps: A homotopy function is constructed; the homotopy function is used to combine a complex strong nonlinear trajectory planning problem with a simple weak nonlinear trajectory planning problem, and to control a transformation degree between the complex strong nonlinear trajectory planning problem and the simple weak nonlinear trajectory planning problem through a homotopy parameter; A trajectory planning problem defined by a homotopy function that needs to be solved at present is determined according to the homotopy parameter of the current step; A Gauss pseudospectral method is used to discretize the continuous trajectory planning problem defined by the homotopy function that needs to be solved at present into a nonlinear programming problem that needs to be solved at present; the discretization process comprises transforming a time interval to a standard interval, discretizing the state vector and the control vector at a collocation point, and converting a dynamics differential equation constraint in the three-dimensional mass center kinematics and dynamics model into an algebraic constraint; Based on the last guess, a nonlinear trajectory planning solver is used to solve the nonlinear programming problem that needs to be solved at present to obtain a current guess; the current guess is a state vector and a control vector under the current homotopy parameter; when the current homotopy parameter is 0, the current guess is the initial control history guess sequence; It is judged whether the homotopy parameter of the current step is 1; if yes, the current guess is output, and the current guess is determined as the optimal trajectory; if not, a homotopy parameter of the next step is calculated based on the homotopy parameter of the current step and a preset value, the homotopy parameter of the current step is updated to the homotopy parameter of the next step, and the step of "determining the trajectory planning problem defined by the homotopy function that needs to be solved at present according to the homotopy parameter of the current step" is returned.

2. The method of trajectory planning for a variant near space vehicle according to claim 1, wherein, The three-dimensional mass center kinematics and dynamics model specifically comprises the following steps: ； wherein, represents a rate of change of the range; represents a rate of change of the lateral position; represents a rate of change of the altitude; represents a rate of change of the velocity; represents a rate of change of the ballistic angle of inclination; represents a rate of change of the ballistic angle of declination; represents the velocity; represents the ballistic angle of inclination; represents the ballistic angle of declination; represents the angle of bank; represents the mass; represents the acceleration of gravity; represents the lift; represents the drag.

3. The method of trajectory planning for a variant near space vehicle according to claim 1, wherein, Based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, a heuristic optimization algorithm and a gradient descent method are used to optimize the flight time of the variant near-space vehicle to obtain the final optimal flight time, specifically comprising the following steps: Based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, a heuristic optimization algorithm is used to perform a global search within a preset flight time range to obtain an approximate optimal flight time; The approximate optimal flight time is determined as an initial time value, and a local fine search is performed based on the initial time value by using an adaptive gradient descent method to obtain a final optimal flight time.

4. The method of trajectory planning for a variant near space vehicle according to claim 3, wherein, The heuristic optimization algorithm is a crested ibis optimization algorithm; based on a three-dimensional centroid kinematics and dynamics model, an initial state vector and a terminal state vector, the heuristic optimization algorithm is used to perform a global search in a preset flight time range to obtain an approximate optimal flight time, and specifically includes: Based on each individual position under the current iteration number, the initial state vector and the terminal state vector, a performance index of each individual under the current iteration number is obtained; when the current iteration number is 1, each individual position is each candidate flight time in the preset flight time range; Based on the current performance index set of each individual, the optimal position of each individual under the current iteration number is determined, and based on the performance index of all individuals under the current iteration number, the optimal position of the population under the current iteration number is determined; the current performance index set of each individual is all performance indexes of each individual obtained by the current iteration number; It is judged whether the current iteration number reaches a maximum iteration number; if yes, the optimal position of the population under the current iteration number is output, and the optimal position of the population under the current iteration number is determined as the approximate optimal flight time; if not, based on the optimal position of each individual under the current iteration number, the optimal position of the population, the speed of each individual and the acceleration of each individual, the dynamics model of the crested ibis optimization algorithm is used to calculate the individual position, the speed of each individual and the acceleration of each individual under the next iteration number, and the optimal position of each individual under the current iteration number, the speed of each individual and the acceleration of each individual are updated to the individual position, the speed of each individual and the acceleration of each individual under the next iteration number, the current iteration number + 1, and the step "based on the individual position under the current iteration number, the initial state vector and the terminal state vector, the performance index of each individual under the current iteration number is obtained" is returned.

5. The method of trajectory planning for a variant near space vehicle according to claim 3, wherein, The iteration formula of the adaptive gradient descent method is specifically: ； wherein, represents the final optimal flight time; represents the approximate optimal flight time; represents the adaptive learning rate; represents the gradient value.

6. The method of trajectory planning for a variant near space vehicle according to claim 4, wherein, The dynamics model of the crested ibis optimization algorithm includes a speed update formula, an acceleration update formula and a position update formula; The speed update formula is: ； The acceleration update formula is: ； The position update formula is: ； wherein, denotes the individual velocity at the current iteration number denotes the individual velocity at the next iteration number denotes the individual velocity at the next iteration number denotes the individual velocity at the next iteration number denotes the velocity memory term; and denote weighting factors, respectively; denotes a random number; denotes the individual best position; denotes the individual position at the current iteration number denotes the individual position at the next iteration number denotes the individual position at the next iteration number denotes the individual position at the next iteration number denotes the swarm best position; denotes the acceleration memory term; denotes the individual acceleration at the current iteration number denotes the individual acceleration at the next iteration number denotes the individual acceleration at the next iteration number denotes the individual acceleration at the next iteration number and denote weighting factors, respectively.

7. The method of trajectory planning of a variant near space vehicle according to claim 1, wherein, The neural network model is a trained back propagation neural network; the trained back propagation neural network includes an output layer, a first hidden layer, a second hidden layer and an output layer; the first hidden layer and the second hidden layer both include a hyperbolic tangent function; wherein the determination process of the trained back propagation neural network is: A sample state vector set is obtained, and the sample state vector is processed by using a Monte Carlo targeting simulation to obtain a sample control vector set; The sample state vector set and the sample control vector set are preprocessed to obtain a preprocessed sample state vector set and a preprocessed sample control vector set; the preprocessing includes data cleaning and normalization; The preprocessed sample state vector set and the sample control vector set are used to train the back propagation neural network to determine the trained back propagation neural network.

8. A computer device comprising: 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 trajectory planning method of the variant near-space vehicle according to any one of claims 1-7.

9. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the trajectory planning method of the variant near-space vehicle according to any one of claims 1-7.

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