A sequence convex optimization based online planning method for hypersonic morphing aircraft

Abstract

The application relates to an online planning method for a hypersonic variable shape aircraft based on sequence convex optimization and belongs to the field of trajectory planning of a hypersonic variable shape aircraft. The application is realized by the following steps: analyzing the influence of variable shape characteristics on the aerodynamic characteristics of the aircraft, constructing a three-degree-of-freedom dynamics model of the hypersonic variable shape aircraft for trajectory planning; taking the maximum of a weighted function of a terminal height and a terminal speed at the end of a task as a performance index, simultaneously considering initial boundary constraints, terminal boundary constraints and control quantity constraints, combining the aircraft dynamics model to construct an initial trajectory optimization problem of the hypersonic variable shape aircraft; performing convex processing and discretization processing on the trajectory planning problem of the variable length aircraft to obtain a trajectory planning convex problem; constructing a sequence convex optimization solving method based on a variable time domain rolling planning considering multi-stage continuous solving to solve the trajectory planning problem of a gliding section with a terminal time freedom, and realizing online planning of the hypersonic variable shape aircraft according to the solving result.

Description

Technical Field

[0001] This invention relates to an online planning method for hypersonic deformable vehicles based on sequential convex optimization, belonging to the field of hypersonic deformable vehicle trajectory planning technology. Background Technology

[0002] Hypersonic vehicles refer to near-space vehicles with Mach numbers greater than 5, possessing advantages such as high speed, long range, high maneuverability, high efficiency in destruction, and strong penetration capabilities. These vehicles, with their unique performance advantages, demonstrate enormous application potential in performing large-scale strategic missions. One development trend is the integration of these vehicles with contemporary variator technologies to improve their flight performance and address the challenge of fixed-layout hypersonic vehicles achieving optimal performance throughout their entire lifecycle. A variator is a vehicle that uses a variator control mechanism to change its shape to meet mission requirements or provide maneuverability. Different aerodynamic configurations can be achieved by altering wing sweep angle, aspect ratio, airfoil thickness, and trailing edge camber. Introducing variator technology into hypersonic vehicles allows for the use of shape parameters to influence aerodynamic characteristics, thereby improving flight performance and adapting to more complex missions and environments. It also enables the achievement of optimal aerodynamic and handling performance, reducing energy consumption during flight and increasing range. Furthermore, variability in ballistic trajectory can be achieved through deformation, further enhancing the penetration capability of hypersonic vehicles. However, the introduction of variant technology increases the dimensionality of hypersonic vehicle models and enhances dynamic nonlinearity, making it more difficult to solve using convex optimization techniques. Therefore, it is necessary to improve the timeliness and stability of hypersonic variant vehicle trajectory planning methods.

[0003] For online planning methods of hypersonic deformable vehicles, a rolling time-domain optimization method needs to be introduced. The core idea of ​​the rolling time-domain optimization principle is to generate the optimal control quantity by solving a sequential convex optimization problem based on the current state at time i. The control quantity of the first guidance cycle is applied to the vehicle to obtain the state at time i+1, and this process is repeated until the last guidance cycle. This method continuously introduces uncertainties into the dynamic differential equations and eliminates the deviations caused by the linearization of the dynamic model in the rolling control commands. In particular, for the terminal time freedom problem studied in this invention, the prediction time domain length gradually shortens as rolling progresses, which may often lead to the occurrence of no solution at the end of the rolling phase. Furthermore, it is difficult to match the time at discrete points by selecting only a fixed execution time domain interval, and the control quantity at the terminal time of each guidance cycle is often obtained by interpolation of adjacent discrete points, which also leads to inaccuracies in the solution.

[0004] Furthermore, hypersonic vehicles may need to perform multiple maneuvers to meet mission requirements, meaning that the vehicle's flight mission needs to be divided into multiple mission intervals. The lack of pre-allocation of time for different phases of the mission makes it difficult to transform the original dynamic optimization problem into a static optimization problem.

[0005] There is still a lack of research on the glide trajectory planning problem for hypersonic, deformable, and online aircraft. It is necessary to carry out cutting-edge technology research in this area to serve future technological needs. Summary of the Invention

[0006] To address the comprehensive problem of hypersonic, deformable, and online glide trajectory planning for hypersonic vehicles, this invention aims to provide an online planning method for hypersonic deformable vehicles based on sequential convex optimization. This method analyzes the impact of deformation on the vehicle's aerodynamic characteristics and constructs aerodynamic and dynamic models for the hypersonic deformable vehicle. For the trajectory planning problem of variable-span vehicles, convexification and discretization are performed to obtain a convex trajectory planning problem. Based on this, a sequential convex optimization solution method based on variable-time-domain rolling planning, considering multi-stage continuous solution, is constructed to solve the glide trajectory planning problem with terminal time freedom. The online planning of the hypersonic deformable vehicle is then realized based on the solution results of the terminal time-free glide trajectory planning problem.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] An online planning method for hypersonic deformable vehicles based on sequential convex optimization includes the following steps:

[0009] Step 1: Analyze the influence of deformation characteristics on the aerodynamic characteristics of the aircraft through the aircraft geometric model, and construct a dynamic model of a three-degree-of-freedom hypersonic deformable aircraft oriented towards trajectory planning;

[0010]

[0011] In equation (1), R0 is the maximum flight distance; V c The upper bound of constant velocity; drag X = qSC x Lift force Y = qSC y C x C y , respectively, are the aerodynamic coefficients for drag X and lift Y, functions of Mach number Ma, angle of attack α, and deformation rate χ = (b - b0) / (b1 - b0), all obtained by least squares fitting, where b0 is the wingspan at 0% wing extension, b1 is the wingspan at 100% wing extension, and b is the current wingspan of the aircraft in deformed state; S is the reference area, and dynamic pressure q = ρV 2 / 2; Atmospheric density ρ=ρ0e-βh ρ0 is the atmospheric density at sea level, a constant value of 1.2258 kg / m³. 3 β is a constant coefficient, with a value of 1.3785 × 10⁻⁶. - 4 m -1 h is the altitude of the aircraft; m is the mass of the missile; gravitational acceleration g = μ / (R e +h) 2 μ is the Earth's gravitational coefficient, a constant value of 3.9860 × 10⁻⁶. 14 m 3 / s 2 R e The average radius of the Earth is 6378 km, a constant value.

[0012] Step 2: Using the maximum weighted function of terminal altitude and terminal velocity at the end of the mission as the performance index, and considering initial boundary constraints, terminal boundary constraints, and control constraints, construct the initial trajectory planning problem P0 for the hypersonic deformable vehicle based on the vehicle dynamics model built in Step 1; the state variables x in the problem are longitudinal stroke x, altitude y, lateral stroke z, missile velocity V, track angle θ, and heading angle ψ. V The control parameters u include the angle of attack α and the heel angle γ. V Deformation rate χ, the state variables and control variables of the problem P0 are all normalized variables;

[0013]

[0014] In equation (2), m1 is V f The corresponding constant weighting coefficients, m2 is y f The corresponding constant weighting coefficient, m3 is ξ x The corresponding constant weighting coefficient, m4 is ξ z The corresponding constant weighting coefficient, m5, is ξ. θ The corresponding constant weighting coefficient, m6 is The corresponding constant weight coefficients, J is the objective function value, V f For the terminal velocity of the aircraft, y f ξ represents the terminal altitude of the aircraft. x ξ z ξ θ , These are the error bounds corresponding to the longitudinal range, lateral range, track angle, and heading angle constraints at the terminal moment of the aircraft; x=[V,θ,ψ V [x,y,z] T Let u = [α, γ] be the state vector. V ,χ] T For control vectors, The equations of the dynamic differential equations of the aircraft are equality constraints; t is time; c(x,u,t)=0 and s(x,u,t)<0 represent the process and terminal equality constraints and inequality constraints that the state and control variables need to satisfy, respectively;

[0015] Step 3: Based on equation (1) obtained in Step 1, introduce an augmented control quantity t. f Let t0 be the initial time of the task. Using the transformation relationship t = t0 + (t f -t0)τ is subjected to time freedom processing. If t0=0, the domain of the independent variable is obtained as τ=t / t f This leads to the augmented dynamics model of the aircraft:

[0016]

[0017] In equation (3), the state variable is Control quantity is

[0018] Step 4: Process equation (3) obtained in Step 3 using the successive linearization method: Given a reference trajectory Given the state trajectory obtained in the k-th iteration, and based on the first-order linearized dynamic nonlinear term of the optimal trajectory generated in the k-th iteration, the problem P0 obtained in step two is transformed into a continuous convex optimization problem. Then, using the equal division method, the continuous optimization problem is discretized over the equally divided domain of independent variables τ = [0,1], with N+1 discrete points, resulting in the discretized convex problem P1 for hypersonic deformable vehicle trajectory planning.

[0019]

[0020] In equation (4), C is the relaxed optimization variable corresponding to the state variable's trust region, D is the relaxed optimization variable corresponding to the control variable's trust region, m7 is the constant weight coefficient corresponding to C, and m8 is the constant weight coefficient corresponding to D. For state vectors, The control vector is i = 1, ..., N, which represent the discrete points after discretizing the problem using the collocation method. For the equality constraints of the dynamic differential equations after convexification; Linear equality constraints; For linear inequality constraints; To perform equality constraints after convexification; For inequality constraints after convexification;

[0021] Step 5: Solve the trajectory planning convex problem P1 to obtain the trajectory planning results of the hypersonic vehicle. This is an online planning method for hypersonic deformable vehicles based on sequential convex optimization.

[0022] The specific implementation method for step two is as follows:

[0023] The initial boundary constraints are the initial values ​​of the spacecraft's state variables at the initial moment of each mission segment, i.e.:

[0024]

[0025] In equation (5): t0 is the initial time of the flight mission segment; x0, y0, z0, V0, θ0, ψ V0 These correspond to the longitudinal range, altitude, lateral range, speed, track angle, and heading angle of the aircraft at the initial moment, respectively.

[0026] Terminal boundary constraints are constraints imposed on the terminal state of an aircraft. For hypersonic deformable aircraft, these constraints include longitudinal, lateral, track angle, and heading angle constraints, namely:

[0027]

[0028] In equation (6): t f For the terminal time of each task segment; x f z f θ f ψ Vf These are the longitudinal range, lateral range, track angle, and heading angle corresponding to the expected terminal moment of the aircraft;

[0029] Process constraints are constraints imposed on the state variables at each moment during the trajectory planning process of a hypersonic deformable vehicle. For example, process constraints for a hypersonic deformable vehicle include velocity V, track angle θ, and heading angle ψ. V Constraints, namely:

[0030]

[0031] In equation (7), V min θ is the lower limit of velocity V; min θ max These are the lower and upper limits of the track angle θ, respectively; ψ Vmin ψ Vmax They are respectively the heading angle ψ V The lower and upper limits;

[0032] Considering angle of attack α and panning angle γ V And the amplitude constraint of the deformation rate χ control variable, that is:

[0033]

[0034] In equation (8), α min α max These are the lower and upper limits of the angle of attack α, respectively; γ Vmin γ Vmax These are the tilt angles γ and γ.V The lower and upper limits of χ; min , χ max These are the lower and upper limits of the deformation rate χ, respectively;

[0035] Secondly, considering that each actuator has a rate of action limit in actual operation, the rate of change of the aircraft control variables is constrained, namely:

[0036]

[0037] In equation (9), These are the rates of change of angle of attack. The lower and upper limits; These are the rates of change of the tilt angle. The lower and upper limits; These are the rates of change of deformation rate. The lower and upper limits;

[0038] The objective function is a weighted function of terminal height and terminal speed, i.e.:

[0039] min J=-m1V f -m2y f (10)

[0040] In equation (10), m1 is V f The corresponding constant weighting coefficients, m2 is y f The corresponding constant weight coefficients, J is the objective function value, V f For the terminal velocity of the aircraft, y f The terminal altitude of the aircraft;

[0041] For the terminal constraint in equation (6) which is an equal-strength equality constraint, a relaxation variable is introduced to relax the terminal position constraint. The terminal position can be rewritten as:

[0042]

[0043] In equation (11): t f For the terminal time of each task segment; x f z f θ f , These correspond to the expected longitudinal range, lateral range, track angle, and heading angle of the aircraft at the terminal moment, respectively; ξ x ξ z ξ θ , These are the error limits corresponding to the longitudinal range, transverse range, track angle, and heading angle constraints of the aircraft at the terminal moment;

[0044] By adding a slack variable penalty term to the objective function to constrain the terminal state, so that the terminal position during the iteration process approaches the specified position, the objective function is rewritten as:

[0045]

[0046] In equation (12), m3 is ξ x The corresponding constant weighting coefficient, m4 is ξ z The corresponding constant weighting coefficient, m5, is ξ. θ The corresponding constant weighting coefficient, m6 is The corresponding constant weighting coefficients;

[0047] Combining the vehicle dynamics model (1), constraints, and objective function information constructed in step one, the initial trajectory planning problem P0 of the hypersonic deformable vehicle is expressed as:

[0048]

[0049] The specific implementation method for step four is as follows:

[0050] First, the successive linearization method is used to handle the nonlinear dynamic equations: given a reference trajectory Given the state trajectory obtained in the k-th iteration, the first-order linearized dynamic nonlinear term is derived from the optimal trajectory generated in the k-th iteration. The linearized dynamic form is: Will Perform a first-order Taylor expansion at the reference trajectory:

[0051]

[0052] In equation (14), Let be the specific constant value of the differential equation at the reference trajectory. for Regarding state variables The derivative, for Regarding control quantity The derivative of, and in the second equation

[0053] Expanding the above equation further, we get:

[0054]

[0055] In equation (15), the expressions for each matrix are as follows:

[0056] ① matrix:

[0057]

[0058] ② matrix:

[0059]

[0060] ③ matrix:

[0061]

[0062] ④ matrix:

[0063]

[0064] ⑤ matrix:

[0065]

[0066] ⑥ matrix:

[0067]

[0068] To ensure the reliability of the above successive linearization method, the following trust region constraint is added:

[0069]

[0070] In equation (16), δ x It is a state variable The constant vector trust region, and with The dimensions are the same, δ u It is a state variable The constant vector trust region, and with The dimensions are the same; based on equation (16), a trust region relaxation variable is introduced, and the relaxed trust region constraint can be expressed as:

[0071]

[0072] In equation (17), C is δ x The corresponding relaxation optimization variable, D, is δ. u The corresponding relaxation optimization variables are used to adjust the trust region size by optimizing the values ​​of C and D;

[0073] By adding a penalty term for the norm of the relaxation variables in the trust region to the objective function, the objective function is rewritten as follows:

[0074]

[0075] In equation (18), m7 is the constant weight coefficient corresponding to C, and m8 is the constant weight coefficient corresponding to D; this objective function is a linear objective function and does not require convexification.

[0076] For nonlinear inequality constraints The convexity is also achieved using a successive linearization method, which... Performing a first-order Taylor expansion at the reference trajectory yields:

[0077]

[0078] In equation (19), and They represent s with respect to state variables respectively. and control quantity The partial derivatives;

[0079] The above convexification method completes the convexification of the problem P0 obtained in step two. Based on this, the problem is discretized: the collocation method is used to simultaneously discretize the state variables. With control variables The continuous optimization problem is discretized over an equally divided domain of independent variables τ = [0,1], with N+1 discrete points; the step size is Δτ = 1 / N, and the discrete points are {τ0, τ1, τ2, ..., τ...}. N}, and τ i =τ0+iΔτ (i=0,1,...,N); then the state variables and control variables in the continuous optimization problem are discretized as and Using the trapezoidal integral formula to discretize the continuous-time problem, we get:

[0080]

[0081] In equation (20),

[0082] Meanwhile, for the control rate constraint equation (9), the position constraint form of discrete points is used to characterize the control variable change rate constraint:

[0083]

[0084] In equation (21),

[0085] After linearizing the dynamics, constraining the convexity, and discretizing the problem P0, we obtain the discretized convex problem P1 for hypersonic deformable vehicle trajectory planning:

[0086]

[0087] The specific implementation method for step five is as follows:

[0088] The complete flight mission is divided into three flight phases, named A, B, and C, by setting different waypoints. Each flight phase is solved sequentially to obtain a continuous solution for all phases. The specific implementation steps are as follows:

[0089] Step 5.1: In flight phase A, based on the initial parameters of this phase, construct the initial trajectory planning problem P0_A of the hypersonic deformable vehicle according to step two, and then construct the discretized convex trajectory planning problem P1_A of the hypersonic deformable vehicle using the convexity and discretization methods in steps three and four.

[0090] Step 5.2: Solve for P1_A using the sequential convex optimization method to obtain the optimal control sequence; select the control sequence for the actual guidance cycle from the optimal control sequence, use it for the aircraft, and update the flight trajectory online for the current guidance cycle;

[0091] Step 5.3: Advance the time online to the next guidance cycle, and return to Step 5.2 to iterate and solve P1_A again; if the time advances to the trajectory planning terminal time t f Flight phase A, trajectory planning has ended, and the flight will proceed to the next phase B.

[0092] Step 5.4: Set the end time t of flight phase A. f The state and control variables at point A are used as the initial state and control variables for flight phase B. Based on the initial parameters of this phase, the initial trajectory planning problem P0_B of the hypersonic deformable vehicle is constructed. Then, the discretized convex trajectory planning problem P1_B of the hypersonic deformable vehicle is constructed through convexity and discretization techniques.

[0093] Step 5.5: Solve for P1_B using the sequential convex optimization method to obtain the optimal control sequence, and apply the control sequence within the actual guidance cycle to the aircraft and update the flight trajectory within the current guidance cycle online;

[0094] Step 5.6: Advance the time online to the next guidance cycle, and return to Step 5.5 to iterate and solve P1_B again; if the time advances to the trajectory planning terminal time t f Flight phase B, trajectory planning is complete, proceeding to the next flight phase C;

[0095] Step 5.7: Set the terminal time t of flight phase B. f The state and control variables at point B are used as the initial state and control variables for flight phase C. Based on the initial parameters of this phase, the initial trajectory planning problem P0_C of the hypersonic deformable vehicle is constructed. Then, the discretized convex trajectory planning problem P1_C of the hypersonic deformable vehicle is constructed through convexity and discretization techniques.

[0096] Step 5.8: Solve for P1_C using the sequential convex optimization method to obtain the optimal control sequence, and apply the control sequence within the actual guidance cycle to the aircraft and update the flight trajectory within the current guidance cycle online;

[0097] Step 5.9: Advance the time online to the next guidance cycle, and return to Step 5.8 to iterate and solve P1_C again; if the time advances to the trajectory planning terminal time t f _C, C flight phase trajectory planning completed;

[0098] Step 5.10: The convex problem of trajectory planning for the hypersonic deformable vehicle after discretization of the ABC flight phase is solved, and thus the continuous trajectory planning results for all phases are obtained.

[0099] Beneficial effects:

[0100] This invention discloses an online planning method for hypersonic deformable aircraft based on sequential convex optimization. It combines sequential convex optimization with rolling time-domain optimization to construct a sequential convex optimization solution method based on variable time-domain rolling planning that considers multi-stage continuous solution. This method solves the problem of planning the glide trajectory of hypersonic, deformable, and online aircraft. It can meet the requirements of real-time performance and robustness of aircraft deformation decision in the online trajectory planning problem of hypersonic deformable aircraft, and demonstrates the flight performance advantages of variable-span aircraft over fixed-shape aircraft. Attached Figure Description

[0101] Figure 1 This is a flowchart of the variable time-domain rolling planning method of the present invention;

[0102] Figure 2 The flowchart of the sequential convex optimization technique based on variable time-domain rolling planning, which considers multi-stage continuous solution, is shown in the present invention.

[0103] Figure 3 This is a comparison diagram of the ballistic ground projection of the deformable / fixed-shape aircraft of the present invention;

[0104] Figure 4 This is a height comparison diagram of the deformable / fixed-shape aircraft of the present invention;

[0105] Figure 5 This is a speed comparison diagram of the deformable / fixed-shape aircraft of the present invention;

[0106] Figure 6 This is a comparison diagram of the flight path angles of the deformable / fixed-shape aircraft of the present invention;

[0107] Figure 7 This is a comparison diagram of the heading angles of the deformable / fixed-shape aircraft of the present invention;

[0108] Figure 8This is a comparison diagram of the angle of attack of the deformable / fixed-shape aircraft of the present invention;

[0109] Figure 9 This is a comparison diagram of the tilt angles of the deformable / fixed-shape aircraft of the present invention;

[0110] Figure 10 This is a comparison chart of the deformation rates of deformable and fixed-shape aircraft of the present invention. Detailed Implementation

[0111] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0112] Example 1:

[0113] like Figure 2 As shown in the figure, this embodiment discloses an online planning method for hypersonic deformable vehicles based on sequential convex optimization. The specific implementation steps are as follows:

[0114] Step 1: Analyze the impact of deformation characteristics on the aerodynamic characteristics of the aircraft through the aircraft geometric model, and construct a dynamic model of a three-degree-of-freedom hypersonic deformable aircraft oriented towards trajectory planning.

[0115] The optimization target of this invention is a gliding-stage unpowered hypersonic variable-span aircraft. The single-side main wing span corresponds to 436.2 mm for the aircraft configuration with 0% wing extension and 1636.2 mm for the aircraft configuration with 100% wing extension. Assuming b0 is the span when the wing extension is 0%, b1 is the span when the wing extension is 100%, and b is the current span of the aircraft in the deformed state, with symmetrical deformation of the left and right wings, the wing span deformation rate can be defined as χ = (b - b0) / (b1 - b0).

[0116] A table of aerodynamic coefficients, including lift coefficient C, was obtained through CFD numerical calculations for each combination of parameters: angle of attack α, Mach number Ma, and deformation rate χ. y and drag coefficient C x Then, by performing polynomial fitting on the various aerodynamic coefficients in the data table, the expression for the lift and drag coefficients can be obtained, thus yielding the aerodynamic model of the hypersonic variable-span aircraft. The sampling points for the variable parameters selected in this invention are shown in Table 1 below:

[0117] Table 1 Sampling points for variable parameters

[0118]

[0119] Numerical calculations show that, compared to conventional hypersonic vehicles, the deformation characteristics of the object in this invention significantly affect the aerodynamic characteristics of the vehicle. Symmetrical deformation of the wings on both sides significantly impacts the vehicle's C-axis. y C x and lift-to-drag ratio. For aircraft C y C x As the angle of attack α increases, the C of different configuration aircraft... y C x Both gradually increase; for a given χ and α, the spacecraft C y C x It decreases accordingly as Ma increases; for a given α and Ma, the spacecraft C y C x The lift-drag ratio increases with increasing χ. For the lift-drag ratio of an aircraft, given χ and α, the maximum lift-drag ratio decreases accordingly with increasing Ma. Analyzing under the condition of given Ma, as α increases, the lift-drag ratio of different configuration aircraft shows a trend of first increasing and then decreasing, reaching the maximum lift-drag ratio approximately when α is 10°. For given α and Ma, the lift-drag ratio of the aircraft increases with increasing χ.

[0120] Further design C y C x The functions relating to α, Ma, and χ are in the form of fourth-degree polynomials. Based on these polynomials, the least squares algorithm is used to perform regression calculations, thereby obtaining the coefficients of the regression polynomials.

[0121] This invention addresses the trajectory planning problem for the unpowered gliding phase of a hypersonic deformable vehicle in three-dimensional space, considering the vehicle's lateral motion by adding a roll angle as a control variable. For ease of study, this invention employs the following assumptions: 1. During flight, the vehicle is considered a rigid body; the variable span only affects the aerodynamic coefficient at each moment, neglecting the additional forces caused by the variable span; 2. The influence of the Earth's rotation is ignored. Under these assumptions, the three-degree-of-freedom equations of motion for the deformable vehicle can be obtained as follows:

[0122]

[0123] In equation (23), the state variables x of the problem are the longitudinal stroke x and altitude y, the transverse stroke z, the missile velocity V, the track angle θ, and the heading angle ψ, respectively. V The control parameters u include the angle of attack α and the heel angle γ. V Deformation rate χ; Resistance X = qSC x Lift force Y = qSC y C x C y, respectively, are the aerodynamic coefficients for drag X and lift Y, functions of Mach number Ma, angle of attack α, and deformation rate χ = (b - b0) / (b1 - b0), all obtained by least squares fitting, where b0 is the wingspan at 0% wing extension, b1 is the wingspan at 100% wing extension, and b is the current wingspan of the aircraft in deformed state; S is the reference area, and dynamic pressure q = ρV 2 / 2; Atmospheric density ρ=ρ0e -βh ρ0 is the atmospheric density at sea level, a constant value of 1.2258 kg / m³. 3 β is a constant coefficient, with a value of 1.3785 × 10⁻⁶. -4 m -1 h is the altitude of the aircraft; m is the mass of the missile; gravitational acceleration g = μ / (R e +h) 2 μ is the Earth's gravitational coefficient, a constant value of 3.9860 × 10⁻⁶. 14 m 3 / s 2 R e The average radius of the Earth is a constant of 6378 km; ε(α,γ) V ,χ)=0 represents the control equation, indicating that the trajectory planning control variables are the angle of attack α and the roll angle γ. V Deformation rate χ.

[0124] The equations of motion are formally consistent with those of conventional aircraft, but differ in aerodynamic drag coefficient, aerodynamic lift coefficient, and wing reference area, all of which are related to the span deformation rate of deformable aircraft. To effectively avoid ill-conditioned Jacobian matrices caused by excessive differences in the magnitudes of state variables, and to avoid singularities in the Jacobian matrix due to large differences in the magnitudes of state variables, and to improve the convergence of the solution process, it is necessary to normalize the relevant variables in the above dynamic equations according to a certain scale.

[0125] For angle γ V Since the values ​​of x, y, z, V, and t are generally small and the unit is radians, no normalization is required. Furthermore, the value range of χ is [0,1], so no normalization is performed on χ. Based on the above analysis, the variables x, y, z, V, and t are normalized using the following normalization scales, as shown in Table 2:

[0126] Table 2 Normalized Scale

[0127]

[0128] Based on the above normalized scaling table, the normalized set of aircraft dynamics equations is obtained:

[0129]

[0130] In the formula, Dimensional velocity before normalization; These are the spatial coordinates before normalization; t represents the time variable before normalization; V represents the normalized aircraft velocity; x, y, and z represent the normalized spatial position coordinates; and t represents the time variable after normalization.

[0131] Step 2: Using the maximum weighted function of terminal altitude and terminal velocity at the end of the mission as the performance index, and considering the initial boundary constraints, terminal boundary constraints, and control constraints, construct the initial trajectory planning problem P0 for the hypersonic deformable vehicle in conjunction with the vehicle dynamics model constructed in Step 1.

[0132] The trajectory planning problem for hypersonic vehicles is described, and necessary information such as constraints and objective functions are clarified to construct the initial trajectory planning problem for hypersonic deformable vehicles. Based on this, the trajectory planning problem for vehicles with variable span is convexized: the dynamic equations and other nonlinear constraints are convexized using the successive linearization method, and the trapezoidal method is selected to discretize the continuous trajectory planning convex problem, thus completely transforming the problem into a discretized hypersonic deformable vehicle trajectory planning convex problem, providing a foundation for subsequent solutions.

[0133] The initial constraints are the initial values ​​of the spacecraft's state variables at the initial moment of each mission segment, i.e.:

[0134]

[0135] In the formula: t0 is the initial time of the flight mission segment; x0, y0, z0, V0, θ0, ψ V0 These correspond to the longitudinal range, altitude, lateral range, speed, track angle, and heading angle of the aircraft at the initial moment, respectively.

[0136] Terminal constraints are constraints imposed on the terminal state of an aircraft. For deformable hypersonic vehicles, these include constraints on longitudinal range, lateral range, track angle, and heading angle, i.e.:

[0137]

[0138] Different terminal constraints can be set depending on the flight mission. Where: t f For the terminal time of each task segment; x f z f θ f , These represent the desired missile terminal state, specifically the longitudinal range, transverse range, track angle, and heading angle at the terminal moment.

[0139] Process constraints are constraints imposed on the state variables at each moment during the trajectory planning process of a spacecraft. For deformable hypersonic vehicles, process constraints include velocity V, track angle θ, and heading angle ψ. V Constraints, namely:

[0140]

[0141] In the formula, V min Let V be the lower limit of V. min =1000m / s; θ min θ max These are the lower and upper limits of θ, respectively. min =-15°, θ max =15°; ψ Vmin ψ Vmax ψ V The lower and upper limits of ψ Vmin =-85°, ψ Vmax =85°.

[0142] Since the variable-span spacecraft has no thrust during reentry, the control variables for the reentry trajectory planning problem are α and γ. V α and γ primarily affect the aerodynamic coefficients of a hypersonic vehicle, altering its aerodynamic characteristics. Appropriately limiting the range of these control variables ensures a smooth trajectory and good flight performance for the hypersonic vehicle. Furthermore, to guarantee attitude stability control during reentry, the angle of attack and elongation deformation rate of the hypersonic vehicle must meet certain boundary constraints. Therefore, this invention first considers α and γ... V The amplitude constraint of the χ control variable, namely:

[0143]

[0144] In the formula, α min α max These are the lower and upper limits of α, respectively. min =0°, α max =25°; γ Vmin γ Vmax γ V The lower and upper limits of γ Vmin =-80°, γ Vmax =80°; χ min , χ max These are the lower and upper limits of χ, respectively. min =0, χ max =1.

[0145] Secondly, considering that each actuator has a rate of action limit in actual operation, it is necessary to constrain the rate of change of the aircraft control variables, that is:

[0146]

[0147] In the formula, These are the rates of change of angle of attack. The lower limit and upper limit, These are the rates of change of the tilt angle. The lower and upper limits, These are the rates of change of elongation deformation rate. The lower limit and upper limit,

[0148] This invention relates to an online trajectory planning method for hypersonic morphing vehicles. Its core focus is on the performance improvements resulting from vehicle morphing: on the one hand, minimizing velocity loss during flight; on the other hand, minimizing altitude loss after the mission. Therefore, this invention uses a weighted function of terminal altitude and terminal velocity as the objective function, namely:

[0149] min J=-m1V f -m2y f (30)

[0150] In the formula, m1 is V f The corresponding constant weighting coefficients, m2 is y f The corresponding constant weight coefficients, J is the objective function value, V f Let y be the terminal velocity of the aircraft. f This refers to the terminal altitude of the aircraft.

[0151] For the terminal constraint in equation (26), which is an equal-strength equality constraint, it is possible to gradually approximate this type of strong equality constraint during the sequential iteration process, without having to constrain it too strongly to the point that the solver has no solution. Therefore, a relaxation variable ξ is introduced to relax the terminal position constraint, and the terminal position can be rewritten as:

[0152]

[0153] In the formula: t f For the terminal time of each task segment; x f z f θ f , These represent the desired missile terminal state, specifically the longitudinal range, transverse range, track angle, and heading angle at the terminal moment; ξ x ξ z ξ θ , These are the error bounds corresponding to the terminal state constraints, both of which are small constants.

[0154] By adding a slack variable penalty term to the objective function to constrain the terminal state, so that the terminal position during the iteration process approaches the specified position, the objective function is rewritten as:

[0155]

[0156] In the formula, m3 is ξ x The corresponding constant weighting coefficient, m4 is ξ z The corresponding constant weighting coefficient, m5, is ξ. θ The corresponding constant weighting coefficient, m6 is The corresponding constant weighting coefficients;

[0157] Based on the above information regarding the aircraft model construction, constraints, and objective function, the initial trajectory planning problem P0 for a hypersonic deformable aircraft is constructed:

[0158]

[0159] In the formula, x is the state vector and u is the control vector. The equations of motion for the aircraft's dynamics are given by equality constraints. c(x,u,t)=0 and s(x,u,t)<0 represent the process and terminal equality constraints and inequality constraints that the state and control variables must satisfy, respectively. For problem P0, its state variables are x=[V,θ,ψ]. V [x,y,z] T The control variables are u = [α, γ] V ,χ] T Due to the existence of nonlinear dynamics and nonlinear constraints, this problem P0 is a nonconvex problem, and it needs to be processed according to convex optimization theory to transform it into a convex optimization problem.

[0160] Step 3: Since the planning problem involved in this invention is a terminal freedom problem, an augmented control quantity t is introduced based on equation (1) obtained in step 1. f Let t0 be the initial time of the task. Using the transformation relationship t = t0 + (t f -t0)τ is subjected to time freedom processing. If t0=0, the domain of the independent variable is obtained as τ=t / t f This leads to the augmented dynamics model of the aircraft:

[0161]

[0162] In equation (34), the state variable is Control quantity is

[0163] Step 4: Process equation (34) obtained in Step 3 using the successive linearization method: Given a reference trajectory Given the state trajectory obtained in the k-th iteration, the problem P0 obtained in step two is transformed into a continuous convex optimization problem based on the first-order linearized dynamic nonlinear term of the optimal trajectory generated in the k-th iteration. Then, using the equal division method, the continuous optimization problem is discretized on the equally divided domain of independent variables τ=[0,1], with the number of discrete points being N+1, resulting in the discretized hypersonic deformable vehicle trajectory planning convex problem P1.

[0164] The successive linearization method is used to handle the nonlinear dynamic equations: given a reference trajectory Assumption Given the state trajectory obtained in the k-th iteration, the first-order linearized dynamic nonlinear term is derived from the optimal trajectory generated in the k-th iteration. The linearized dynamic form is: Will Perform a first-order Taylor expansion at the reference trajectory:

[0165]

[0166] In equation (35), Let be the specific constant value of the differential equation at the reference trajectory. for Regarding state variables The derivative, for Regarding control quantity The derivative of, and in the second equation

[0167] Expanding the above equation further, we get:

[0168]

[0169] The expressions for each matrix are as follows:

[0170] ① matrix:

[0171]

[0172] ② matrix:

[0173]

[0174] ③ matrix:

[0175]

[0176] ④ matrix:

[0177]

[0178] ⑤ matrix:

[0179]

[0180] ⑥ matrix:

[0181]

[0182] A crucial step in the linearization process described above is the selection of the Taylor expansion reference point. In sequential convex optimization algorithms, the reference point for the first iteration is provided by the initial optimization value, and during subsequent iterations, the reference point is taken as the optimal solution obtained in the previous iteration. Based on the characteristics of the first-order Taylor expansion, in the iterative process of sequential convex optimization, the linearization dynamics and state constraints only provide a good approximation of the original nonlinear form when the optimization variables take values ​​near the reference point. Therefore, the following trust region constraint is added to the sequential convex optimization algorithm:

[0183]

[0184] Where, δ x and δ u It is a constant vector trust region. Trust region constraints can affect algorithm iterations; generally, a smaller trust region is set to reduce the error caused by linearization. The above inequalities satisfy for each state and control component, and are consistent with... and The dimensions are the same. However, the size of the trust region has a significant impact on the convergence of the problem: if the trust region is too small, there may be no solution that satisfies the constraints of the current iteration, resulting in poor convergence and reduced timeliness; if the trust region is too large, the linearization of the dynamics cannot guarantee the effectiveness of the approximation.

[0185] Based on equation (37), trust region relaxation variables C and D are introduced. The relaxed trust region constraint can be expressed as:

[0186]

[0187] In the formula, C and D are respectively δ x δ u The corresponding relaxation optimization variables are used to adjust the trust region size by optimizing the values ​​of C and D.

[0188] By adding a penalty term for the norm of the relaxation variables in the trust region to the objective function, the size of the trust region is reduced by the penalty if a solution exists in this iteration, thus balancing efficiency and convergence. The objective function is rewritten as follows:

[0189]

[0190] In the formula, m7 is the constant weight coefficient corresponding to C, and m8 is the constant weight coefficient corresponding to D; this objective function is a linear objective function and does not require convexity processing.

[0191] For nonlinear inequality constraints Convexification mainly employs successive linearization methods, Performing a first-order Taylor expansion at the reference trajectory yields:

[0192]

[0193] Among them, s x and s u They represent s with respect to state variables respectively. and control quantity The partial derivatives of .

[0194] The problem obtained after dynamic linearization and other convexification processes is a continuous optimization problem, where both the state and control variables are continuous variables, making it difficult to solve directly. Therefore, it is necessary to transform the problem into a planning problem that seeks to optimize finite parameters, and then use numerical methods to solve it.

[0195] This invention employs the collocation method to simultaneously discretize state variables. With control variables The continuous optimization problem is discretized over an equally divided domain of independent variables τ = [0, 1], with N+1 discrete points. The step size is then Δτ = 1 / N, and the discrete points are {τ0, τ1, τ2, ..., τ...}. N}, and τ i =τ0+iΔτ (i=0,1,...,N); then the state variables and control variables in the continuous optimization problem are discretized as and This invention uses the trapezoidal integral formula to discretize continuous-time problems to obtain:

[0196]

[0197] In the formula,

[0198] Meanwhile, for the control rate constraint equation (29), this invention uses the position constraint form of discrete points to characterize the control variable change rate constraint:

[0199]

[0200] In the formula,

[0201] After performing dynamic linearization, constraint convexization, and problem discretization on the original initial trajectory planning problem P0, we obtain the discretized convex trajectory planning problem P1 for a hypersonic deformable vehicle:

[0202]

[0203] In the formula, i = 1, ..., N represents the discrete points after discretizing the problem using the collocation method; For the equality constraints of the dynamic differential equations after convexification; Linear equality constraints; For linear inequality constraints; To perform equality constraints after convexification; These are the inequality constraints after convexification.

[0204] Step 5: Solve the trajectory planning convex problem P1 to obtain the trajectory planning result of the hypersonic vehicle, that is, realize the online planning of the hypersonic deformable vehicle based on sequential convex optimization.

[0205] To achieve online planning for aircraft, the rolling time-domain optimization principle needs to be introduced. The core idea of ​​this principle is to generate the optimal control quantity by solving a sequential convex optimization problem based on the state at the current time *i*. Only the control quantity for the first guidance cycle is applied to the aircraft to obtain the state at time *i+1*, and this process is repeated until the last guidance cycle. This method continuously introduces uncertainties and potential disturbances into the dynamic differential equations and eliminates deviations caused by the linearization of the dynamic model in the rolling control commands.

[0206] To solve the continuous optimization problem constructed in this invention, the continuous optimization problem needs to be discretized on the equally divided domain of independent variables τ = [0,1] in each solution of the sequential convex optimization problem, with N+1 discrete points. Specifically, for the terminal time-free problem studied in this invention, as the rolling iteration progresses, the prediction time domain length T1 gradually shortens, often leading to a situation where there is no solution at the end of the rolling iteration. Furthermore, selecting only a fixed execution time domain interval T2 makes it difficult to match the time t(τ) at the discrete points. i To match the control input at the end of each guidance cycle, an approximation method using interpolation of adjacent discrete points is often used. Therefore, a variable-time-domain rolling method is designed to determine the actual execution time interval T3 for each rolling cycle. The specific steps are as follows: Figure 1 The corresponding steps are as follows:

[0207] Step 5.1.1: Determine the prediction time domain length T1 by solving the trajectory planning convex problem, and proceed to step 5.1.2;

[0208] Step 5.1.2: Determine the magnitudes of T1 and 2T2. If T1 ≥ 2T2, then use NT² / t fThe integer value determines the number of the discrete point closest to T2, and then determines the actual execution time domain interval T3. After solving the convex problem of trajectory planning through numerical integration, return to step 5.1.1; if T1≤2T2, then proceed to step 5.1.3.

[0209] Step 5.1.3: Obtain the final result through numerical integration, and the trajectory planning ends.

[0210] This invention combines sequential convex optimization with variable time-domain rolling planning, designing a sequential convex optimization technique based on variable time-domain rolling planning. This technique can solve multi-configuration switching trajectory planning problems with different guidance cycles. Hypersonic vehicles may need to perform multiple maneuvers to meet mission requirements, and the flight mission needs to be divided into multiple mission intervals. The lack of pre-allocation of time for different mission phases makes it difficult to transform the original dynamic optimization problem into a static optimization problem. To overcome this difficulty, this invention divides the entire flight mission into multiple flight phases based on a multi-stage continuous solution method, and solves each phase sequentially to obtain a continuous solution for all phases. The flowchart of the sequential convex optimization technique based on variable time-domain rolling planning considering multi-stage continuous solution is shown below. Figure 2 As shown, the specific steps are as follows:

[0211] Step 5.2.1: First, design different flight phases according to mission requirements, then proceed to step 5.2.2;

[0212] Step 5.2.2: Initialize the parameters for this stage, construct the initial trajectory planning problem P0, and then construct the convex trajectory planning problem P1 through convexization and discretization techniques, proceeding to step 5.2.3;

[0213] Step 5.2.3: Solve for P1 using the sequence convex optimization method to obtain the optimal control sequence and the prediction time domain length T1, then proceed to step 5.2.4;

[0214] Step 5.2.4: Determine the magnitudes of T1 and 2T2. If T1 ≥ 2T2, then set T3 = t f / N×[NT2 / t f The control variables within ] are applied to the aircraft, thereby updating the time and flight trajectory, and returning to step 5.2.3; if T1≤2T2, then the control variables within T3=T1 are applied to the aircraft, and proceed to step 5.2.5;

[0215] Step 5.2.5: Determine if there is a next flight phase. If there is, proceed to the next flight phase and return to step 5.2.2; if there is no next flight phase, the algorithm ends and the trajectory planning task is completed.

[0216] The following simulations using Matlab illustrate the specific process of the online planning method for hypersonic deformable vehicles based on sequential convex optimization, as presented in this invention. Numerical calculations were performed on a laptop computer equipped with a Core i7-12700H processor with a clock speed of 2.30 GHz. All programs ran in the Matlab 2022a environment, and the convex subproblem generated by the algorithm was solved using the interior-point method via the MOSEK software API.

[0217] In a specific mission context, the flight mission of an aircraft is decomposed into different stages. This invention simplifies the specific flight missions of each stage, meaning the differences between the stages lie only in the different initial conditions and terminal constraints. To verify the superiority of variable-span aircraft in trajectory planning, the trajectory planning results of variable-span aircraft and fixed-shape aircraft are compared and analyzed. Fixed-shape aircraft refers to aircraft whose deformation rate remains at 0%.

[0218] Selecting a fixed execution time interval T2 = 10s, the initial conditions for the deformable / fixed shape aircraft are: x0 = 0, y0 = 31.5km, z0 = 0, V0 = 2125m / s, θ0 = 0, ψ V0 =0, the objective function is to minimize the weighted sum of terminal velocity loss and terminal altitude loss: min J = -m1V f -m2y f Based on the method constructed in this invention, three-stage flight termination conditions are set as shown in Table 3 below:

[0219] Table 3 Termination conditions for different flight phases

[0220]

[0221] Based on the above conditions, the simulation results of the novel rolling time-domain multi-stage continuous convex optimization method proposed in this invention are as follows. Figure 3-10 The solid lines represent the flight trajectories of deformable and fixed-shape aircraft, while the dashed lines represent their respective trajectories. Analysis of the simulation results reveals the changes in altitude and velocity for both deformable and fixed-shape aircraft, as shown in Table 4 below.

[0222] Table 4. Altitude and velocity variations of deformable and fixed-shape aircraft

[0223]

[0224] Depend on Figure 3It is known that a fixed-shape aircraft cannot reach the predetermined waypoint during the initial left maneuver, thus failing to meet reconnaissance needs; while compared to a fixed-shape aircraft, a deformable aircraft can accurately reach the flight waypoint and achieve precise connection between the three flight phases. This indicates that a deformable aircraft can improve its lateral maneuverability by extending and retracting its wings.

[0225] Figure 4 The altitude changes of the two types of aircraft are shown in Table 4, and their terminal altitudes are as follows. It can be seen that the deformable aircraft has a significant advantage in terms of altitude: the terminal altitude of the deformable aircraft is 33.0 km, which is 1.5 km higher than that of the fixed-shape aircraft; the terminal altitude of the fixed-shape aircraft is 30.2 km, which is 1.3 km lower than that of the fixed-shape aircraft; the terminal altitude of the deformable aircraft is 2.8 km higher than that of the fixed-shape aircraft.

[0226] Depend on Figure 5 As can be seen, the deformable aircraft also has a significant advantage in terms of speed. The terminal values ​​are shown in Table 4: the terminal speed of the deformable aircraft is 1233.4 m / s, and the speed loss is 891.6 m / s; the terminal speed of the fixed-shape aircraft is 1000 m / s, and the speed loss is 1125 m / s; the terminal speed loss of the deformable aircraft is reduced by 20.7% compared with that of the fixed-shape aircraft.

[0227] Figure 6 The changes in the flight path angles of two types of aircraft are given, combined with Figure 8 Angle of attack changes Figure 9 Changes in yaw angle and Figure 10 The changes in deformation rate show that during the left maneuver phase, the deformation rate of the deformable aircraft increases, and the lift-to-drag ratio of the aircraft increases significantly, resulting in a larger track angle for the deformable aircraft compared to the fixed-shape aircraft. In the initial phase of the right maneuver, the amplitude of the fixed-shape aircraft's roll angle decreases, and its angle of attack first decreases and then increases, resulting in a smaller track angle for the fixed aircraft. In the final phase of the right maneuver, the amplitude of the fixed-shape aircraft's roll angle increases, and its angle of attack first decreases and then increases, resulting in a larger track angle for the fixed aircraft. Meanwhile, the deformable aircraft has a larger roll angle amplitude, causing its track angle to continuously decrease.

[0228] Figure 7 Two types of aircraft heading angle changes are given, combined with Figure 8 Angle of attack changes Figure 9 Changes in yaw angle and Figure 10The deformation rate changes show that during the left maneuver phase, the deformation rate of the deformable aircraft is at a relatively high level, which significantly increases the lift coefficient and lift-to-drag ratio, making the directional angular velocity of the deformable aircraft significantly greater than that of the fixed-shape aircraft. In the initial stage of the right maneuver, in order to minimize the loss of altitude and speed, the deformable aircraft reduces drag by decreasing the deformation rate. At the same time, the trajectory angle amplitude of the deformable aircraft is smaller, making the directional angular velocity of the deformable aircraft less than that of the fixed-shape aircraft. In the final stage of the right maneuver, the angle of attack, deformation rate, and roll angle of the deformable aircraft are larger, so the directional angular velocity of the deformable aircraft is significantly greater than that of the fixed-shape aircraft.

[0229] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A sequence-based convex optimization method for online planning of hypersonic morphing aircraft, characterized in that: Includes the following steps: Step 1: Analyze the influence of deformation characteristics on the aerodynamic characteristics of the aircraft through the aircraft geometric model, and construct a dynamic model of a three-degree-of-freedom hypersonic deformable aircraft oriented towards trajectory planning; In formula (1), R0 is the maximum flight distance; V c is the upper limit of constant speed; drag X = qSC x , lift Y = qSC y , C x , C y are the aerodynamic coefficients of drag X and lift Y respectively, which are functions of Mach number Ma, angle of attack a and deformation rate χ = (b-b0) / (b1-b0), and are obtained by least square fitting, wherein b0 is the wing span at 0% wing extension, b1 is the wing span at 100% wing extension, and b is the current wing span of the aircraft in the deformed state. S is the reference area, dynamic pressure q = pV 2 , atmospheric density p = p0e -βh , p0is the sea level atmospheric density; b is a constant coefficient; h is the aircraft height; m is the missile mass; gravitational acceleration g = μ / (R e +h) 2 , μ is the earth's gravity coefficient, R e is the average radius of the earth; Step two, taking the maximum of the weighted function of the terminal height and terminal velocity at the end of the task as the performance index, considering the initial boundary constraint, terminal boundary constraint and control constraint, and combining the aircraft dynamics model constructed in step one, the initial trajectory planning problem P0 of the hypersonic morphing aircraft is constructed; the state variables x of the problem are respectively the longitudinal distance x and the height y, the lateral distance z, the missile speed V, the flight path angle θ and the heading angle ψ V , the control variables u include the attack angle α, the roll angle γ V and the morphing rate χ, and the state variables and control variables of the problem P0 are normalized variables; In formula (2), m1 is V f The corresponding constant weight coefficient, m2 is y f The corresponding constant weight coefficient, m3 is ξ x The corresponding constant weight coefficient, m4 is ξ z The corresponding constant weight coefficient, m5 is ξ θ The corresponding constant weight coefficient, m6 is The corresponding constant weight coefficient, J is the objective function value, V f is the terminal speed of the aircraft, y f is the terminal altitude of the aircraft, ξ x , ξ z , ξ θ , The longitudinal distance, the lateral distance, the track angle, the heading angle constraint corresponding error boundary of the aircraft at the terminal time respectively; x = [V, θ, ψ V , x, y, z] T is the state vector, u = [α, γ V , χ] T is the control vector, is the dynamic differential equation constraint of the aircraft; t is time; c(x, u, t) = 0 and s(x, u, t) < 0 respectively represent the process and terminal equation constraints and inequality constraints that the state quantity and the control quantity need to satisfy; Step three, introducing the augmented control variable t on the basis of formula (1) obtained in step one f , let t0 be the initial time of the task, and use the conversion relationship t = t0 + (t f -t0)τ to perform time liberalization processing, if t0 = 0, obtain the independent variable definition domain τ = t / t f , and further obtain the augmented dynamics model of the aircraft: In formula (3), the state quantity is The control quantity is Step four, process the formula (3) obtained in step three by using the successive linearization method: given a reference trajectory The state trajectory obtained for the kth iteration, according to the first-order linearization dynamics nonlinear term of the optimal trajectory generated in the kth iteration, converts the problem P0 obtained in step two into a continuous convex optimization problem; and then using the bisection method, the continuous optimization problem is discretized on the bisection independent variable domain τ = [0, 1], and the number of discrete points is N + 1, to obtain the discretized hypersonic variable shape aircraft trajectory planning convex problem P1: In formula (4), C is a relaxation optimization variable corresponding to a state quantity dependent domain, D is a relaxation optimization variable corresponding to a control quantity dependent domain, m7 is a constant weight coefficient corresponding to C, m8 is a constant weight coefficient corresponding to D, is a state vector, is a control vector, i = 1, …, N represents a discrete point after the problem is discretized by a collocation method; is a convexified kinetic differential equation equality constraint; is a linear equality constraint; is a linear inequality constraint; for the convexified equality constraints; for the convexified inequality constraints; Step 5: Solve the trajectory planning convex problem P1 to obtain the trajectory planning result of the hypersonic vehicle, that is, realize the online planning of the hypersonic deformable vehicle based on sequential convex optimization.

2. The method of claim 1, wherein: The specific implementation method of step two is as follows: The initial boundary constraints are the initial values ​​of the spacecraft's state variables at the initial moment of each mission segment, i.e.: In formula (5): t0 is an initial time of a flight mission segment; x0, y0, z0, V0, θ0, ψ0 respectively correspond to a longitudinal distance, a height, a lateral distance, a speed, a track angle, and a heading angle of the aircraft at the initial time; V0 In formula (5): t0 is an initial time of a flight mission segment; x0, y0, z0, V0, θ0, ψ0 respectively correspond to a longitudinal distance, a height, a lateral distance, a speed, a track angle, and a heading angle of the aircraft at the initial time; Terminal boundary constraints are constraints imposed on the terminal state of an aircraft. For hypersonic deformable aircraft, these constraints include longitudinal, lateral, track angle, and heading angle constraints, namely: In formula (6): t f is the terminal time of each task segment; x f , z f , θ f , are the longitudinal distance, lateral distance, track angle, and heading angle corresponding to the desired aircraft terminal time, respectively. Process constraints are constraints on state variables at each time instant in the trajectory planning process of the aircraft. The process constraints of the hypersonic morphing aircraft include velocity V, flight path angle θ, heading angle ψ V Constraints, i.e.: In formula (7), V min is a lower limit value of the speed V; θ min , θ max are a lower limit value and an upper limit value of the track angle θ, respectively; ψ Vmin , ψ Vmax are a lower limit value and an upper limit value of the heading angle ψ V , respectively. Consider the angle of attack α, roll angle γ V and the amplitude constraint of the deformation rate χ control variable, i.e.: In formula (8), α min and α max are lower and upper limit values of the attack angle α, respectively; γ Vmin and γ Vmax are lower and upper limit values of the roll angle γ V , respectively; χ min and χ max are lower and upper limit values of the deformation rate χ, respectively. Secondly, considering that each actuator has a rate of action limit in actual operation, the rate of change of the aircraft control variables is constrained, namely: In formula (9), respectively a lower limit value and an upper limit value of a rate of change of the angle of attack respectively a lower limit value and an upper limit value of a rate of change of the angle of attack respectively a lower limit value and an upper limit value of a rate of change of the angle of roll respectively a lower limit value and an upper limit value of a rate of change of the angle of roll respectively a lower limit value and an upper limit value of a rate of change of the deformation rate respectively a lower limit value and an upper limit value of a rate of change of the deformation rate The objective function is a weighted function of terminal height and terminal speed, i.e.: min J = -m1V f -m2y f (10) In formula (10), m1 is V f corresponding constant weight coefficient, m2 is y f corresponding constant weight coefficient, J is a target function value, V f is a terminal speed of the aircraft, y f is a terminal altitude of the aircraft; For the terminal constraint in equation (6), a relaxation variable is introduced to relax the terminal position constraint. The terminal position is then rewritten as: in formula (11): t f is the terminal time of each task segment; x f , z f , θ f , correspond to the longitudinal distance, lateral distance, track angle, heading angle of the desired aircraft terminal time respectively; ξ x , ξ z , ξ θ , are the error bounds of the longitudinal distance, lateral distance, track angle, heading angle constraints of the aircraft terminal time respectively; By adding a slack variable penalty term to the objective function to constrain the terminal state, so that the terminal position during the iteration process approaches the specified position, the objective function is rewritten as: In formula (12), m3 is ξ x The corresponding constant weight coefficient, m4 is ξ z The corresponding constant weight coefficient, m5 is ξ θ The corresponding constant weight coefficient, m6 is The corresponding constant weight coefficient; Combining the vehicle dynamics model (1), constraints, and objective function information constructed in step one, the initial trajectory planning problem P0 of the hypersonic deformable vehicle is expressed as: 。 3. The method of claim 2, wherein: The specific implementation method for step four is as follows: The successive linearization method is used to deal with the nonlinear dynamics equation: given a reference trajectory For the state trajectory obtained in the kth iteration, the first-order linearization dynamics nonlinear term is generated according to the optimal trajectory generated in the kth iteration, and the linearized form of the dynamics is The first-order Taylor expansion is performed at the reference trajectory: The first-order Taylor expansion is performed at the reference trajectory: In formula (14), is a specific constant value of the differential equation at the reference trajectory, is is the derivative with respect to the state variable , is is the derivative with respect to the control variable , and in the second formula Expanding the above equation further, we get: In equation (15), the expressions for each matrix are as follows: Matrix:​ ② matrix: ③ matrix ④ matrix ⑤ matrix ⑥ matrix To ensure the reliability of the above successive linearization method, the following trust region constraint is added: In equation (16), δ x It is a state variable The constant vector trust region, and with The dimensions are the same, δ u It is a state variable The constant vector trust region, and with The dimensions are the same; based on equation (16), a trust region relaxation variable is introduced, and the relaxed trust region constraint can be expressed as: In formula (17), C is δ x Corresponding to the relaxation optimization variable, D is δ u Corresponding to the relaxation optimization variable, the size of the trust region is adjusted by optimizing the values of C and D; By adding a penalty term for the norm of the relaxation variables in the trust region to the objective function, the objective function is rewritten as follows: In equation (18), m7 is the constant weight coefficient corresponding to C, and m8 is the constant weight coefficient corresponding to D; this objective function is a linear objective function and does not require convexification. For nonlinear inequality constraints The convexity is also achieved using a successive linearization method, which... Performing a first-order Taylor expansion at the reference trajectory, we obtain: In equation (19), and They represent s with respect to state variables respectively. and control quantity The partial derivatives; The above convexification method completes the convexification of the problem P0 obtained in step two. Based on this, the problem is discretized: the collocation method is used to simultaneously discretize the state variables. With control variables The continuous optimization problem is discretized over an equally divided domain of independent variables τ = [0,1], with N+1 discrete points; the step size is Δτ = 1 / N, and the discrete points are {τ0, τ1, τ2, ..., τ...}. N }, and τ i =τ0+iΔτ (i=0,1,...,N); then the state variables and control variables in the continuous optimization problem are discretized as and Using the trapezoidal integral formula to discretize the continuous-time problem, we get: In equation (20), Meanwhile, for the control rate constraint equation (9), the position constraint form of discrete points is used to characterize the control variable change rate constraint: In equation (21), After linearizing the dynamics, constraining the convexity, and discretizing the problem P0, we obtain the discretized convex problem P1 for hypersonic deformable vehicle trajectory planning: 。 4. The online planning method for hypersonic deformable vehicles based on sequential convex optimization as described in claim 3, characterized in that: The specific implementation method of step five is as follows: The complete flight mission is divided into three flight phases by setting different waypoints, named A, B and C respectively; each flight phase is solved sequentially to obtain a continuous solution for all phases. Step 5.1: In flight phase A, based on the initial parameters of this phase, construct the initial trajectory planning problem P0_A of the hypersonic deformable vehicle according to step two, and then construct the discretized convex trajectory planning problem P1_A of the hypersonic deformable vehicle using the convexity and discretization methods in steps three and four. Step 5.2: Solve for P1_A using the sequential convex optimization method to obtain the optimal control sequence; select the control sequence for the actual guidance cycle from the optimal control sequence, use it for the aircraft, and update the flight trajectory online for the current guidance cycle; Step 5.3: Roll forward the time to the next guidance cycle and return to Step 5.2 to re-iterate the solution of P1_A; if the time rolls forward to the trajectory planning terminal time t f _A, the A flight phase trajectory planning is finished and enters the next flight phase B; Step 5.4: The state variable at time t f The state variable and control variable at A are taken as the initial state variable and control variable of B flight phase, and the initial trajectory planning problem P0_B of hypersonic morphing aircraft is constructed according to the initial parameters of this phase, and then the discrete trajectory planning convex problem P1_B of hypersonic morphing aircraft is constructed through convexization and discretization technology. Step 5.5: Solve for P1_B using the sequential convex optimization method to obtain the optimal control sequence, and apply the control sequence within the actual guidance cycle to the aircraft and update the flight trajectory within the current guidance cycle online; Step 5.6: Roll forward the time to the next guidance cycle and return to Step 5.5 to re-iterate the solution of P1_B; if the time rolls forward to the trajectory planning terminal time t f _B, the B flight phase trajectory planning is finished and enters the next flight phase C; Step 5.7: The state variable at time t f The state variable and control variable at B are taken as the initial state variable and control variable of the C flight phase, and the initial trajectory planning problem P0_C of the hypersonic morphing aircraft is constructed according to the initial parameters of this phase, and then the discrete trajectory planning convex problem P1_C of the hypersonic morphing aircraft is constructed through convexization and discretization techniques. Step 5.8: Solve for P1_C using the sequential convex optimization method to obtain the optimal control sequence, and apply the control sequence within the actual guidance cycle to the aircraft and update the flight trajectory within the current guidance cycle online; Step 5.9: Roll forward the time to the next guidance cycle and return to Step 5.8 to re-iterate the solution of P1_C; if the time rolls forward to the trajectory planning terminal time t f _C, C flight phase trajectory planning is finished. Step 5.10: The convex problem of trajectory planning for the hypersonic deformable vehicle after discretization of the ABC flight phase is solved, and thus the continuous trajectory planning results for all phases are obtained.

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