Trajectory planning method of variant near space aircraft and related device

Abstract

The invention discloses a trajectory planning method for a variant near space aircraft and a related device, and relates to the technical field of aerospace guidance control, and the method comprises the steps: constructing a three-dimensional mass center kinematics and dynamics model; state vectors of the model comprise a voyage, a lateral position, a height, a speed, a ballistic inclination angle and a ballistic deflection angle, and control vectors comprise an attack angle, a heeling angle and a variable configuration ratio; based on the three-dimensional centroid kinematics and dynamics model, an initial state vector and a terminal state vector are obtained, flight time optimization is carried out through a heuristic optimization algorithm and a gradient descent method, and the final optimal flight time is obtained; inputting the initial state vector, the terminal state vector and the final optimal flight time into a neural network model to obtain an initial control historical conjecture sequence; and based on the initial control historical conjecture sequence, trajectory planning and solving are carried out by using a homotopy method and a Gaussian pseudo-spectral method to obtain an optimal trajectory. According to the invention, the planning precision and calculation efficiency of the flight path are obviously improved.

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- terminal guidance handover area. However, existing guidance methods often ignore the control of the mid- 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 angle and ballistic angle of attack through control variables such as attack angle, roll angle and variable configuration ratio, so as to constitute 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 of the planning process, and 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: In a first aspect, the present application provides a trajectory planning method for a morphing near space vehicle, comprising: construct 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 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; obtain 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, a heuristic optimization algorithm and a gradient descent method are used to optimize a flight time of the variant near space vehicle, to obtain a final optimal flight time; the initial state vector, the terminal state vector and the final optimal flight time are input into the 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.

[0006] In a second aspect, the present application provides a computer device, comprising: a memory, a processor to store a computer program on the memory and run the computer program 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.

[0007] In a third aspect, the present application provides a computer readable storage medium, which stores 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.

[0008] In a fourth aspect, the present application provides a computer program product, which comprises 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.

[0009] According to the specific embodiments provided by the present application, the present application has the following technical effects: 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 to improve performance indexes in a flight process, and an optimal flight time is obtained, so that the smoothness of a control curve can be further improved. Meanwhile, the optimal flight time and a state vector are input into a neural network model, an initial control history guess sequence is obtained through network learning, convergence can be ensured under the same condition, and the occurrence of iteration divergence or non-convergence is further avoided, so that accurate initial control information is provided for subsequent trajectory planning. Moreover, a homotopy method and a Gauss pseudospectrum method are used to accurately solve a three-dimensional centroid kinematics and dynamics model, a reference solution output by a simple trajectory planning problem is used as a good input of a complex trajectory planning problem, and an optimal solution of a complex, fast time-varying and nonlinear planning problem can be obtained under the condition of a small convergence radius, so that optimal trajectory planning of the vehicle from an initial state to a terminal state is realized. Through optimization of the flight time, neural network prediction of the control sequence and an efficient trajectory solving method, the calculation efficiency and precision of the trajectory planning of the vehicle are significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0010] 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 as follows. 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.

[0011] 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; Figure 2 A flowchart of a trajectory planning method of a variant near-space vehicle provided by an embodiment of the present application; Figure 3 A framework diagram of a trajectory planning method of a variant near-space vehicle provided by an embodiment of the present application; Figure 4 A coordinate system diagram of a variant near-space vehicle provided by an embodiment of the present application; Figure 5 A structure diagram of a back propagation neural network provided by an embodiment of the present application; Figure 6 A simulation diagram of a trajectory curve of a variant near-space vehicle provided by an embodiment of the present application; Figure 7 A simulation diagram of a time-attack angle curve provided by an embodiment of the present application; Figure 8A simulation schematic diagram of a time-tilt angle curve provided by an embodiment of the present application is shown in the following figure. Figure 9 A simulation schematic diagram of a time-deformation ratio curve provided by an embodiment of the present application is shown in the following figure. Figure 10 A simulation schematic diagram of a time-velocity curve provided by an embodiment of the present application is shown in the following figure. Figure 11 A simulation schematic diagram of a time-trajectory inclination angle curve provided by an embodiment of the present application is shown in the following figure. Figure 12 A simulation schematic diagram of a time-trajectory deflection angle curve provided by an embodiment of the present application is shown in the following figure. Figure 13 A structural schematic diagram of a computer device provided by an embodiment of the present application is shown in the following figure. DETAILED DESCRIPTION

[0012] The technical solutions in the embodiments of the present application will be clearly and completely described 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 other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of the present application.

[0013] The above purposes, features and advantages of the present application will be more apparent and understandable. The present application will be further described in detail below with reference to the drawings and specific embodiments.

[0014] The trajectory planning method of the variant near space vehicle provided by the embodiments of the present application can be applied to the application environment as shown in the following figure. Figure 1 The terminal 102 communicates with the server 104 through a network. The data storage system can store data required to be processed by the server 104. The data storage system can be separately arranged, can be integrated on the server 104, or can be placed on the cloud or other servers. The terminal 102 can send an initial state vector and a terminal state vector of a vehicle to the server 104. The server 104 performs flight time optimization based on a three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, by using a heuristic optimization algorithm and a gradient descent method, 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. The optimal trajectory is obtained by using a homotopy method and a Gauss pseudospectrum method to solve the trajectory planning based on the initial control history guess sequence. The server 104 can feed back the obtained optimal trajectory to the terminal 102.

[0015] The terminal 102 can be, but is not limited to, various desktop computers, notebook computers, Internet of Things devices, and portable wearable devices. The server 104 can be implemented by a single server or a server cluster composed of multiple servers, and can also be a cloud server.

[0016] In an exemplary embodiment, as shown in Figures 2-3 , a trajectory planning method of a variant near-space vehicle is provided, which is executed by a computer device, specifically, can be executed by a terminal or a server, or both. In the embodiments of the present application, the method is applied to the server 104 in Figure 1 , including the following steps 201 to 204. Wherein: Step 201, a three-dimensional mass center kinematics and dynamics model of the variant near-space vehicle is constructed, the state vector of the three-dimensional mass center kinematics and dynamics model includes a range, a lateral position, a height, a speed, a ballistic inclination angle and a ballistic declination angle, and the control vector of the three-dimensional mass center kinematics and dynamics model includes an attack angle, a roll angle and a variable configuration ratio.

[0017] Step 202, an initial state vector and a terminal state vector of the variant near-space vehicle are obtained, and 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 a final optimal flight time.

[0018] Step 203, 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.

[0019] Step 204, based on the initial control history guess sequence, a homotopy method and a Gauss pseudospectral method are used to solve the trajectory planning of the three-dimensional mass center kinematics and dynamics model, to obtain an optimal trajectory.

[0020] By implementing steps 201 to 204 described above, the 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 same situation can be quickly converged, and the iteration divergence or non-convergence situation is further avoided, and accurate initial control information is provided for subsequent trajectory planning. Moreover, by using the homotopy method and the Gauss pseudospectral method to accurately solve the three-dimensional mass center 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, so as to ensure that the optimal solution of the complex, fast time-varying and nonlinear planning problem can be obtained in the case 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.

[0021] Further, in step 201, the trajectory curve of the variant near-space vehicle is researched, and only the three-degree-of-freedom mass center model needs to be researched, without considering the attitude motion. Therefore, the motion model only needs to research the three-dimensional mass center kinematics and dynamics model. Without considering the earth rotation and curvature, the trajectory coordinate system of the variant near-space vehicle is as shown in Figure 4 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. Therefore, the three-dimensional mass center kinematics and dynamics model is specifically as follows: (1); wherein, represents the change rate of the range; represents the change rate of the lateral position; represents the change rate of the height; represents the change rate of the velocity; represents the change rate of the ballistic dip angle; represents the change rate of the ballistic deflection angle; represents the velocity; represents the ballistic dip angle; represents the ballistic deflection angle; represents the roll angle; represents the mass; represents the gravitational acceleration; represents the lift; represents the drag.

[0022] In formula (1), L and D represent the lift and the drag respectively, and the expression is as follows: (2); wherein, denotes the reference area; denotes the atmospheric density, in particular: (3); wherein, denotes the reference atmospheric density; denotes the atmospheric altitude.

[0023] denotes the lift coefficient and the drag coefficient, respectively, in particular: (4); wherein, denotes the Mach number; denotes the angle of attack, defined as the angle between the projection of the velocity vector on the longitudinal symmetry plane and the longitudinal axis of the vehicle, with positive nose-up; denotes the term related to the lift coefficient; denotes the term related to the drag coefficient; , , , , denote the terms related to the lift coefficient, the above coefficients being calculated by aerodynamic simulation or wind tunnel tests; denotes the deformation ratio, ranging in [0.8, 1.2]. It is important to note that, generally, is not variable, but the vehicle used in the present application is of variable configuration, which can be dynamically adjusted.

[0024] The state vector composed of the six states is , is the range, is the lateral position, is the altitude, denotes the speed, denotes the ballistic angle of inclination, denotes the ballistic angle of declination; the control vector composed of the three control quantities (i.e. the guidance commands) is , denotes the angle of attack, denotes the angle of bank, denotes the variable configuration ratio. Therefore, the trajectory planning problem requires precise control of the six terminal states through the three control quantities.

[0025] ​Further, in the aerospace trajectory planning problem, the terminal flight time is usually insensitive, and the performance index is sensitive. Therefore, by optimizing the flight time, the performance index is further improved. The heuristic optimization algorithm and the gradient descent method are combined to realize the optimization of the terminal flight time, wherein the headdress optimization algorithm is an improved heuristic algorithm, which aims 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.

[0026] In step 202, based on the three-dimensional centroid 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, and the final optimal flight time is obtained, which specifically includes: Step a1, based on the three-dimensional centroid kinematics and dynamics model, the initial state vector and the terminal state vector, the heuristic optimization algorithm is used to perform global search in the preset flight time range, and the approximate optimal flight time is obtained.

[0027] Step a2, the approximate optimal flight time is determined as the initial time value, and based on the initial time value, the adaptive gradient descent method is used to perform local fine search, and the final optimal flight time is obtained.

[0028] Further, inspired by existing heuristic algorithms, the headdress optimization algorithm aims to simulate the foraging behavior of a headdress group by computer, i.e. the heuristic optimization algorithm is the headdress optimization algorithm. This algorithm simulates the natural foraging behavior of the headdress group, searches for the optimal flight time in one-dimensional space by a group of headdress individuals, updates their own position, speed and acceleration through information interaction, and finally obtains the optimal solution. Each headdress has an independent position, speed and acceleration array in 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 headdress optimization algorithm requires fewer parameters to be set, the theory is intuitive, and it 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 headdress optimization algorithm is used to perform global search in the preset flight time range, and the approximate optimal flight time is obtained, which specifically includes: Step b1, initialize the position, speed and acceleration of all individuals.

[0029] Step b2: Based on the position, initial state vector and terminal state vector of each individual at the current iteration number, obtain the performance index of each individual at the current iteration number; when the current iteration number is 1, the position of each individual is each candidate flight time within the preset flight time range.

[0030] Step b3: Based on the current performance index set of each individual (i.e., the current performance index set of each individual is all the performance indices of each individual obtained up to the current iteration number), select the smallest performance index among all the performance indices of each individual to determine the optimal position of each individual under the current iteration number, and based on the performance indices of all individuals under the current iteration number, select the smallest performance index among all the performance indices of all individuals under the current iteration number to determine the optimal position of the group under the current iteration number.

[0031] Step b4: Determine if the current iteration count has reached the maximum iteration count. If yes, output the optimal position of the group under the current iteration count and determine the optimal group position under the current iteration count as the approximate optimal flight time. If no, based on the optimal position of each individual, the optimal position of the group, the velocity of each individual, and the acceleration of each individual under the current iteration count, use the dynamic model of the crested ibis optimization algorithm to calculate the position, velocity, and acceleration of each individual under the next iteration count, update the optimal position, velocity, and acceleration of each individual under the current iteration count to the position, velocity, and acceleration of each individual under the next iteration count, increment the current iteration count by 1, consider a discrete time interval of 1 (i.e., a step size of 1), and return to step "Based on the position, initial state vector, and terminal state vector of each individual under the current iteration count, obtain the performance index of each individual under the current iteration count".

[0032] The dynamic model of the crested ibis optimization algorithm includes velocity update formula, acceleration update formula, and position update formula. The speed update formula is: (5); The acceleration update formula is: (6); The position update formula is: (7); in, Indicates the current iteration number The individual speed below; Indicates the next iteration number The individual speed below; Indicates speed memory item; and respectively represent weighting coefficients. represents a random number. represents an individual optimal position. represents the current iteration number of the individual position. represents the next iteration number of the individual position. represents a group optimal position. represents an acceleration memory term. represents the current iteration number of the individual acceleration. represents the next iteration number of the individual acceleration. and respectively represent weighting coefficients.

[0033] Further, the above mentioned mandarin duck 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: (8). wherein, represents the final optimal flight time; represents an approximate optimal flight time; represents an adaptive learning rate, which is calculated by an adaptive theory; represents a gradient value.

[0034] 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.

[0035] The BP neural network is a kind of 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 present embodiment is a trained back propagation neural network, such as Figure 5The illustrated; 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: Step c1, obtain a sample state vector set, and process the sample state vector set by using Monte Carlo targeting simulation to obtain a sample control vector set.

[0036] Step c2, pre-process the sample state vector set and the sample control vector set to obtain a pre-processed sample state vector set and a pre-processed sample control vector set; the pre-processing includes data cleaning and normalization.

[0037] Step c3, train the back propagation neural network using the pre-processed sample state vector set and the pre-processed sample control vector set to determine a trained back propagation neural network. Thus, the control actions at each discrete point are obtained using the trained back propagation neural network, and an initial control history guess sequence is obtained.

[0038] Further, the activation function is selected as the hyperbolic tangent function, and the expression is: (9); wherein, represents the hyperbolic tangent function; represents the hyperbolic sine function; represents the hyperbolic cosine function; the function represents the natural exponential function exp( x ), that is, the exponential function with the natural constant e ( e ≈2.71828) as the base; the function represents exp(- x ).

[0039] Further, the Gauss pseudospectral method and the nonlinear programming method are used to solve the trajectory planning problem. However, the existing methods have the problems of not converging or even directly diverging when solving complex strong nonlinear trajectory planning problems. Therefore, the homotopy method is used to improve the above problems.

[0040] Homotopy method, also known as homotopy extension method or homotopy continuation method. Homotopy method is a numerical technique to solve complex optimization problems by constructing a path of functions that are connected to each other. It connects the original complex strongly nonlinear trajectory planning problem to a simple weakly nonlinear trajectory planning problem that is easy to solve. In other words, it gradually transforms a simple weakly nonlinear trajectory planning problem into the original complex strongly nonlinear trajectory planning problem by changing the homotopy parameter. Therefore, by controlling the change of the homotopy parameter, a relatively easy-to-solve 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.

[0041] In simple terms, the process of solving a trajectory planning problem using the homotopy method is as follows: (1) Define the homotopy function vector ; (2) Select the auxiliary function ; (3) When s = 0, solve the simple weakly nonlinear trajectory planning problem; (4) When s gradually changes from 0 to 1, solve the homotopy function vector by using the solution of the previous iteration as the initial guess . When s equals 1, the original complex strongly nonlinear trajectory planning problem is solved.

[0042] 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.

[0043] 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 three-dimensional mass center kinematics and dynamics model for trajectory planning to obtain the optimal trajectory, which specifically includes: Step d1, construct a homotopy function; the homotopy function is used to combine the complex strongly nonlinear trajectory planning problem with the simple weakly nonlinear trajectory planning problem, and to control the degree of transformation between the complex strongly nonlinear trajectory planning problem and the simple weakly nonlinear trajectory planning problem through the homotopy parameter; the expression of the homotopy function is: (10); wherein represents the function vector reconstructed by the homotopy method; denotes the state vector; denotes the homotopy parameter, ranging from [0, 1]; denotes the complex strong nonlinear trajectory planning problem that needs to be solved finally; denotes the simple weak nonlinear trajectory planning problem that is initially constructed.

[0044] Step d2, according to the homotopy parameter of the current step, determine the trajectory planning problem defined by the homotopy function that needs to be solved currently.

[0045] Step d3, use the Gauss pseudospectral method to discretize the continuous trajectory planning problem defined by the homotopy function that needs to be solved currently into a nonlinear programming problem that needs to be solved currently; the discretization process includes transforming the time interval to a standard interval, discretizing the state vector and control vector at the collocation points, and converting the dynamic differential equation constraints in the three-dimensional mass center kinematics and dynamics model into algebraic constraints, specifically: The performance index of the nonlinear trajectory planning problem is designed as: (11); wherein, denotes the performance index; denotes the initial time; denotes the deformation ratio; denotes the penalty coefficient for the deformation ratio. The dynamic differential equation constraint in the three-dimensional mass center kinematics and dynamics model of formula (1) can be expressed as: (12); wherein, denotes the derivative of the state vector, ; is the function in formula (11) ; is the control vector.

[0046] The expression of the initial state vector constraint and the terminal state vector constraint is: (13); wherein, denotes the initial state vector value; denotes the desired terminal state vector value.

[0047] The Gauss pseudospectral method converts the continuous time in the original simple weak nonlinear trajectory planning problem to a standard interval , and the conversion relationship is: (14); wherein, denotes the normalized time.

[0048] In the optimal control problem, the state vector can be approximated as: (15); where, denotes the state vector in continuous time; denotes the state vector in discrete time; subscript denotes the th collocation point; denotes the last collocation point; denotes the interpolation basis function, which is expressed as: (16); where, denotes the function related to the interpolation point; subscript denotes the th collocation point.

[0049] The numerical integration problem is calculated by weight summation, which ensures high computational efficiency of the pseudospectral method. The numerical integration equation is: (17); where, and denote the lower and upper limits of the integration interval, respectively; denotes the integration weight matrix; denotes the function value of the homotopy function at normalized time τ ; denotes the function value of the homotopy function at normalized time , denotes the time at the normalized discrete point i .

[0050] In the Gauss pseudospectral method, the dynamic constraint equation of the terminal state can be rewritten according to formula (10) as: (18); where, 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.

[0051] Based on formula (17), formula (18) can be rewritten as: (19); where, denotes the discretized terminal state vector; denotes the discretized initial state vector; denotes the last discretization point; denotes the time i corresponding discretization point.

[0052] The dynamics equation constraint can be derived from formula (15) as follows: (20); wherein, denotes the normalized time corresponding state vector derivative; denotes the normalized time discretized form of the corresponding state vector derivative; denotes the normalized time discretized form of the corresponding interpolation basis function; subscript denotes the thnode; denotes the differential matrix.

[0053] (21); wherein, the function denotes the Legendre interpolation polynomial; denotes the normalized time discretized form of the corresponding Legendre interpolation polynomial; denotes the normalized time derivative of the discretized form of the corresponding Legendre interpolation polynomial; denotes the normalized time derivative of the discretized form of the corresponding Legendre interpolation polynomial.

[0054] Therefore, according to the weighted residual method, the dynamics constraint of formula (20) can be rewritten as an algebraic constraint: (22); wherein, denotes the algebraic constraint.

[0055] 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; Step d5, judging whether the homotopy parameter of the current step is 1; if yes, outputting the current guess and determining the current guess as the optimal trajectory; if no, calculating the homotopy parameter of the next step based on the homotopy parameter of the current step and the preset value, updating the homotopy parameter of the current step to the homotopy parameter of the next step, and returning to the step of determining the trajectory planning problem defined by the homotopy function to be solved in the current step according to the homotopy parameter of the current step.

[0056] In an exemplary embodiment, in order to verify the effectiveness and feasibility of the variant near-space vehicle homotopy trajectory planning method based on the optimization estimation of the optimal flight time of the red-crowned crane, the present application faces the simulation verification of the midcourse guidance of the variant near-space vehicle. The initial state and the desired terminal state constraints of the vehicle are shown in Table 1.

[0057] Table 1 Initial state and desired terminal state of the variant near-space vehicle

[0058] The flight trajectory of the variant near-space vehicle is shown in Figure 6 The control amount attack angle, roll angle, and variable configuration ratio (referred to as deformation ratio) curve are shown in Figures 7-9 The speed curve is shown in Figure 10 The ballistic inclination angle and ballistic deflection angle curve are shown in Figures 11-12 The terminal state control error is: the range error is -0.5810 meters; the height error is 1.3592 meters; the lateral position error is -23.0420 meters; the speed error is 0.0123 meters / second; the ballistic inclination angle error is -0.0011 degrees; and the ballistic deflection angle error is -0.0037 degrees.

[0059] The above error statistics and Figure 6 It is shown that the homotopy trajectory optimization method based on the optimization estimation of the optimal flight time of the red-crowned crane under the limited computing resources of the variant near-space vehicle 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 section 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 roll 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 amount (deformation ratio) has a small overall amplitude, the guidance task can be achieved through configuration fine-tuning. Figure 11 The ballistic inclination angle curve shown in is slightly disturbed at about 3 seconds. The disturbance amplitude is small, and has little effect on the actual flight performance of the vehicle. Figure 12The ballistic inclination angle curve changes smoothly, and has high terminal control precision.

[0060] In an example embodiment, a computer device is provided, which can be a server or a terminal, and an internal structure diagram thereof can be as shown in 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 configured 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 running the operating system and the computer program in the non-volatile storage medium. The database of the computer device is configured to store processing data. The input / output interface of the computer device is configured to exchange information between the processor and external devices. The communication interface of the computer device is configured to communicate with external terminals through a network connection. The computer program is executed by the processor to implement a trajectory planning method for a variable near-space vehicle.

[0061] Those skilled in the art can understand that Figure 13 The 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 example embodiment, a computer device is provided, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above method embodiments.

[0062] In an example embodiment, a computer readable storage medium is provided, which stores a computer program. The computer program is executed by a processor to implement the steps in the above method embodiments.

[0063] In an example embodiment, a computer program product is provided, which includes a computer program. The computer program is executed by a processor to implement the steps in the above method embodiments.

[0064] 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.

[0065] 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 executed, can include the processes of the above-mentioned embodiment methods. Any reference to memory, database or other medium 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.

[0066] 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.

[0067] The technical features of the above embodiments can be combined arbitrarily. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, however, as long as the combinations of the technical features do not exist contradictory, they should be considered as the scope of the present application.

[0068] The principles and implementation manners of the present application are described herein by using specific examples, and the above examples are only used to help understand the method of the present application and its core idea; meanwhile, for those skilled in the art, according to the idea of the present application, the specific implementation manners and application ranges will have changes. In conclusion, the content of the specification should not be understood as a limitation of the present application.

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 trajectory planning of the three-dimensional mass center kinematics and dynamics model to obtain an optimal trajectory.

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 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, The heuristic optimization algorithm and the gradient descent method are used to optimize the 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 the final optimal flight time, which comprises the following steps: The heuristic optimization algorithm is used to perform a global search within a preset flight time range based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, so as to obtain an approximate optimal flight time; The approximate optimal flight time is determined as an initial time value, and the adaptive gradient descent method is used to perform a local fine search based on the initial time value, so as to obtain the 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 the shacheng optimization algorithm; the heuristic optimization algorithm is used to perform a global search within a preset flight time range based on the three-dimensional mass center kinematics and dynamics model, the initial state vector and the terminal state vector, so as to obtain an approximate optimal flight time, which comprises the following steps: A performance index of each individual at a current iteration number is obtained based on each individual position at the current iteration number, the initial state vector and the terminal state vector; when the current iteration number is 1, each individual position is each candidate flight time within the preset flight time range; A current performance index set of each individual is determined, and a group optimal position at the current iteration number is determined based on performance indexes of all individuals at the current iteration number; the current performance index set of each individual comprises all performance indexes of each individual obtained up to the current iteration number. determining whether the current iteration number reaches the maximum iteration number; if yes, outputting the group optimal position under the current iteration number, and determining the group optimal position under the current iteration number as the approximate optimal flight time; if no, based on each individual optimal position, the group optimal position, each individual speed and each individual acceleration under the current iteration number, using the dynamics model of the sheldrake optimization algorithm, calculating each individual position, each individual speed and each individual acceleration under the next iteration number, and updating each individual optimal position, each individual speed and each individual acceleration under the current iteration number to each individual position, each individual speed and each individual acceleration under the next iteration number, the current iteration number + 1, and returning to the step of "obtaining the performance index of each individual under the current iteration number based on each individual position, the initial state vector and the terminal state vector under the current iteration number".

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 sheldrake 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 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 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 and denote weighting factors, respectively.​​​​​​ 7. The method of trajectory planning for a variant near space vehicle of 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 each include a hyperbolic tangent function; wherein the determination process of the trained back propagation neural network is: Obtaining a sample state vector set, and processing the sample state vector by using Monte Carlo targeting simulation to obtain a sample control vector set; Pretreating the sample state vector set and the sample control vector set to obtain a pretreated sample state vector set and a pretreated sample control vector set; the pretreatment includes data cleaning and normalization; Training the back propagation neural network by using the pretreated sample state vector set and the pretreated sample control vector set to obtain the trained back propagation neural network.

8. The method of trajectory planning for a variant near space vehicle of claim 1, wherein, Based on an initial control history guess sequence, using homotopy method and Gauss pseudospectral method to solve the trajectory planning of the three-dimensional centroid kinematics and dynamics model to obtain an optimal trajectory, specifically including: Constructing a homotopy function; 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 the transformation degree between the complex strong nonlinear trajectory planning problem and the simple weak nonlinear trajectory planning problem through a homotopy parameter; According to the homotopy parameter of the current step, determining the trajectory planning problem defined by the homotopy function that needs to be solved at present; Using the Gauss pseudospectral method, discretizing 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 includes transforming the time interval to a standard interval, discretizing the state vector and the control vector at the collocation points, and converting the dynamic differential equation constraints in the three-dimensional centroid kinematics and dynamics model into algebraic constraints; Based on the previous guess, a nonlinear trajectory planning solver is used to solve the nonlinear programming problem to be solved at present to obtain the current guess; the current guess is the state vector and 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, the homotopy parameter of the next step is calculated based on the homotopy parameter of the current step and the 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 to be solved at present according to the homotopy parameter of the current step" is returned.

9. 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 1-8.

10. 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 1-8.

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