A method and system for optimally generating the coverage area of ​​a cross-domain transformable aircraft based on virtual points

Abstract

The present invention proposes a method and system for optimally generating the coverage area of ​​a cross-domain variable-configuration aircraft based on virtual points, which belongs to the field of aircraft dynamics and guidance. The method includes: constructing a re-entry trajectory optimization problem model, and converting the re-entry trajectory optimization problem model into a multi-segment form for description to obtain a multi-segment optimal control problem model; then, discretizing the multi-segment optimal control problem model using the piecewise Gaussian pseudo-spectral method, thereby parameterizing the trajectory optimization problem and converting it into a nonlinear programming problem for solution; finally, setting a series of virtual points, and based on the obtained optimal control and optimal trajectory, using the piecewise Gaussian pseudo-spectral method to solve the optimal trajectory landing point with the smallest distance to each virtual point in turn, thereby obtaining the coverage area of ​​the aircraft. The present invention provides effective technical support for the trajectory planning and guidance method of cross-domain variable-configuration aircraft.

Description

Technical Field

[0001] The present invention belongs to the field of aircraft dynamics and guidance, and in particular relates to a method and system for optimally generating the coverage area of ​​a cross-domain variable-configuration aircraft based on virtual points. Background Art

[0002] Determining the target coverage area for an unpowered reentry vehicle is a challenging problem, especially when the coordinated control of angle of attack, roll angle, and deformation control variables is required to maximize the maneuverability coverage. On the one hand, the coverage area is determined by the optimal extreme trajectory landing points that satisfy all constraints. However, quickly solving for the maximum extreme trajectory under all feasible constraints requires constructing and solving a complex, nonlinear, and strongly coupled, equation and inequality constraint model, which is labor-intensive and difficult. On the other hand, compared with traditional trajectory control methods that use a fixed configuration, a proposed angle of attack profile, and only adjust the roll angle, the coordinated, on-demand allocation of angle of attack, roll angle, and deformation control variables can more easily leverage the vehicle's inherent maneuverability. However, due to the highly nonlinear and strongly coupled relationship between the control variables and the state variables, accurate and stable trajectory control is more difficult, posing a significant challenge.

[0003] At present, there have been many studies on coverage area calculation at home and abroad, but most of them are still aimed at fixed-configuration re-entry vehicles, and the control strategy is mainly based on the traditional pre-given angle of attack profile and only adjusts the roll angle. However, there are few studies on the coverage area of ​​cross-domain variable-configuration aircraft that adjust the angle of attack, roll angle and deformation control amount on demand. In order to give full play to the inherent maneuverability potential of the aircraft, the inventor's team previously designed a three-dimensional profile planning strategy based on lateral priority, and solved the three-dimensional profile coverage area with on-demand allocation of control amount by combining multiple groups of different corridor boundary interpolation results. However, this method calculates all feasible trajectories of multiple groups of different three-dimensional profile interpolations, and the calculation amount is too large. In addition, this method is mainly carried out for traditional fixed-configuration re-entry vehicles, and the coverage area obtained is only an approximation. It is difficult to theoretically guarantee that the result obtained is the maximum range. Therefore, how to study the rapid generation method of coverage area under the coordinated control of attack angle, roll angle and deformation control quantity based on optimal control theory is of great significance for trajectory planning, especially for trajectory planning in some extreme target situations. Accurately and quickly obtaining the coverage area of ​​cross-domain variable-configuration aircraft will be an important support for the implementation of trajectory planning and guidance methods. Summary of the Invention

[0004] Aiming at the problem of optimal generation of the coverage area of ​​a cross-domain transformable aircraft in which the angle of attack, roll angle and deformation control quantities are simultaneously allocated and coordinated as needed, the present invention proposes a method and system for optimal generation of the coverage area of ​​a cross-domain transformable aircraft based on virtual points.

[0005] The first aspect of the present invention discloses a method for optimally generating a coverage area of ​​a cross-domain transformable aircraft based on virtual points, the method comprising:

[0006] Step S1: construct a re-entry trajectory optimization problem model; wherein, the re-entry trajectory optimization problem model takes into account process constraints, control quantity constraints, and initial and terminal constraints; the re-entry trajectory optimization problem model is expressed as:

[0007]

[0008] Where J represents the performance index function value; Φ(·) represents the performance index function; x and u represent the motion state and control quantity of the reentry vehicle, respectively. Specifically, x = [r, V, θ, σ, λ, φ] T They represent the distance from the center of mass of the aircraft to the center of the earth, speed, speed inclination, speed azimuth, longitude and latitude respectively, and the control quantity u=[α,υ,η,δ] T are the angle of attack, roll angle, telescopic ratio and sweep angle respectively; t is the flight time, and the subscripts (·)0 and (·) f denote the initial and terminal moments, respectively, and the superscript (·) * Indicates the corresponding expected terminal state; represents the constraints of the differential equation of motion state; f(x,u,t) represents the three-degree-of-freedom center-of-mass motion model equation of the aircraft; g i (x,u,t) represents the inequality constraints of overload, dynamic pressure and stagnation point heat flow that need to be considered in the reentry trajectory planning process; h j (x0,t0,x f ,t f ) is the equality constraint; x min and x max They represent the minimum and maximum allowable values ​​of the motion state, respectively, and u min and u max are the minimum and maximum allowable values ​​of the control quantity;

[0009] Step S2: converting the reentry trajectory optimization problem model into a multi-segment form for description to obtain a multi-segment optimal control problem model;

[0010] Step S3: discretizing the multi-segment optimal control problem model using a piecewise Gaussian pseudospectral method, thereby parameterizing the trajectory optimization problem and converting it into a nonlinear programming problem for solution; wherein, for each trajectory segment, a preset number of discrete points are selected to discretize the state variables and control variables, and the inter-segment connection conditions are satisfied between the trajectory segments to ensure the continuity of the state variables and control variables; after the entire trajectory is discretized into segments, all the discrete point state variables and control variables are used as optimization parameters for simultaneous optimization design, and finally the corresponding optimal control and optimal trajectory are obtained through interpolation;

[0011] Step S4: Set a series of virtual points. Based on the obtained optimal control and optimal trajectory, use the piecewise Gaussian pseudospectral method to solve the optimal trajectory landing point with the minimum distance to each virtual point in turn, and then obtain the coverage area of ​​the aircraft; wherein the coverage range of the series of virtual points is greater than the maximum capability range of the aircraft.

[0012] According to the method of the first aspect of the present invention, in step S1, the performance indicator function J is:

[0013]

[0014] Where ω1, ω2 represent the corresponding weight coefficients, λ f ,φ f Represent the terminal longitude and latitude respectively, Indicates the desired terminal longitude and latitude respectively.

[0015] According to the method of the first aspect of the present invention, in step S1, the three-degree-of-freedom center-of-mass motion model equation f(x, u, t) of the aircraft is specifically in the form of:

[0016]

[0017] Among them, ω e is the angular velocity of the Earth's rotation, t is the time variable, g is the Earth's gravitational acceleration; L and D represent the lift and drag accelerations, respectively. The specific form is:

[0018]

[0019] Where M is the mass of the aircraft, S ref is the aerodynamic reference area of ​​the aircraft, ρ is the atmospheric density, C L ,C D are the aerodynamic lift and drag coefficients, C L ,C D It is not only related to the angle of attack α and the Mach number Ma, but also to the expansion ratio coefficient η and the sweep angle δ of the deformation control amount.

[0020] According to the method of the first aspect of the present invention, in step S1, g i The specific form of (x,u,t) is:

[0021]

[0022] in, q max and n max They represent the maximum stagnation heat flux, maximum dynamic pressure and maximum overload allowed by the aircraft respectively; K h and m are constants in the heat flux formula; g0 is the gravitational acceleration at sea level.

[0023] According to the method of the first aspect of the present invention, step S2 specifically includes:

[0024] Assume that the number of trajectory segments to be optimized is P, let (·) (p) Denotes the parameters corresponding to the trajectory of the pth segment, p∈[1,...,P]; the multi-segment optimal control problem can be described as: finding the control variable And, minimize the performance index J; where:

[0025]

[0026] And at the same time satisfy the dynamic system differential equation constraints:

[0027]

[0028] Boundary conditions:

[0029]

[0030] Connection conditions:

[0031]

[0032] And other inequality constraints:

[0033]

[0034] Among them, the state variable is a constant, R is a set of real numbers, where and They are the state quantities x corresponding to the pth segment respectively (p) , constant q (p) and control quantity u (p) The dimension of ; t represents the time variable, The initial time and terminal time of the p-th trajectory are respectively; L (s) is the connection constraint function at the sth connection point, and are the lower and upper limits of the connection constraint, and L is the number of connection points that need to meet the connection condition; and They represent the sequence numbers of the two adjacent trajectory segments at the sth connection point, and are the minimum and maximum values ​​of the boundary conditions corresponding to the pth segment, respectively. When the two values ​​are equal, it means that it is an equality constraint; C (p) is the equality or inequality constraint function corresponding to the pth segment, and Set minimum and maximum values ​​for the corresponding equality or inequality constraints.

[0035] According to the method of the first aspect of the present invention, step S3 specifically includes:

[0036] The independent variable t of each segment is changed from [t0,t f ] is converted to [-1,1], τ satisfies

[0037]

[0038] Let the number of points on the pth trajectory be N (p) , respectively constrain the inequalities and equalities of the motion model differential equations, process constraints, initial and terminal conditions at each segmented point and perform discretization processing; where:

[0039] Take N on the interval [-1,1) (p) +1 discrete point as interpolation point, with N (p) +1st order Lagrange interpolation polynomial As the basis function approximate state variable, we get:

[0040]

[0041] in:

[0042]

[0043] Similarly, the control variables satisfy:

[0044]

[0045] Assign point τ to the trajectory of segment p k The state quantity X (p) (τ k ) is recorded as Control quantity U (p) (τ k ) is recorded as Use together and Represent the starting and terminal states respectively;

[0046] After discretizing other constraints of the multi-stage optimal control problem, its boundary conditions can be expressed as

[0047] Equality and inequality constraints are expressed as:

[0048]

[0049] The join condition is expressed as:

[0050]

[0051] Where L is the number of connection points; and Respectively represent the sequence numbers of the two adjacent trajectory segments. For the performance indicator function, the discretization is described as:

[0052]

[0053] The second aspect of the present invention discloses a system for optimally generating the coverage area of ​​a cross-domain variable-structure aircraft based on virtual points, characterized in that the system comprises:

[0054] The first processing module is configured to construct a re-entry trajectory optimization problem model; wherein the re-entry trajectory optimization problem model takes into account process constraints, control quantity constraints, and initial and terminal constraints; the re-entry trajectory optimization problem model is expressed as:

[0055]

[0056] Where J represents the performance index function value; Φ(·) represents the performance index function; x and u represent the motion state and control quantity of the reentry vehicle, respectively. Specifically, x = [r, V, θ, σ, λ, φ] T They represent the distance from the center of mass of the aircraft to the center of the earth, speed, speed inclination, speed azimuth, longitude and latitude respectively, and the control quantity u=[α,υ,η,δ] T are the angle of attack, roll angle, telescopic ratio and sweep angle respectively; t is the flight time, and the subscripts (·)0 and (·) f denote the initial and terminal moments, respectively, and the superscript (·) * Indicates the corresponding expected terminal state; represents the constraints of the differential equation of motion state; f(x,u,t) represents the three-degree-of-freedom center-of-mass motion model equation of the aircraft; g i (x,u,t) represents the inequality constraints of overload, dynamic pressure and stagnation point heat flow that need to be considered in the reentry trajectory planning process; h j (x0,t0,x f ,t f ) is the equality constraint; x min and x max They represent the minimum and maximum allowable values ​​of the motion state, respectively, and u min and u max are the minimum and maximum allowable values ​​of the control quantity;

[0057] The second processing module is configured to convert the reentry trajectory optimization problem model into a multi-segment form for description to obtain a multi-segment optimal control problem model;

[0058] The third processing module is configured to discretize the multi-segment optimal control problem model using a piecewise Gaussian pseudospectral method, thereby parameterizing the trajectory optimization problem and converting it into a nonlinear programming problem for solution; wherein a preset number of discrete points are selected for each trajectory segment to discretize the state variables and control variables, and the inter-segment connection conditions are satisfied between the trajectory segments to ensure the continuity of the state variables and control variables; after the entire trajectory is discretized into segments, all the discrete point state variables and control variables are used as optimization parameters for simultaneous optimization design, and ultimately the corresponding optimal control and optimal trajectory are obtained through interpolation;

[0059] The fourth processing module is configured to set a series of virtual points, and based on the obtained optimal control and optimal trajectory, use the piecewise Gaussian pseudo-spectral method to solve the optimal trajectory landing point with the minimum distance to each virtual point in turn, and then obtain the coverage area of ​​the aircraft; wherein the coverage range of the series of virtual points is greater than the maximum capability range of the aircraft.

[0060] A third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the steps of the method for optimally generating the coverage area of ​​a cross-domain transformable aircraft based on virtual points described in the first aspect of the present invention.

[0061] A fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon. When executed by a processor, the computer program implements the steps of the method for optimally generating a coverage area for a cross-domain transformable aircraft based on virtual points described in the first aspect of the present invention.

[0062] In summary, the solution proposed in the present invention has the following technical effects: Compared with the existing methods, the present invention solves the problem that under the simultaneous action of the angle of attack control quantity, the roll angle control quantity, the telescopic ratio, the sweep angle and other deformation control quantities of the cross-domain variable configuration aircraft, there is no need to optimize the design of the reference control quantity schemes such as the angle of attack and the roll angle in advance. It only sets a series of virtual points and uses the piecewise Gaussian pseudo-spectral method to find the optimal ballistic landing point close to the virtual point, thereby obtaining the target coverage area range. Because the constraints such as heat flux density, dynamic pressure, and overload have been taken into account in the construction of the trajectory optimization problem model, the obtained trajectory will not exceed the set constraint value, and the feasibility of the trajectory has been verified by the numerical integration algorithm. The longitudinal and lateral motion coupling is taken into account in the design process, so that the maneuverability of the aircraft is fully exerted, and theoretically ensures that the re-entry maneuver coverage range of the cross-domain variable configuration re-entry aircraft is optimal. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0064] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0065] Figure 2 A flowchart of solving the coverage area according to an embodiment of the present invention;

[0066] Figure 3 A schematic diagram of a virtual point according to an embodiment of the present invention;

[0067] Figure 4 A schematic diagram of the longitude and latitude of the trajectory planned under the set virtual point according to an embodiment of the present invention;

[0068] Figures 5(a) and (b) are respectively graphs showing the velocity and height variation of the trajectory planned according to an embodiment of the present invention;

[0069] Figures 6(a)-(d) are schematic diagrams showing the optimization results of various control variables according to an embodiment of the present invention;

[0070] Figure 7 This is a diagram showing coverage area changes under different scaling ratios according to an embodiment of the present invention;

[0071] Figure 8 This is a diagram showing coverage area changes at different sweep angles according to an embodiment of the present invention;

[0072] Figure 9 This is a structural diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0073] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0074] Aiming at the problem of optimal generation of the coverage area of ​​a cross-domain variable-property aircraft with coordinated control of the angle of attack, roll angle and deformation control quantities allocated on demand, the present invention is based on optimal control theory. By constructing a coverage area problem-solving model that satisfies multiple constraints, and using virtual points and multi-segment Gaussian pseudo-spectral method, the complex multi-constraint continuous nonlinear optimal control problem is converted into a discrete nonlinear programming problem for solution, thereby quickly obtaining the coverage area that satisfies the constraints and optimal performance indicators.

[0075] like Figure 1 As shown, in this embodiment, a method for optimally generating a coverage area of ​​a cross-domain transformable aircraft based on virtual points includes the following steps:

[0076] (1) Set a series of appropriate virtual points;

[0077] (2) Construct a reentry trajectory optimization model that satisfies the minimum distance to a given target point;

[0078] (3) Dimensionless treatment of the reentry trajectory optimization problem of cross-domain variable-property aircraft;

[0079] (4) Generate the initial trajectory for the reentry trajectory optimization problem of the cross-domain variable-property vehicle;

[0080] (5) Using piecewise Gaussian pseudospectral method to solve the established trajectory optimization problem;

[0081] (6) Solve the optimal trajectory landing point to all given virtual points and generate the coverage area.

[0082] In this embodiment, the above implementation process can be used Figure 2 The coverage area flow chart is given as follows. In step (1), in order to obtain the coverage area, a series of virtual points are set as Figure 3 The position of the virtual point can be set arbitrarily as long as it exceeds the maximum capability of the aircraft.

[0083] In this embodiment, step (2) is defined as follows: a reentry trajectory optimization problem model is constructed that comprehensively considers process constraints such as heat flux density, dynamic pressure, overload, and the control variables such as attack angle and roll angle amplitude constraints and initial and terminal constraints, and satisfies the minimum distance to the given target point:

[0084] The reentry trajectory optimization problem model that satisfies the minimum distance to a given target point can be expressed as:

[0085]

[0086] Where x and u represent the motion state and control quantity of the reentry vehicle, respectively. Specifically, x=[r,V,θ,σ,λ,φ] TThey represent the distance from the center of mass of the aircraft to the center of the earth, speed, speed inclination, speed azimuth, longitude and latitude respectively, and the control quantity u=[α,υ,η,δ] T are the angle of attack, roll angle, telescopic ratio coefficient and sweep angle respectively; t is the flight time, subscripts (·)0 and (·) f Represent the state and control quantity corresponding to the initial and terminal moments, respectively. The superscript (·) * is the corresponding expected terminal state; x min and x max Respectively represent the minimum and maximum allowable values ​​of the motion state quantity, and u min and u max are the minimum and maximum allowable values ​​of the control quantity. The performance index function J is:

[0087]

[0088] Where ω1, ω2 are weight coefficients, λ f ,φ f are the terminal longitude and latitude, is the desired terminal longitude and latitude; f(x,u,t) is the three-degree-of-freedom center-of-mass motion model equation of the aircraft, which is in the form of:

[0089]

[0090] Among them, ω e is the angular velocity of the Earth's rotation, t is the time variable, g is the Earth's gravitational acceleration; L and D represent the lift and drag accelerations, respectively. The specific form is:

[0091]

[0092] Where M is the mass of the aircraft, S ref is the aerodynamic reference area of ​​the aircraft, ρ is the atmospheric density, C L ,C D are the aerodynamic lift and drag coefficients respectively. Different from the traditional reentry vehicle, the cross-domain variable-configuration reentry vehicle adopted in the present invention can simultaneously perform telescopic and sweep angle changes, so its C L ,C D It is not only related to the angle of attack α and the Mach number Ma, but also to the expansion ratio coefficient η and the sweep angle δ of the deformation control amount.

[0093] In formula (1), g i (x,u,t) represents the inequality constraints such as overload, dynamic pressure, and stagnation point heat flow that need to be considered in the reentry trajectory planning process. Its specific forms are:

[0094]

[0095] in, q max and n max They represent the maximum stagnation heat flux, maximum dynamic pressure and maximum overload allowed by the aircraft respectively; K h , m and n are constants in the heat flux formula. There is no n in the formula. g0 is the gravitational acceleration at sea level. According to experience, m = 3.15, n = 0.5, and K h The size of is related to the flight environment and the stationary end radius of the aircraft.

[0096] The equality constraint h in formula (1) j (x0,t0,x f ,t f ) are mainly:

[0097]

[0098] In step (3), use V c ,R c ,T c The trajectory optimization problem is dimensionless, where g0 is the gravitational acceleration at sea level, R c is the average radius of the homogeneous spherical earth, V c and T c The calculation formula is:

[0099]

[0100] In step (4), in order to generate the initial reference trajectory, based on the dimensionless motion model obtained in step (2), the attack angle control value α is designed in the form of:

[0101]

[0102] Where V e , V f are the initial reentry velocity and the terminal glide velocity, respectively. V1 and V2 are the segmentation point velocities, i.e., the design parameters of the angle of attack model. max ,α max L / D Denote the maximum angle of attack and the angle of attack with the maximum lift-to-drag ratio, respectively. Meanwhile, the bank angle is set to 0, and the terminal altitude or velocity is used as the simulation end condition to generate the initial reference trajectory.

[0103] In step (5) of this embodiment, in order to solve the problem using the segmented Gaussian pseudospectral method, the trajectory optimization problem model (1) is first converted into a multi-segment form for description. Assume that the number of trajectory segments to be optimized is P, and let (·) (p) Denotes the parameters corresponding to the trajectory of the pth segment, p∈[1,...,P]. The multi-segment optimal control problem can be described as: finding the control variable ( is the dimension of the p-th segment control quantity), minimize the general Bolza-type comprehensive performance index J, where:

[0104]

[0105] And at the same time satisfy the dynamic system differential equation constraints:

[0106]

[0107] Boundary conditions:

[0108]

[0109] And other inequality constraints (equality constraints can also be equivalently converted into two inequality constraints):

[0110]

[0111] In formulas (9)-(12), the state variables To control the amount, is a constant, where and They are the state quantities x corresponding to the pth segment respectively (p) , constant q (p) and control quantity u (p) The dimension of ; t represents the time variable, They are the initial time and terminal time corresponding to the pth segment of the trajectory; and are the minimum and maximum values ​​of the boundary conditions corresponding to the pth segment, respectively. When the two values ​​are equal, it means that it is an equality constraint, such as the initial condition; C (p) is the equality or inequality constraint function corresponding to the pth segment, and are the corresponding equality or inequality constraints for minimum and maximum values. In addition, unlike general optimal control problems, multi-segment optimal control problems also require that the segments satisfy connection conditions to ensure good continuity between segments. That is, for the sth connection point, the two segments on the left and right should satisfy:

[0112]

[0113] Where, L (s) is the connection constraint function, and are the lower and upper limits of the connection constraint, and L is the number of connection points that need to meet the connection condition; and They represent the sequence numbers of the two adjacent trajectory segments at the connection point.

[0114] Then, for the above multi-segment optimal control problem, the segmented GPM is used for discretization processing, thereby parameterizing the trajectory optimization problem and converting it into a nonlinear programming problem for solution. For each segment of the trajectory, an appropriate number of discrete points are selected to discretize the state variables and control variables. The inter-segment connection conditions are met between the segments to ensure the continuity of the state and control variables. After the entire trajectory is discretized into segments, all the discrete point state variables and control variables are used as optimization parameters for simultaneous optimization design, and finally the corresponding optimal control and optimal trajectory are obtained through interpolation. The specific steps are as follows:

[0115] Step 1: Conversion of the value range of independent variables;

[0116] Since the Gaussian pseudospectral method is optimized on [-1,1], it is necessary to change the independent variable t of each segment from [t0,t f ] is converted to [-1,1], that is, τ satisfies:

[0117]

[0118] Step2: Solve the Gauss-Legendre configuration point;

[0119] Let the number of points on the pth trajectory (excluding the two end points) be N (p) ,make For the matching point, it is as follows N (p) Roots of a Legendre polynomial of order:

[0120]

[0121] Obviously τ k ∈(-1,1), where k=1,...,N (p) . In addition, let τ0 = -1, Together with κ, it constitutes the discrete points of the p-th segment of the trajectory, which are the matching points for subsequent optimization solutions.

[0122] Step 3: Discretization;

[0123] The inequalities and equality constraints such as the motion model differential equations, process constraints and initial and terminal conditions are discretized at each segment point. (p) +1 discrete point as interpolation point, with N (p) +1st order Lagrange interpolation polynomial As the basis function approximate state variable, we get:

[0124]

[0125] Where:

[0126]

[0127] Similarly, the control variables can be approximated as:

[0128]

[0129] For the convenience of the following description, the trajectory of the pth segment is assigned point τ k The state quantity X (p) (τ k ) is recorded as Control quantity U (p) (τ k ) is recorded as Use together and Represent the starting and terminal states respectively. Therefore, the derivative of the left side of the motion model differential constraint (10) can also be approximated by the derivative of the Lagrange interpolation polynomial, that is:

[0130]

[0131] in, The expression is:

[0132]

[0133] Therefore, in order to satisfy the constraints of the motion model differential equation shown in Equation (10), the state variables and control variables should satisfy the algebraic constraint equations at each collocation point:

[0134]

[0135] Since the end point of each trajectory segment coincides with the starting point of the next segment, the points in each segment naturally satisfy the constraints of the differential equation of motion. However, the end point of the last segment (the Pth segment) is not at the selected points and is not constrained by the differential equation of motion imposed by Equation (21). According to the differential equation of motion system, we have:

[0136]

[0137] Therefore, the state constraint condition of the terminal point of the P segment can be discretized and approximated by Gauss integral, that is:

[0138]

[0139] in, is the Gauss quadrature coefficient, and Determined by formula (15). Similarly, after further discretization of other constraints of the multi-stage optimal control problem, its boundary conditions can be expressed as:

[0140]

[0141] Equality and inequality constraints can be expressed as:

[0142]

[0143] The join condition can be expressed as:

[0144]

[0145] Where L is the number of connection points; and Respectively represent the sequence numbers of the two adjacent trajectory segments. For the Bolza type comprehensive performance index function, it can also be discretized and described as:

[0146]

[0147] Step 4: Solve the discrete multi-segment nonlinear programming problem;

[0148] Currently, there are many software packages for solving nonlinear programming problems. Among them, the SNOPT software package, developed by Gill et al. and suitable for solving large-scale nonlinear programming problems, has been widely used due to its excellent performance. It is worth noting that the above-mentioned segmented optimization method appears to be a serial optimization problem on the surface, because after segmentation, the terminal conditions of the first segment of the trajectory serve as the initial conditions for the subsequent segments. However, in reality, when converted to a nonlinear programming method for solution, all discrete points corresponding to the entire flight trajectory are optimized simultaneously, rather than determining the previous segment of the trajectory and then determining the subsequent segments sequentially. Therefore, segmented optimization is actually a parallel optimization problem, ensuring that the combined solution of the optimal trajectory for each segment is the optimal solution for the entire trajectory.

[0149] In step (6) of this embodiment, for the set virtual points, the segmented Gaussian pseudo-spectral method is used to solve the optimal trajectory landing point with the smallest distance to each virtual point in turn, and then the coverage area of ​​the aircraft is obtained. Since the optimization solution efficiency of the Gaussian pseudo-spectral method is related to the initial value trajectory setting, in order to speed up the coverage area solution efficiency, except for the first calculation, each subsequent optimization result is used as the initial value for optimization when solving the optimal trajectory of a given virtual point. Figure 3 As shown in the figure, according to the setting rules of virtual points, the two virtual points are very close to each other. Therefore, using the optimal solution of the previous time as the initial value of the next solution will greatly accelerate the efficiency of coverage area generation. This is also an important reason why the present invention uses virtual points to solve the coverage area.

[0150] In order to verify the feasibility and effectiveness of the optimal generation method of the coverage area of ​​a cross-domain variable-mode aircraft based on virtual points, the cross-domain variable-mode aircraft model used in this embodiment is as follows: the example sets the re-entry starting point longitude and latitude (0°, 0°), the initial direction is due east, the initial altitude is 80km, the initial speed is 6500m / s, the terminal altitude is required to be 30km, and the handover speed is 2500m / s.

[0151] Figure 4 It is the latitude and longitude of the trajectory planned under the set virtual point in the embodiment of the present invention.

[0152] FIG5 is a velocity and altitude variation curve diagram of the trajectory planned by the embodiment of the present invention. It can be seen from the terminal that the terminal requirements of an altitude of 30 km and a handover speed of 2500 m / s are met.

[0153] FIG6 shows the optimized control variables according to an embodiment of the present invention, including the angle of attack, the roll angle, the sweep angle, and the telescopic ratio.

[0154] Figure 7 2 is a diagram showing changes in coverage areas under different scaling ratios according to an embodiment of the present invention. As can be seen from the diagram, the larger the scaling ratio, the smaller the coverage area.

[0155] Figure 8 2 is a diagram showing the coverage area changes at different sweep angles according to an embodiment of the present invention. As can be seen from the diagram, the larger the sweep angle, the larger the coverage area.

[0156] It can be seen from the simulation results that by using the piecewise Gaussian pseudo-spectral method to obtain a series of virtual point trajectories that are close to the optimal capability, the coverage area of ​​the cross-domain variable configuration aircraft can be quickly obtained.

[0157] A third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the steps of the method for optimally generating the coverage area of ​​a cross-domain transformable aircraft based on virtual points described in the first aspect of the present invention.

[0158] Figure 9 FIG. 1 is a structural diagram of an electronic device according to an embodiment of the present invention. Figure 9As shown, the electronic device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. The processor of the electronic device is used to provide computing and control capabilities. The memory of the electronic device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the electronic device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, near field communication (NFC) or other technologies. The display screen of the electronic device can be a liquid crystal display or an electronic ink display screen, and the input device of the electronic device can be a touch layer covering the display screen, or a button, trackball or touchpad provided on the electronic device housing, or an external keyboard, touchpad or mouse.

[0159] Those skilled in the art will understand that Figure 9 The structure shown in the figure is only a structural diagram of the part related to the technical solution of the present disclosure, and does not constitute a limitation on the electronic device to which the solution of the present application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0160] A fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon. When executed by a processor, the computer program implements the steps of the method for optimally generating a coverage area for a cross-domain transformable aircraft based on virtual points described in the first aspect of the present invention.

[0161] In summary, the present invention can be widely used in the maneuverability analysis and coverage area calculation of aircraft such as lift-type reentry vehicles, hypersonic gliding vehicles, and cross-domain variable-speed aircraft, providing support for their trajectory planning and guidance technology, and has broad military and civilian application prospects and value.

[0162] The above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may be modified or some or all of the technical features thereof may be replaced with equivalents, and such modifications or replacements do not deviate from the essence of the corresponding technical solutions within the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimally generating the coverage area of ​​a cross-domain transformable aircraft based on virtual points, characterized in that: The method comprises: Step S1: construct a re-entry trajectory optimization problem model; wherein, the re-entry trajectory optimization problem model takes into account process constraints, control quantity constraints, and initial and terminal constraints; the re-entry trajectory optimization problem model is expressed as: Where J represents the performance index function value; Φ(·) represents the performance index function; x and u represent the motion state and control quantity of the reentry vehicle, respectively. Specifically, x = [r, V, θ, σ, λ, φ] T They represent the distance from the center of mass of the aircraft to the center of the earth, speed, speed inclination, speed azimuth, longitude and latitude respectively, and the control quantity u=[α,υ,η,δ] T are the angle of attack, roll angle, telescopic ratio coefficient and sweep angle respectively; t is the flight time, and the subscripts (·)0 and (·) f denote the initial and terminal moments, respectively, and the superscript (·) * Indicates the corresponding expected terminal state; represents the constraints of the differential equation of motion state; f(x,u,t) represents the three-degree-of-freedom center-of-mass motion model equation of the aircraft; g i (x,u,t) represents the inequality constraints of overload, dynamic pressure and stagnation point heat flow that need to be considered in the reentry trajectory planning process; h j (x0,t0,x f ,t f ) is the equality constraint; x min and x max Respectively represent the minimum and maximum allowable values ​​of the motion state quantity, and u min and u max are the minimum and maximum allowable values ​​of the control quantity; Step S2: converting the reentry trajectory optimization problem model into a multi-segment form for description to obtain a multi-segment optimal control problem model; Step S3: discretizing the multi-segment optimal control problem model using a piecewise Gaussian pseudospectral method, thereby parameterizing the trajectory optimization problem and converting it into a nonlinear programming problem for solution; wherein, for each trajectory segment, a preset number of discrete points are selected to discretize the state variables and control variables, and the inter-segment connection conditions are satisfied between the trajectory segments to ensure the continuity of the state variables and control variables; after the entire trajectory is discretized into segments, all the discrete point state variables and control variables are used as optimization parameters for simultaneous optimization design, and finally the corresponding optimal control and optimal trajectory are obtained through interpolation; Step S4: Set a series of virtual points. Based on the obtained optimal control and optimal trajectory, use the piecewise Gaussian pseudospectral method to solve the optimal trajectory landing point with the minimum distance to each virtual point in turn, and then obtain the coverage area of ​​the aircraft; wherein the coverage range of the series of virtual points is greater than the maximum capability range of the aircraft.

2. The method according to claim 1, characterized in that In the step S1, the performance indicator function J is: Where ω1, ω2 represent the corresponding weight coefficients, λ f ,φ f Represent the terminal longitude and latitude respectively, Indicates the desired terminal longitude and latitude respectively.

3. The method according to claim 1, characterized in that In step S1, the three-degree-of-freedom center-of-mass motion model equation f(x, u, t) of the aircraft is specifically in the form of: Among them, ω e is the angular velocity of the Earth's rotation, t is the time variable, g is the Earth's gravitational acceleration; L and D represent the lift and drag accelerations, respectively. The specific form is: Where M is the mass of the aircraft, S ref is the aerodynamic reference area of ​​the aircraft, ρ is the atmospheric density, C L ,C D are the aerodynamic lift and drag coefficients, C L ,C D It is not only related to the angle of attack α and the Mach number Ma, but also to the expansion ratio coefficient η and the sweep angle δ of the deformation control amount.

4. The method according to claim 3, characterized in that In the step S1, g i The specific form of (x,u,t) is: in, q max and n max They represent the maximum stagnation heat flux, maximum dynamic pressure and maximum overload allowed by the aircraft respectively; K h and m are constants in the heat flux formula; g0 is the gravitational acceleration at sea level.

5. The method according to claim 1, wherein Step S2 specifically includes: Assume that the number of trajectory segments to be optimized is P, let (·) (p) Denotes the parameters corresponding to the trajectory of the pth segment, p∈[1,...,P]; the multi-segment optimal control problem can be described as: finding the control variable And, minimize the performance index J; where: And at the same time satisfy the dynamic system differential equation constraints: Boundary conditions: Connection conditions: And other inequality constraints: Among them, the state variable is a constant, R is a set of real numbers, where and They are the state quantities x corresponding to the pth segment respectively (p) , constant q (p) and control quantity u (p) The dimension of ; t represents the time variable, The initial time and terminal time of the p-th trajectory are respectively; L (s) is the connection constraint function at the sth connection point, and are the lower and upper limits of the connection constraint, and L is the number of connection points that need to meet the connection condition; and They represent the sequence numbers of the two adjacent trajectory segments at the sth connection point, and are the minimum and maximum values ​​of the boundary conditions corresponding to the pth segment, respectively. When the two values ​​are equal, it means that it is an equality constraint; C (p) is the equality or inequality constraint function corresponding to the pth segment, and Set minimum and maximum values ​​for the corresponding equality or inequality constraints.

6. The method according to claim 5, characterized in that Step S3 specifically includes: The independent variable t of each segment is changed from [t0,t f ] is converted to [-1,1]; Let the number of points on the pth trajectory be N (p) , respectively constrain the inequalities and equalities of the motion model differential equations, process constraints, initial and terminal conditions at each segmented point and perform discretization processing; where: Take N on the interval [-1,1) (p) +1 discrete point as interpolation point, with N (p) +1st order Lagrange interpolation polynomial As the basis function approximate state variable, we get: in: Similarly, the control variables satisfy: Assign point τ to the trajectory of segment p k The state quantity X (p) (τ k ) is recorded as Control quantity U (p) (τ k ) is recorded as Use together and Represent the starting and terminal states respectively; After discretizing other constraints of the multi-stage optimal control problem, its boundary conditions can be expressed as Equality and inequality constraints are expressed as: The join condition is expressed as: Where L is the number of connection points; and Respectively represent the sequence numbers of the two adjacent trajectory segments. For the performance indicator function, the discretization is described as:

7. A system for optimally generating the coverage area of ​​a cross-domain variable-structure aircraft based on virtual points, characterized in that: The system comprises: The first processing module is configured to construct a re-entry trajectory optimization problem model; wherein the re-entry trajectory optimization problem model takes into account process constraints, control quantity constraints, and initial and terminal constraints; the re-entry trajectory optimization problem model is expressed as: Where J represents the performance index function value; Φ(·) represents the performance index function; x and u represent the motion state and control quantity of the reentry vehicle, respectively. Specifically, x = [r, V, θ, σ, λ, φ] T They represent the distance from the center of mass of the aircraft to the center of the earth, speed, speed inclination, speed azimuth, longitude and latitude respectively, and the control quantity u=[α,υ,η,δ] T are the angle of attack, roll angle, telescopic ratio and sweep angle respectively; t is the flight time, subscripts (·)0 and (·)f are the initial and terminal time respectively, and superscript (·) * Indicates the corresponding expected terminal state; represents the constraints of the differential equation of motion state; f(x,u,t) represents the three-degree-of-freedom center-of-mass motion model equation of the aircraft; g i (x,u,t) represents the inequality constraints of overload, dynamic pressure and stagnation point heat flow that need to be considered in the reentry trajectory planning process; h j (x0,t0,x f ,t f ) is the equality constraint; x min and x max They represent the minimum and maximum allowable values ​​of the motion state, respectively, and u min and u max are the minimum and maximum allowable values ​​of the control quantity; The second processing module is configured to convert the reentry trajectory optimization problem model into a multi-segment form for description to obtain a multi-segment optimal control problem model; The third processing module is configured to discretize the multi-segment optimal control problem model using a piecewise Gaussian pseudospectral method, thereby parameterizing the trajectory optimization problem and converting it into a nonlinear programming problem for solution; wherein a preset number of discrete points are selected for each trajectory segment to discretize the state variables and control variables, and the inter-segment connection conditions are satisfied between the trajectory segments to ensure the continuity of the state variables and control variables; after the entire trajectory is discretized into segments, all the discrete point state variables and control variables are used as optimization parameters for simultaneous optimization design, and ultimately the corresponding optimal control and optimal trajectory are obtained through interpolation; The fourth processing module is configured to set a series of virtual points, and based on the obtained optimal control and optimal trajectory, use the piecewise Gaussian pseudo-spectral method to solve the optimal trajectory landing point with the minimum distance to each virtual point in turn, and then obtain the coverage area of ​​the aircraft; wherein the coverage range of the series of virtual points is greater than the maximum capability range of the aircraft.

8. An electronic device, characterized in that: The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, it implements the steps in the method for optimally generating the coverage area of ​​a cross-domain variable-configuration aircraft based on virtual points according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the steps of the method for optimally generating the coverage area of ​​a cross-domain variable-mode aircraft based on virtual points according to any one of claims 1 to 6 are implemented.

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