Online planning method for hypersonic deformation aircraft based on sequence convex optimization

Abstract

The invention discloses a hypersonic-speed deformable aircraft online planning method based on sequence convex optimization, and belongs to the field of hypersonic-speed deformable aircraft trajectory planning. The implementation method comprises the following steps: analyzing the influence of deformation characteristics on aerodynamic characteristics of the aircraft, and constructing a trajectory planning-oriented dynamic model of the three-degree-of-freedom hypersonic deformation aircraft; taking the maximum weighting function of the terminal height and the terminal speed at the end of the task as a performance index, considering the initial boundary constraint, the terminal boundary constraint and the control quantity constraint, and combining an aircraft dynamics model to construct an initial trajectory optimization problem of the hypersonic deformation aircraft; performing convexity processing and discretization processing on the variable-elongation aircraft trajectory planning problem to obtain a trajectory planning convex problem; and a sequence convex optimization solving method based on variable time domain rolling planning and considering multi-stage continuous solving is constructed to solve the problem of gliding section trajectory planning with free terminal time, and online planning of the hypersonic deformation aircraft is realized according to a solving result.

Description

Technical Field

[0001] The invention relates to an online planning method for a hypersonic deformable aircraft based on sequential convex optimization, and belongs to the technical field of trajectory planning for hypersonic deformable aircraft. Background Art

[0002] Hypersonic aircraft refers to near-space aircraft with a Mach number greater than 5, which has the advantages of high speed, long range, high maneuverability, efficient destruction, and strong penetration. With its unique performance advantages, this type of aircraft has shown great application potential in carrying out a wide range of strategic tasks. One of its development trends is to combine it with the contemporary hot variant technology to improve its flight performance, so as to solve the problem that hypersonic aircraft with fixed layout are difficult to achieve optimal performance in the entire stage. Variant aircraft is an aircraft that uses variant control mechanisms to change the shape of the aircraft to meet mission requirements or provide maneuver control. Different aircraft aerodynamic configurations can be achieved by changing the wing sweep angle, aspect ratio, airfoil thickness, and trailing edge curvature. Introducing variant technology into hypersonic aircraft can use the shape parameters to affect aerodynamic characteristics to improve its flight performance, thereby adapting to more complex flight missions and environments; at the same time, it can also obtain the optimal aerodynamic performance and maneuverability, reduce energy consumption during flight, and increase range; it can also make the trajectory form variable through deformation, further enhancing the penetration capability of hypersonic aircraft. However, the introduction of variant technology increases the dimension of the hypersonic aircraft model and enhances the dynamic nonlinearity, making it more difficult to solve using convex optimization technology. Therefore, it is necessary to improve the timeliness and stability of the trajectory planning method for hypersonic variant aircraft.

[0003] For the online planning method of hypersonic deformable aircraft, it is necessary to introduce the rolling time domain optimization method. The core idea of ​​the rolling time domain optimization principle is to generate the optimal control quantity by solving the sequential convex optimization problem according to the current state at time i, and only apply the control quantity of the first guidance cycle to the aircraft to obtain the state at time i+1, and repeat this process until the last guidance cycle. This method is used to continuously introduce uncertain factors into the dynamic differential equation, and eliminate the deviation caused by the linearization of the dynamic model in the rolling control instructions. In particular, for the terminal time freedom problem studied in the present invention, as the rolling proceeds, the predicted time domain length is gradually shortened, which may often lead to the occurrence of no solution at the end of the rolling; and only selecting a fixed execution time domain interval is difficult to match the time at the discrete point, and the adjacent discrete point interpolation approximation method is often used to obtain the control quantity at the terminal moment of each guidance cycle, which also leads to the inaccuracy of the solution.

[0004] In addition, a hypersonic vehicle may need to perform multiple maneuvers to achieve mission requirements, which means that the flight mission of the vehicle needs to be divided into multiple mission intervals. The time when the vehicle performs different phases of the mission is not pre-allocated, which makes it difficult to convert the original dynamic optimization problem into a static optimization problem.

[0005] There is still little research on the trajectory planning problem of the gliding phase of a hypersonic, deformable, and online aircraft. It is necessary to carry out cutting-edge technology research to serve future technological needs. Summary of the invention

[0006] In order to solve the problem of trajectory planning for the gliding segment of a hypersonic, deformable, and online aircraft, the purpose of the present invention is to provide an online planning method for a hypersonic deformable aircraft based on sequential convex optimization, analyze the influence of deformation on the aerodynamic characteristics of the aircraft, and construct an aerodynamic model and a dynamic model of the hypersonic deformable aircraft; perform convexification and discretization processing on the trajectory planning problem of a variable-length aircraft to obtain a trajectory planning convex problem; on this basis, construct a sequential convex optimization solution method based on variable time domain rolling planning that considers multi-stage continuous solution to solve the trajectory planning problem of the gliding segment with terminal time freedom, and realize the online planning of the hypersonic deformable aircraft according to the solution result of the trajectory planning problem of the gliding segment with terminal time freedom.

[0007] The objective of the present invention is achieved through the following technical solutions:

[0008] An online planning method for a hypersonic deformable aircraft based on sequential convex optimization comprises the following steps:

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

[0010]

[0011] In formula (1), R0 is the maximum flight distance; V c is the upper limit of constant speed; resistance 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 α and deformation rate χ=(b-b0) / (b1-b0), all of which are obtained by least squares fitting, where b0 is the span when the wing is extended by 0%, b1 is the span when the wing is extended by 100%, and b is the current span of the aircraft in the deformed state; S is the reference area, and the dynamic pressure q=ρV 2 / 2; atmospheric density ρ = ρ0e-βh , ρ0 is the atmospheric density at sea level, which is a constant of 1.2258 kg / m 3 ; β is a constant coefficient, which is 1.3785×10 - 4 m -1 ; h is the height of the aircraft; m is the mass of the missile; gravitational acceleration g = μ / (R e +h) 2 , μ is the gravitational coefficient of the earth, which is a constant value of 3.9860×10 14 m 3 / s 2 , R e is the average radius of the Earth, which is a constant value of 6378km;

[0012] Step 2: Taking the maximum weighted function of the terminal height and the terminal speed at the end of the mission as the performance index, considering the initial boundary constraints, the terminal boundary constraints and the control quantity constraints, and combining the aircraft dynamics model constructed in step 1 to construct the initial trajectory planning problem P0 of the hypersonic deformable aircraft; the state quantities x of the problem are respectively the longitudinal range x and the height y, the lateral range z, the missile speed V, the track angle θ, the heading angle ψ V , the control quantity u includes the angle of attack α, the roll angle γ V , deformation rate χ, the state quantity and control quantity of the problem P0 are normalized variables;

[0013]

[0014] 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 velocity of the aircraft, y f is the terminal altitude of the aircraft, ξ x , z , θ , are the error bounds corresponding to the longitudinal range, lateral range, track angle, and heading angle constraints of the aircraft at the terminal moment; 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 equation constraint of the dynamic differential equation of the aircraft; 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 quantity and control quantity need to satisfy respectively;

[0015] Step 3: Based on the formula (1) obtained in step 1, the augmented control quantity t is introduced f , let t0 be the initial time of the task, and use the conversion relationship t=t0+(t f -t0)τ is used for time liberalization. If t0=0, we get the domain of independent variable τ=t / t f , and then the augmented dynamics model of the aircraft is obtained:

[0016]

[0017] In formula (3), the state quantity is The control amount is

[0018] Step 4: Use the successive linearization method to process the equation (3) obtained in step 3: Given a reference trajectory is the state trajectory obtained at the kth iteration. According to the first-order linearized dynamic nonlinear term of the optimal trajectory generated by the kth iteration, the problem P0 obtained in step 2 is transformed into a continuous convex optimization problem. Then, the equal division method is used to discretize the continuous optimization problem on the equally divided independent variable definition domain τ=[0,1], and the number of discrete points is N+1, and the discretized hypersonic deformable vehicle trajectory planning convex problem P1 is obtained:

[0019]

[0020] In formula (4), C is the relaxation optimization variable corresponding to the trust region of the state quantity, D is the relaxation optimization variable corresponding to the trust region of the control quantity, m7 is the constant weight coefficient corresponding to C, and m8 is the constant weight coefficient corresponding to D. is the state vector, is the control vector, i=1,…,N represents the discrete points after the problem is discretized by the collocation method; The equality constraints of the dynamic differential equations after convexification; is a linear equality constraint; is a linear inequality constraint; To perform the equality constraint after convexification; is the convexified inequality constraint;

[0021] Step 5: Solve the trajectory planning convex problem P1, obtain the trajectory planning result of the hypersonic vehicle, and perform online planning of the hypersonic deformable vehicle based on sequential convex optimization.

[0022] The specific implementation method of step 2 is as follows:

[0023] The initial boundary constraints are the initial values ​​of the state variables of the aircraft at the initial moment of each mission segment, namely:

[0024]

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

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

[0027]

[0028] In formula (6): t f is the terminal time of each task segment; x f 、z f ,θ f , Vf are the longitudinal range, lateral range, track angle, and heading angle corresponding to the desired aircraft terminal time, respectively;

[0029] Process constraints are constraints on the state quantities at each moment in the process of aircraft trajectory planning. The process constraints of hypersonic deformable aircraft include speed V, track angle θ, heading angle ψ V Constraints, namely:

[0030]

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

[0032] Considering the angle of attack α and the tilt angle γ V and the amplitude constraint of the deformation rate χ control variable, namely:

[0033]

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

[0035] Secondly, considering that each actuator has a speed limit in actual work, the change rate of the control amount of the aircraft is constrained, that is:

[0036]

[0037] In formula (9), The rate of change of angle of attack The lower and upper limits of are the roll angle change rates The lower and upper limits of Deformation rate change rate The lower and upper limits of

[0038] The weighted function of terminal height and terminal speed is taken as the objective function, that is:

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

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

[0041] For strong equality constraints such as the terminal constraint in equation (6), slack variables are introduced to relax the terminal position constraint. The terminal position can be rewritten as:

[0042]

[0043] In formula (11): t f is the terminal time of each task segment; x f 、z f ,θ f , Corresponding to the longitudinal range, lateral range, track angle and heading angle of the desired aircraft terminal time respectively; ξ x , z , θ , They are the error bounds corresponding to the longitudinal range, lateral range, track angle, and heading angle constraints of the aircraft at the terminal moment;

[0044] Add the slack variable penalty term for the terminal state constraint to the objective function so that the terminal position in the iteration process approaches the specified position. Then the objective function is rewritten as:

[0045]

[0046] 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;

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

[0048]

[0049] The specific implementation method of step 4 is as follows:

[0050] First, the nonlinear dynamic equations are processed by successive linearization: given a reference trajectory is the state trajectory obtained at the kth iteration. According to the optimal trajectory generated at the kth iteration, the first-order linearized dynamic nonlinear term is obtained. The dynamic linearization form is: Will Perform a first-order Taylor expansion at this reference trajectory:

[0051]

[0052] In formula (14), is the specific constant value of the differential equation at the reference trajectory, for About state quantity The derivative of for About Control Volume The derivative of

[0053] Further expand the above formula to get:

[0054]

[0055] In formula (15), the matrix expressions 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] The following trust region constraints are added to the above successive linearization method to ensure its reliability:

[0069]

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

[0071]

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

[0073] By adding a penalty term for the norm of the trust region slack variable to the objective function, the objective function is rewritten as:

[0074]

[0075] In formula (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 convexification of Performing a first-order Taylor expansion at the reference trajectory yields:

[0077]

[0078] In formula (19), and Respectively represent s with respect to the state quantity and control volume The partial derivative of

[0079] The above convexification method is used to complete the convexification of the problem P0 obtained in step 2, and on this basis, the problem is discretized: the state variables are discretized simultaneously using the collocation method With control variables The continuous optimization problem is discretized on the equally divided independent variable domain τ=[0,1], and the number of discrete points is N+1; the discrete step length 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 and control variables in the continuous optimization problem are discretized as and Discretizing the continuous-time problem using the trapezoidal integral formula yields:

[0080]

[0081] In formula (20),

[0082] At the same time, for the control rate constraint formula (9), the position constraint form of discrete points is used to represent the control variable change rate constraint:

[0083]

[0084] In formula (21),

[0085] After the problem P0 is subjected to dynamic linearization, constraint convexification and problem discretization, the discretized hypersonic deformable vehicle trajectory planning convex problem P1 is obtained:

[0086]

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

[0088] 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 successively to obtain a continuous full-phase solution; the specific implementation steps are as follows:

[0089] Step 5.1: In the A flight phase, according to the initial parameters of this phase, the initial trajectory planning problem P0_A of the hypersonic deformable aircraft is constructed according to step 2, and then the discretized hypersonic deformable aircraft trajectory planning convex problem P1_A is constructed through the convexification and discretization methods of steps 3 and 4;

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

[0091] Step 5.3: Online rolling advance time to the next guidance cycle, and return to step 5.2 to iterate and solve P1_A again; if time advances to the trajectory planning terminal time t f _A, the trajectory planning of flight phase A is completed and the next flight phase B is entered;

[0092] Step 5.4: Set the terminal time of flight phase A to t f The state and control quantity at _A are taken as the initial state and control quantity of the flight phase B. According to the initial parameters of this phase, the initial trajectory planning problem P0_B of the hypersonic deformable aircraft is constructed, and then the discretized convex problem P1_B of the trajectory planning of the hypersonic deformable aircraft is constructed through convexification and discretization technology;

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

[0094] Step 5.6: Online rolling advances the time to the next guidance cycle, and returns to step 5.5 to iterate and solve P1_B again; if the time advances to the trajectory planning terminal time t f _B, the trajectory planning of flight phase B ends and enters the next flight phase C;

[0095] Step 5.7: Set the terminal time of flight phase B to t f The state and control quantity at _B are taken as the initial state and control quantity of the flight stage C. According to the initial parameters of this stage, the initial trajectory planning problem P0_C of the hypersonic deformable aircraft is constructed, and then the discretized convex problem P1_C of the trajectory planning of the hypersonic deformable aircraft is constructed through convexification and discretization technology.

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

[0097] Step 5.9: Online rolling advance time to the next guidance cycle, and return to step 5.8 to iterate and solve P1_C again; if time advances to the trajectory planning terminal time t f _C, trajectory planning of C flight phase ends;

[0098] Step 5.10: The convex problem of trajectory planning for a hypersonic deformable vehicle after discretization of the ABC flight phases is solved, and then a continuous full-stage trajectory planning result is obtained.

[0099] Beneficial effects:

[0100] The present invention discloses an online planning method for a hypersonic deformable aircraft based on sequential convex optimization. The method combines the sequential convex optimization method with the rolling time domain optimization method to construct a sequential convex optimization solution method based on variable time domain rolling planning that considers multi-stage continuous solution. The method solves the trajectory planning problem of the gliding segment of a hypersonic, deformable, and online aircraft, and can meet the requirements of real-time and robustness of aircraft deformation decision-making in the online trajectory planning problem of a hypersonic deformable aircraft, and proves the flight performance advantage of a variable-length aircraft over a fixed-shape aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 It is a flow chart of the variable time domain rolling planning method of the present invention;

[0102] Figure 2 This is a flow chart of the sequential convex optimization technology based on variable time domain rolling programming considering multi-stage continuous solution of the present invention;

[0103] Figure 3 A comparison diagram of the ground projection of the trajectory of a 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 A speed comparison diagram of a deformable / fixed-shape aircraft of the present invention;

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

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

[0108] Figure 8A comparison diagram of the attack angles of the deformable / fixed-shape aircraft of the present invention;

[0109] Fig. 9 A comparison diagram of the roll angles of the deformable / fixed shape aircraft of the present invention;

[0110] Fig.10 It is a comparison chart of deformation rates of the deformable / fixed shape aircraft of the present invention. DETAILED DESCRIPTION

[0111] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0112] Embodiment 1:

[0113] like Figure 2 As shown, the present embodiment discloses an online planning method for a hypersonic deformable aircraft based on sequential convex optimization, and the specific implementation steps are as follows:

[0114] 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 for trajectory planning.

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

[0116] Through CFD numerical calculation, the aerodynamic coefficient data table under different attack angles α, Mach numbers Ma, and deformation rates χ for each parameter point combination is obtained, including the lift coefficient C y and the drag coefficient C x , and then use the various aerodynamic coefficients in the data table to perform polynomial fitting to obtain the expression of the lift and drag coefficient, and then the aerodynamic model of the hypersonic variable-length aircraft can be obtained. The variable parameter sampling points selected by the present invention are shown in Table 1 below:

[0117] Table 1 Variable parameter sampling points

[0118]

[0119] According to the numerical calculation results, it can be analyzed that compared with conventional hypersonic aircraft, the deformation characteristics of the object in the present invention will have a significant impact on the aerodynamic characteristics of the aircraft. When the wings on both sides are symmetrically deformed, the C of the aircraft will be significantly affected. y , C x And lift-to-drag ratio. For aircraft C y , C x , with the increase of the angle of attack α, the C of different configurations of aircraft y , C x Both increase gradually; for a given χ and α, the aircraft C y , C x As Ma increases, it decreases accordingly; for a given α and Ma, the aircraft C y , C x As χ increases, it increases. For the lift-to-drag ratio of the aircraft, for given χ and α, the maximum lift-to-drag ratio of the aircraft decreases accordingly as Ma increases; under the condition of given Ma, the lift-to-drag ratio of aircrafts with different configurations shows a trend of increasing first and then decreasing as α increases, and reaches the maximum lift-to-drag ratio roughly when α is 10°; for given α and Ma, the lift-to-drag ratio of the aircraft increases as χ increases.

[0120] Further design of C y , C x The function forms between α, Ma, and χ are respectively quartic polynomials. According to the above polynomials, the least squares algorithm is used to perform regression calculation to obtain the regression polynomial coefficients.

[0121] The present invention aims at the trajectory planning problem of the unpowered gliding segment of a hypersonic deformable aircraft in three-dimensional space, and considers the movement of the aircraft in the lateral direction, that is, adding the roll angle as the control variable. For the convenience of research, the present invention adopts the following assumptions: 1. During the flight, the aircraft is regarded as a rigid body, and the variable length only affects the aerodynamic coefficient at each moment, while the additional force brought by the variable length is ignored; 2. The influence of the earth's rotation is ignored. Under the above assumptions, the three-degree-of-freedom motion equations of the deformable aircraft can be obtained as:

[0122]

[0123] In formula (23), the state variables x of the problem are respectively the longitudinal range x and the height y, the lateral range z, the missile speed V, the track angle θ, and the heading angle ψ V , the control quantity u includes the angle of attack α, the roll angle γ V , deformation rate χ; resistance X = qSC x , lift Y = qSC y , C x , C yare the aerodynamic coefficients of drag X and lift Y, respectively, which are functions of Mach number Ma, angle of attack α and deformation rate χ=(b-b0) / (b1-b0), all of which are obtained by least squares fitting, where b0 is the span when the wing is extended by 0%, b1 is the span when the wing is extended by 100%, and b is the current span of the aircraft in the deformed state; S is the reference area, and the dynamic pressure q=ρV 2 / 2; atmospheric density ρ = ρ0e -βh , ρ0 is the atmospheric density at sea level, which is a constant of 1.2258 kg / m 3 ; β is a constant coefficient, which is 1.3785×10 -4 m -1 ; h is the height of the aircraft; m is the mass of the missile; gravitational acceleration g = μ / (R e +h) 2 , μ is the gravitational coefficient of the earth, which is a constant value of 3.9860×10 14 m 3 / s 2 , R e is the average radius of the Earth, which is a constant value of 6378 km; ε(α,γ V ,χ)=0 represents the control equation, indicating that the trajectory planning control quantity is the attack angle α, the roll angle γ V , deformation rate χ.

[0124] The motion equations of this group are consistent with those of conventional aircraft in form, but there are differences in aerodynamic drag coefficient, aerodynamic lift coefficient, and wing reference area, all of which are related to the length deformation rate of the deformable aircraft. In order to effectively avoid the matrix morbidity caused by the large difference in the order of magnitude of the state quantities in the Jacobian matrix, avoid the Jacobian matrix singularity caused by the large difference in the order of magnitude between the state quantities, and 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 the angle γ V , θ, α, because their values ​​are generally small and the unit is radian, they can be normalized without processing; in addition, the value range of χ is [0,1], so it is also not normalized. Based on the above analysis, the variables x, y, z, V, t are normalized, and the following normalization scales are selected, as shown in Table 2:

[0126] Table 2 Normalized scale

[0127]

[0128] According to the above normalized scale table, the normalized aircraft dynamics equations are obtained:

[0129]

[0130] In the formula, is the dimensionless velocity before normalization; are the spatial coordinates before normalization; is the time variable before normalization; V is the normalized aircraft speed; x, y, z are the normalized spatial position coordinates respectively; t is the time variable after normalization.

[0131] Step 2: Taking the maximum weighted function of the terminal altitude and terminal velocity at the end of the mission as the performance indicator, considering the initial boundary constraints, terminal boundary constraints and control quantity constraints, and combining the aircraft dynamics model constructed in step 1 to construct the initial trajectory planning problem P0 of the hypersonic deformable aircraft.

[0132] The trajectory planning problem of hypersonic vehicle is described, and necessary information such as constraints and objective functions are clarified, and the initial trajectory planning problem of hypersonic deformable vehicle is constructed. On this basis, the trajectory planning problem of variable-length vehicle is convexified: based on the successive linearization method, the dynamic equations and other nonlinear constraints are convexified, and the trapezoidal method is used to discretize the continuous trajectory planning convex problem, thereby completely transforming the problem into a discretized convex problem of hypersonic deformable vehicle trajectory planning, which provides a basis for subsequent solution.

[0133] The initial constraints are the initial values ​​of the state variables of the aircraft at the initial moment of each mission segment, namely:

[0134]

[0135] Where: t0 is the initial time of the flight mission; x0, y0, z0, V0, θ0, ψ V0 They 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 the aircraft. For deformable hypersonic aircraft, they include longitudinal range, lateral range, track angle and heading angle constraints, namely:

[0137]

[0138] Different terminal constraints can be set according to different flight missions. f is the terminal time of each task segment; x f 、z f ,θ f , are the expected terminal states of the missile, and are the longitudinal range, lateral range, track angle, and heading angle at the terminal moment, respectively;

[0139] The process constraints are constraints on the state quantities at each moment in the process of trajectory planning of the aircraft. The process constraints of the deformable hypersonic aircraft include speed V, track angle θ, heading angle ψ V Constraints, namely:

[0140]

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

[0142] Since there is no thrust during the reentry of the variable-length aircraft, the control variables for the reentry trajectory planning problem are α, γ V , χ, α and χ mainly affect the aerodynamic coefficients of the aircraft and change the aerodynamic characteristics of the aircraft. Appropriately limiting the range of control variables can ensure the smoothness of the trajectory of the deformed aircraft and good flight performance; in addition, in order to ensure the attitude stability control during the reentry process, the angle of attack and the length deformation rate of the hypersonic aircraft must meet certain boundary constraints. Therefore, the present invention first considers α, γ V , the amplitude constraint of the χ control variable, that is:

[0143]

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

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

[0146]

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

[0148] The present invention is an online trajectory planning method for a hypersonic deformable aircraft, and its core focus is on the improvement of flight performance brought about by aircraft deformation: on the one hand, the speed loss of the aircraft during flight is minimized through deformation; on the other hand, the height loss of the aircraft after the mission is completed is minimized. Therefore, the present invention takes the weighted function of terminal height and terminal speed as the objective function, that is:

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

[0150] Where m1 is V f The corresponding constant weight coefficient, m2 is y f The corresponding constant weight coefficient, J is the objective function value, V f is the terminal velocity of the aircraft, y f is the aircraft terminal altitude.

[0151] For strong equality constraints such as the terminal constraint in equation (26), such strong equality constraints can be gradually approximated in the process of sequence iteration, without making the constraint too strong and causing the solver to have no solution. Therefore, the slack variable ξ is introduced to relax the terminal position constraint, and the terminal position can be rewritten as:

[0152]

[0153] Where: t f is the terminal time of each task segment; x f 、z f ,θ f , are the expected terminal states of the missile, respectively, the longitudinal range, lateral range, track angle, and heading angle at the terminal moment; ξ x , z , θ , are the error bounds corresponding to the terminal state constraints, both are small constants.

[0154] Add the slack variable penalty term for the terminal state constraint to the objective function so that the terminal position in the iteration process approaches the specified position. Then the objective function is rewritten as:

[0155]

[0156] Where 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;

[0157] Based on the above aircraft model construction, constraint conditions and objective function information, the initial trajectory planning problem P0 of the hypersonic deformable aircraft is constructed:

[0158]

[0159] In the formula, x is the state vector, u is the control vector, is the equality constraint of the dynamic differential equation of the aircraft. 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. For problem P0, its state variable is x=[V,θ,ψ V ,x,y,z] T , the control variable is u=[α,γ V ,χ] T Due to the existence of nonlinear dynamic models and nonlinear constraints, this problem P0 is a non-convex problem and needs to be processed accordingly based on convex optimization theory to transform it into a convex optimization problem.

[0160] Step 3: Since the planning problem involved in the present invention is a terminal freedom problem, the augmented control quantity t is introduced based on the formula (1) obtained in step 1 f , let t0 be the initial time of the task, and use the conversion relationship t=t0+(t f -t0)τ is used for time liberalization. If t0=0, we get the domain of independent variable τ=t / t f , and then the augmented dynamics model of the aircraft is obtained:

[0161]

[0162] In formula (34), the state quantity is The control amount is

[0163] Step 4: Use the successive linearization method to process the equation (34) obtained in step 3: Given a reference trajectory is the state trajectory obtained at the kth iteration. According to the first-order linearized dynamic nonlinear term of the optimal trajectory generated by the kth iteration, the problem P0 obtained in step 2 is transformed into a continuous convex optimization problem. Then, the equal division method is used to discretize the continuous optimization problem on the equally divided independent variable definition domain τ = [0,1], and the number of discrete points is N + 1, and the discretized hypersonic deformable vehicle trajectory planning convex problem P1 is obtained.

[0164] The nonlinear dynamic equations are processed by successive linearization method: Given a reference trajectory Assumptions is the state trajectory obtained at the kth iteration. According to the optimal trajectory generated at the kth iteration, the first-order linearized dynamic nonlinear term is obtained. The dynamic linearization form is: Will Perform a first-order Taylor expansion at the reference trajectory:

[0165]

[0166] In formula (35), is the specific constant value of the differential equation at the reference trajectory, for About state quantity The derivative of for About Control Volume The derivative of

[0167] Further expand the above formula to get:

[0168]

[0169] In the formula, the matrix expressions 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] An important part of the above linearization process is the selection of the reference point of the Taylor expansion. In the sequential convex optimization algorithm, the reference point of the first iteration is provided by the initial optimization value, and the reference point during the iteration is taken as the optimal solution obtained in the previous iteration. According to the characteristics of the first-order Taylor expansion, in the sequential convex optimization iteration process, only when the optimization variable takes values ​​near the reference point, the linearized dynamics and state constraints are a good approximation of the original nonlinear form. Therefore, the following trust region constraints are added to the sequential convex optimization algorithm:

[0183]

[0184] Among them, δ x and δ u is the constant vector trust region. The trust region constraint will affect the algorithm iteration. Generally, a smaller trust region is set to reduce the error caused by linearization. The above inequality is satisfied for each state and control component separately, and is related to and The dimension of is 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 in the domain that satisfies the constraints of this iteration, resulting in poor convergence and reduced timeliness; if the trust region is too large, the dynamic linearization cannot guarantee the validity of the approximation.

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

[0186]

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

[0188] A penalty term for the norm of the trust region slack variable is added to the objective function. In the case of the existence of this iterative solution, the size of the trust region is reduced by penalty, so that both effectiveness and convergence are taken into account. The objective function is rewritten as:

[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 convexification.

[0191] For nonlinear inequality constraints The convexification of Performing a first-order Taylor expansion at the reference trajectory yields:

[0192]

[0193] Among them, s x and u Respectively represent s with respect to the state quantity and control volume The partial derivative of .

[0194] After convexification processing such as dynamic linearization, the problem is a continuous optimization problem, whose state and control quantity are both continuous variables, and it is difficult to solve it directly. Therefore, it is necessary to transform the problem into a planning problem for optimizing finite parameters, and then use numerical methods to solve it.

[0195] The present invention adopts the collocation method to simultaneously discretize state variables With control variables The continuous optimization problem is discretized on the equally divided independent variable domain τ=[0,1], and the number of discrete points is N+1. At this time, the discrete step length 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 and control variables in the continuous optimization problem are discretized as and The present invention uses the trapezoidal integral formula to discretize the continuous time problem and obtains:

[0196]

[0197] In the formula,

[0198] At the same time, for the control rate constraint formula (29), the present invention adopts the position constraint form of discrete points to characterize the control variable change rate constraint:

[0199]

[0200] In the formula,

[0201] After the original initial trajectory planning problem P0 is subjected to dynamic linearization, constraint convexification and problem discretization, the discretized hypersonic deformable vehicle trajectory planning convex problem P1 is obtained:

[0202]

[0203] In the formula, i=1,…,N represents the discrete points after the problem is discretized by the collocation method; is the equality constraint of the dynamic differential equation after convexification; is a linear equality constraint; is a linear inequality constraint; To perform the equality constraint after convexification; is the convexified inequality constraint.

[0204] Step 5: Solve the trajectory planning convex problem P1 and 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] In order to realize the online planning of the aircraft, the rolling horizon optimization principle needs to be introduced. The core idea of ​​the rolling horizon optimization principle is to generate the optimal control quantity by solving the sequential convex optimization problem according to the state at the current time i, and only apply the control quantity of the first guidance cycle to the aircraft to obtain the state at time i+1, and repeat this process until the last guidance cycle. This method is used to continuously introduce uncertain factors and possible interference into the dynamic differential equation, and eliminate the deviation caused by the linearization of the dynamic model in the rolling control instructions.

[0206] In order to solve the continuous optimization problem constructed by the present invention, it is necessary to discretize the continuous optimization problem on the equally divided independent variable definition domain τ=[0,1] each time the sequential convex optimization problem is solved, and the number of discrete points is N+1. In particular, for the terminal time freedom problem studied by the present invention, as the rolling iteration proceeds, the prediction time domain length T1 is gradually shortened, which often leads to the occurrence of no solution at the end of the rolling, and only selecting a fixed execution time domain interval T2 is difficult to match the time t(τ i ), and the adjacent discrete point interpolation approximation method is often used to obtain the control quantity at the terminal moment of each guidance cycle. Therefore, a variable time domain rolling method is designed to determine the actual execution time domain interval T3 of each rolling. The specific steps are as follows Figure 1 , the corresponding steps are as follows:

[0207] Step 5.1.1: Determine the predicted 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 size of T1 and 2T2. If T1 ≥ 2T2, then calculate the value based on NT2 / t fThe rounded value of determines the discrete point number closest to T2, and then determines the actual execution time domain interval T3. After solving the convex problem of numerical integration and trajectory planning, return to step 5.1.1; if T1≤2T2, go to step 5.1.3;

[0209] Step 5.1.3: The final result is obtained through numerical integration, and the trajectory planning is completed.

[0210] The present invention combines the sequential convex optimization method with the variable time domain rolling planning method, and designs a sequential convex optimization technology based on variable time domain rolling planning, which can solve multi-configuration switching trajectory planning problems for different guidance cycles. Hypersonic aircraft may need to perform multiple maneuvers to achieve mission requirements, and the flight mission of the aircraft needs to be divided into multiple mission intervals. The time when the aircraft performs tasks in different stages is not pre-allocated, which makes it difficult to convert the original dynamic optimization problem into a static optimization problem. In order to overcome this difficulty, the present invention divides the entire flight mission into multiple flight stages based on a multi-stage continuous solution method, and solves each flight stage in sequence and continuously, thereby obtaining a continuous full-stage solution. The algorithm flow chart of the sequential convex optimization technology based on variable time domain rolling planning considering multi-stage continuous solution is as follows: Figure 2 The specific steps are as follows:

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

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

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

[0214] Step 5.2.4: Determine the size of T1 and 2T2. If T1 ≥ 2T2, set T3 = t f / N×[NT2 / t f ] is applied to the aircraft, and then the time and flight trajectory are updated, and the process returns to step 5.2.3; if T1≤2T2, the control amount within T3=T1 is applied to the aircraft, and the process goes to step 5.2.5;

[0215] Step 5.2.5: Determine whether there is a next flight phase. If so, enter the next flight phase and return to step 5.2.2; if not, the algorithm ends and the trajectory planning task is completed.

[0216] The following Matlab simulation is used to illustrate the specific process of the online planning method of the hypersonic deformable aircraft based on sequential convex optimization of the present invention. The numerical calculation is performed on a laptop computer equipped with a core i7-12700H processor with a main frequency of 2.30GHz. All programs are run in the Matlab 2022a environment, and the convex subproblems generated by the algorithm are solved based on the interior point method by calling the API of the MOSEK software.

[0217] In a special mission context, the aircraft flight mission is decomposed into different stages. The present invention simplifies the specific flight missions of different stages, that is, the differences in the flight missions of different stages are only reflected in the different initial conditions and terminal constraints of each stage. In order to verify the superiority of the variable-length aircraft in the trajectory planning problem, the trajectory planning results of the variable-length aircraft and the fixed-shape aircraft are compared and analyzed, where the fixed-shape aircraft refers to an aircraft with a deformation rate of 0%.

[0218] Select the fixed execution time interval T2 = 10s, and the initial conditions of 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 value of terminal speed loss and terminal height loss: min J = -m1V f -m2y f Based on the method constructed by the present invention, three-stage flight termination conditions are set respectively, as shown in Table 3 below:

[0219] Table 3 Termination conditions for different flight phases

[0220]

[0221] Based on the above conditions, the new rolling time domain multi-stage continuous solution convex optimization method proposed in this invention is adopted, and the simulation results are as follows Figure 3-10 , where the solid line represents the flight trajectory of the deformable aircraft, and the dotted line represents the flight trajectory of the fixed-shape aircraft. Through the analysis of the simulation results, the height and speed changes of the deformable aircraft and the fixed-shape aircraft are obtained, and the comparison results are shown in Table 4 below:

[0222] Table 4 Altitude and speed changes of deformable aircraft and fixed shape aircraft

[0223]

[0224] Depend on Figure 3It can be seen that the fixed-shape aircraft cannot reach the predetermined waypoint during the initial left maneuver and cannot meet the reconnaissance needs; compared with the fixed-shape aircraft, the deformable aircraft can accurately reach the flight waypoint and achieve precise connection between the three flight phases. This shows that the deformable aircraft can improve the lateral maneuverability of the aircraft by retracting the wings.

[0225] Figure 4 The altitude changes of the two aircraft are given, and their terminal altitudes are shown in Table 4. It can be seen that the deformable aircraft has a great advantage in altitude: the terminal altitude of the deformable aircraft is 33.0 km, an increase of 1.5 km; the terminal altitude of the fixed-shape aircraft is 30.2 km, a decrease of 1.3 km; the terminal altitude of the deformable aircraft is 2.8 km higher than that of the fixed-shape aircraft.

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

[0227] Figure 6 Two types of aircraft track angle changes are given, combined with Figure 8 Changes in angle of attack, Fig. 9 The change of the roll angle Fig.10 From the change of deformation rate, it can be seen that in the left maneuvering flight stage, the deformation rate of the deformable aircraft increases, and the lift-to-drag ratio of the aircraft increases significantly, making the track angle of the deformable aircraft greater than that of the fixed-shape aircraft; in the initial stage of the right maneuvering flight, the amplitude of the bank angle of the fixed aircraft decreases, and its angle of attack first decreases and then increases, causing the track angle of the fixed aircraft to first decrease and then increase; and in the final stage of the right maneuvering flight, the amplitude of the bank angle of the fixed-shape aircraft increases, and its angle of attack first decreases and then increases, causing the track angle of the fixed aircraft to first increase and then decrease; and the amplitude of the bank angle of the deformable aircraft is large, causing the track angle of the deformable aircraft to continue to decrease.

[0228] Figure 7 Two types of aircraft heading angle changes are given, combined with Figure 8 Changes in angle of attack, Fig. 9 The change of the roll angle Fig.10From the change of deformation rate, it can be seen that in the left maneuvering flight stage, the deformation rate of the deformable aircraft is at a relatively large level, which significantly increases the lift coefficient and lift-to-drag ratio of the aircraft, making the heading angle growth rate of the deformable aircraft significantly greater than that of the fixed-shape aircraft; in the initial stage of the right maneuvering flight, in order to minimize the aircraft's altitude speed loss, the deformable aircraft reduces the drag by reducing the deformation rate. At the same time, the amplitude of the deformable aircraft's track angle is small, which makes the deformable aircraft's heading angular velocity lower than that of the fixed-shape aircraft; and in the final stage of the right maneuvering flight, the deformable aircraft's angle of attack, deformation rate, and roll angle are large, so the deformable aircraft's heading angular velocity is significantly greater than that of the fixed-shape aircraft.

[0229] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above 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 in the scope of protection of the present invention.

Claims

1. An online planning method for a hypersonic deformable aircraft based on sequential convex optimization, characterized in that: The following steps are involved: Step 1: Analyze the influence of deformation characteristics on the aerodynamic characteristics of the aircraft through the aircraft geometry model, and construct a dynamic model of a three-degree-of-freedom hypersonic deformable aircraft for trajectory planning; In formula (1), R0 is the maximum flight distance; V c is the upper limit of constant speed; resistance 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 α and deformation rate χ = (b-b0) / (b1-b0), all of which are obtained by least squares fitting, where b0 is the span when the wing is extended by 0%, b1 is the span when the wing is extended by 100%, and b is the current span of the aircraft in the deformed state; S is the reference area, dynamic pressure q = ρV 2 / 2; atmospheric density ρ = ρ0e -βh , ρ0 is the atmospheric density at sea level; β is a constant coefficient; h is the height 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, R e is the average radius of the Earth; Step 2: Taking the maximum weighted function of the terminal height and the terminal speed at the end of the mission as the performance index, considering the initial boundary constraints, the terminal boundary constraints and the control quantity constraints, and combining the aircraft dynamics model constructed in step 1 to construct the initial trajectory planning problem P0 of the hypersonic deformable aircraft; the state quantities x of the problem are respectively the longitudinal range x and the height y, the lateral range z, the missile speed V, the track angle θ, the heading angle ψ V , the control quantity u includes the angle of attack α, the roll angle γ V , deformation rate χ, the state quantity and control quantity 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 velocity of the aircraft, y f is the terminal altitude of the aircraft, ξ x , z , θ , are the error bounds corresponding to the longitudinal range, lateral range, track angle, and heading angle constraints of the aircraft at the terminal moment; 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 equation constraint of the dynamic differential equation of the aircraft; 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 quantity and control quantity need to satisfy respectively; Step 3: Based on the formula (1) obtained in step 1, the augmented control quantity t is introduced f , let t0 be the initial time of the task, and use the conversion relationship t=t0+(t f -t0)τ is used for time liberalization. If t0=0, we get the domain of independent variable τ=t / t f , and then the augmented dynamics model of the aircraft is obtained: In formula (3), the state quantity is The control amount is Step 4: Use the successive linearization method to process the equation (3) obtained in step 3: Given a reference trajectory is the state trajectory obtained at the kth iteration. According to the first-order linearized dynamic nonlinear term of the optimal trajectory generated by the kth iteration, the problem P0 obtained in step 2 is transformed into a continuous convex optimization problem. Then, the equal division method is used to discretize the continuous optimization problem on the equally divided independent variable definition domain τ=[0,1], and the number of discrete points is N+1, and the discretized hypersonic deformable vehicle trajectory planning convex problem P1 is obtained: In formula (4), C is the relaxation optimization variable corresponding to the trust region of the state quantity, D is the relaxation optimization variable corresponding to the trust region of the control quantity, m7 is the constant weight coefficient corresponding to C, and m8 is the constant weight coefficient corresponding to D. is the state vector, is the control vector, i=1,…,N represents the discrete points after the problem is discretized by the collocation method; The equality constraints of the dynamic differential equations after convexification; is a linear equality constraint; is a linear inequality constraint; To perform the equality constraint after convexification; is the convexified inequality constraint; Step 5: Solve the trajectory planning convex problem P1 and 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 for online planning of a hypersonic deformable aircraft based on sequential convex optimization according to claim 1, characterized in that: The specific implementation method of step 2 is as follows: The initial boundary constraints are the initial values ​​of the state variables of the aircraft at the initial moment of each mission segment, namely: In formula (5), t0 is the initial time of the flight mission; x0, y0, z0, V0, θ0, ψ V0 They correspond to the longitudinal range, altitude, lateral range, speed, track angle, and heading angle of the aircraft at the initial moment respectively; The terminal boundary constraints are constraints imposed on the terminal state of the aircraft. For hypersonic deformable aircraft, they include longitudinal range, lateral range, 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 range, lateral range, track angle, and heading angle corresponding to the desired aircraft terminal time, respectively; Process constraints are constraints on the state quantities at each moment in the process of aircraft trajectory planning. The process constraints of hypersonic deformable aircraft include speed V, track angle θ, heading angle ψ V Constraints, namely: In formula (7), V min is the lower limit of speed V; θ min ,θ max are the lower and upper limits of the track angle θ respectively; ψ Vmin , Vmax are the heading angle ψ V The lower and upper limits of Considering the angle of attack α and the tilt angle γ V and the amplitude constraint of the deformation rate χ control variable, namely: In formula (8), α min , α max are the lower and upper limits of the angle of attack α, respectively; Vmin , γ Vmax are the tilt angles γ V The lower and upper limits of min , χ max are the lower and upper limits of the deformation rate χ, respectively; Secondly, considering that each actuator has a speed limit in actual work, the change rate of the control amount of the aircraft is constrained, that is: In formula (9), The rate of change of angle of attack The lower and upper limits of are the roll angle change rates The lower and upper limits of Deformation rate change rate The lower and upper limits of The weighted function of terminal height and terminal speed is taken as the objective function, that is: min J=-m1V f -m2y f (10) In formula (10), m1 is V f The corresponding constant weight coefficient, m2 is y f The corresponding constant weight coefficient, J is the objective function value, V f is the terminal velocity of the aircraft, y f is the aircraft terminal altitude; For strong equality constraints such as the terminal constraint in equation (6), slack variables are introduced to relax the terminal position constraint, and the terminal position is rewritten as: In formula (11): t f is the terminal time of each task segment; x f 、z f ,θ f , Corresponding to the longitudinal range, lateral range, track angle and heading angle of the desired aircraft terminal time respectively; ξ x , z , θ , They are the error bounds corresponding to the longitudinal range, lateral range, track angle, and heading angle constraints of the aircraft at the terminal moment; Add the slack variable penalty term for the terminal state constraint to the objective function so that the terminal position in the iteration process approaches the specified position. Then 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 aircraft dynamics model (1), constraints and objective function information constructed in step 1, the initial trajectory planning problem P0 of the hypersonic deformable aircraft is expressed as:

3. The method for online planning of a hypersonic deformable aircraft based on sequential convex optimization as claimed in claim 2, characterized in that: The specific implementation method of step 4 is as follows: The nonlinear dynamic equations are processed by successive linearization method: Given a reference trajectory is the state trajectory obtained at the kth iteration. According to the optimal trajectory generated at the kth iteration, the first-order linearized dynamic nonlinear term is obtained. The dynamic linearization form is: Will Perform a first-order Taylor expansion at this reference trajectory: In formula (14), is the specific constant value of the differential equation at the reference trajectory, for About state quantity The derivative of for About Control Volume The derivative of Further expand the above formula to get: In formula (15), the matrix expressions are as follows: ① matrix: ② matrix: ③ matrix ④ matrix ⑤ matrix ⑥ matrix The following trust region constraints are added to the above successive linearization method to ensure its reliability: In formula (16), δ x It is the state quantity The constant vector trust region of The dimension of δ is the same as u It is the state quantity The constant vector trust region of The dimension of is the same; based on formula (16), the trust region relaxation variable is introduced, and the relaxed trust region constraint can be expressed as: In formula (17), C is δ x The corresponding relaxation optimization variable, D is δ u The corresponding relaxed optimization variables adjust the trust region size by optimizing the values ​​of C and D; By adding a penalty term for the norm of the trust region slack variable to the objective function, the objective function is rewritten as: In formula (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 convexification of Performing a first-order Taylor expansion at the reference trajectory yields: In formula (19), and Respectively represent s with respect to the state quantity and control volume The partial derivative of The above convexification method is used to complete the convexification of the problem P0 obtained in step 2, and on this basis, the problem is discretized: the state variables are discretized simultaneously using the collocation method With control variables The continuous optimization problem is discretized on the equally divided independent variable domain τ=[0,1], and the number of discrete points is N+1; the discrete step length 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 and control variables in the continuous optimization problem are discretized as and Discretizing the continuous-time problem using the trapezoidal integral formula yields: In formula (20), At the same time, for the control rate constraint formula (9), the position constraint form of discrete points is used to represent the control variable change rate constraint: In formula (21), After the problem P0 is subjected to dynamic linearization, constraint convexification and problem discretization, the discretized hypersonic deformable vehicle trajectory planning convex problem P1 is obtained:

4. The method for online planning of a hypersonic deformable aircraft based on sequential convex optimization as claimed 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 successively to obtain a continuous full-phase solution; Step 5.1: In the A flight phase, according to the initial parameters of this phase, the initial trajectory planning problem P0_A of the hypersonic deformable aircraft is constructed according to step 2, and then the discretized hypersonic deformable aircraft trajectory planning convex problem P1_A is constructed through the convexification and discretization methods of steps 3 and 4; Step 5.2: Solve P1_A by using the sequential convex optimization method to obtain the optimal control sequence; select the control sequence within the actual guidance cycle from the optimal control sequence, use it for the aircraft, and update the flight trajectory within this guidance cycle online; Step 5.3: Online rolling advance time to the next guidance cycle, and return to step 5.2 to iterate and solve P1_A again; if time advances to the trajectory planning terminal time t f _A, the trajectory planning of flight phase A is completed and the next flight phase B is entered; Step 5.4: Set the terminal time of flight phase A to t f The state and control quantity at _A are taken as the initial state and control quantity of the flight phase B. According to the initial parameters of this phase, the initial trajectory planning problem P0_B of the hypersonic deformable aircraft is constructed, and then the discretized convex problem P1_B of the trajectory planning of the hypersonic deformable aircraft is constructed through convexification and discretization technology; Step 5.5: Solve P1_B by using the sequential convex optimization method to obtain the optimal control sequence, and apply the control sequence in the actual guidance cycle to the aircraft and update the flight trajectory in this guidance cycle online; Step 5.6: Online rolling advances the time to the next guidance cycle, and returns to step 5.5 to iterate and solve P1_B again; if the time advances to the trajectory planning terminal time t f _B, the trajectory planning of flight phase B ends and enters the next flight phase C; Step 5.7: Set the terminal time of flight phase B to t f The state and control quantity at _B are taken as the initial state and control quantity of the flight stage C. According to the initial parameters of this stage, the initial trajectory planning problem P0_C of the hypersonic deformable aircraft is constructed, and then the discretized convex problem P1_C of the trajectory planning of the hypersonic deformable aircraft is constructed through convexification and discretization technology. Step 5.8: Solve P1_C by using the sequential convex optimization method to obtain the optimal control sequence, and apply the control sequence in the actual guidance cycle to the aircraft and update the flight trajectory in this guidance cycle online; Step 5.9: Online rolling advance time to the next guidance cycle, and return to step 5.8 to iterate and solve P1_C again; if time advances to the trajectory planning terminal time t f _C, trajectory planning of C flight phase ends; Step 5.10: The convex problem of trajectory planning for a hypersonic deformable vehicle after discretization of the ABC flight phases is solved, and then a continuous full-stage trajectory planning result is obtained.

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