Track planning method of deformation aircraft in discrete deformation mode

Abstract

The invention provides a trajectory planning method for a deformation aircraft in a discrete deformation mode, and belongs to the technical field of aircraft guidance and control. According to the method, a trajectory planning model of a deformation aircraft in a discrete deformation mode is established based on a kinetic equation, and the model is a mixed integer optimal control problem; converting the mixed integer optimal control problem into a continuous optimal control problem in a plurality of continuous [0, 1] ranges, and further performing linearization and discretization near a reference trajectory taking the current position of the transformable aircraft as a starting point to obtain a convex discretization trajectory planning model; and solving the discretized trajectory planning model, and if a solving result converges, converting the solving result into a solution of a mixed integer optimal control problem to obtain a trajectory planning result of the transformable aircraft. According to the invention, the efficiency and accuracy of trajectory planning of the deformation aircraft in the discrete deformation mode can be improved, and the method has a very high application value.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft guidance and control, and in particular relates to a trajectory planning method for a deformable aircraft in a discrete deformation mode. Background Art

[0002] A shape-shifting aircraft refers to an aircraft that changes its partial or overall appearance parameters to achieve better aerodynamic efficiency and maneuverability, making its flight trajectory, altitude, speed and other maneuvers more variable, improving its ability to adapt to the environment and missions, and maintaining optimal efficiency and performance in a variety of flight environments.

[0003] The reentry trajectory planning technology of the deformable aircraft is an important part of the deformable aircraft to complete the flight mission efficiently and reliably. It has strong real-time, multi-constraint and high-precision requirements. There are two types of deformable aircraft: continuous deformation mode and discrete deformation mode. The continuous deformation mode means that the deformation space of the deformable aircraft is continuous, such as the sweep angle can take any value between 30° and 60°; while the discrete deformation mode means that the deformation space of the deformable aircraft is discrete, such as the sweep angle is selected from the elements in the set {30°, 45°, 60°}. Most of the existing deformable aircraft trajectory planning methods are aimed at deformable aircraft in continuous deformation mode, and there are few studies on the trajectory planning problem of deformable aircraft in discrete deformation mode. Compared with the continuous deformation mode, the optimization in the discrete deformation mode loses the gradient information, which greatly increases the difficulty and time of solution. Therefore, it is of great significance to study the trajectory planning of the deformable aircraft in the discrete deformation mode and improve the accuracy and real-time performance of the trajectory planning algorithm. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and to propose a trajectory planning method for a deformable aircraft in a discrete deformation mode. The present invention can improve the efficiency and accuracy of trajectory planning for a deformable aircraft in a discrete deformation mode and has high application value.

[0005] An embodiment of the present invention provides a trajectory planning method for a deformable aircraft in a discrete deformation mode, comprising:

[0006] Construct the dynamic equations of the deformable aircraft under discrete deformation mode;

[0007] Based on the dynamic equations, a trajectory planning model of the deformable aircraft is established, wherein the model is a mixed integer optimal control problem;

[0008] Convert the mixed integer optimal control problem into a plurality of continuous optimal control problems in the range of [0,1];

[0009] The continuous optimal control problem is linearized and discretized near a preset reference trajectory starting from the current position of the deformable aircraft to obtain a convex discretized trajectory planning model;

[0010] The discretized trajectory planning model is solved, and if the solution result converges, the solution result is converted into a solution to the mixed integer optimal control problem to obtain the trajectory planning result of the deformable aircraft.

[0011] In a specific embodiment of the present invention, the kinetic equation is expressed as follows:

[0012]

[0013] Among them, the state variables r, λ, φ, V, θ, σ are the distance from the center of the earth, longitude, latitude, speed, ballistic inclination, and ballistic deviation of the aircraft respectively; the control variables α, ν, k represent the angle of attack, roll angle, and deformation coefficient respectively, where the deformation coefficient k = 1, 2, ..., n w Corresponding to aircraft n w different deformations; L, D represent lift and drag respectively; C L ,C D They represent lift coefficient and drag coefficient respectively; ρ represents air density; S ref represents the reference area of ​​the aircraft; Ma represents the Mach number; g represents the acceleration due to gravity.

[0014] In a specific embodiment of the present invention, the step of establishing a trajectory planning model for the deformable aircraft includes:

[0015] 1) Establish the process constraints of the deformable aircraft during flight as follows:

[0016]

[0017] Among them, k q is the heat flow coefficient, n max ,q max ,p max They represent the maximum values ​​of vehicle overload, heat flow, and dynamic pressure respectively;

[0018] 2) Construct performance optimization goals, the expression is as follows:

[0019]

[0020] Among them, C1 and C2 are index coefficients, both of which are positive numbers. C1 reflects the accumulation of the heat flux rate of the aircraft during the flight, and C2 reflects the smoothness of the angle of attack and the roll angle during the flight.

[0021] 3) Based on the results of steps 1) and 2), combined with the dynamic equation, the trajectory planning model of the deformable aircraft in the discrete deformation mode is established, and the expression is as follows:

[0022]

[0023] in, Simplified from formula (3), t f represents the flight cut-off time; x(t) is the state of the aircraft, Simplified from formula (1), it represents the dynamic equation; 0≤c(x(t),u(t),ε(t)), simplified from formula (3), it represents the process constraint; u(t) is the continuous control variable, including the angle of attack and the roll angle, is a set of continuous control value; ε(t) is an integer variable, indicating the deformation coefficient; is a set of discrete control values, including n w Discrete control quantity;

[0024] x, u, ε represent the vehicle state quantity, vehicle continuous control quantity, and vehicle discrete control quantity respectively; c represents the inequality constraint; Φ represents the integral index.

[0025] In a specific embodiment of the present invention, the converting the mixed integer optimal control problem into a plurality of continuous optimal control problems in the range of [0, 1] comprises:

[0026] 1) The trajectory planning model is equivalently converted into a mixed integer optimal control problem with multiple {0,1} binary variables;

[0027] Among them, the integer variable ε(t) of the trajectory planning model is converted into several {0,1} binary variables, then the mixed integer optimal control problem shown in formula (4) is equivalent to:

[0028]

[0029] Among them, ω(t) is a binary variable {0,1} obtained by converting the integer variable ε(t);

[0030] 2) converting the mixed integer optimal control problem of multiple {0,1} binary variables obtained in step 1) into the optimal control problem of multiple [0,1] continuous variables;

[0031] Among them, the {0,1} binary variable is converted to a [0,1] continuous variable, and the problem shown in formula (5) is transformed into:

[0032]

[0033] Among them, μ(t) is the [0,1] continuous variable obtained by converting the integer variable ω(t), and Λ is the value set of μ(t).

[0034] In a specific embodiment of the present invention, the convex discretized trajectory planning model includes:

[0035] 1) Linearize the kinetic equations, process constraints, and performance indicators;

[0036] The kinetic equation Linearize about a reference trajectory:

[0037]

[0038] Among them, κ * represents the value of any variable κ on the reference trajectory; δx represents the deviation of the aircraft state relative to the reference state; δu represents the deviation of the aircraft control quantity u relative to the reference control quantity u*; δμ represents [0,1] The control quantity μ is relative to the reference [0,1] Deviation of the control quantity μ*;

[0039] Linearize the process constraint 0≤c(x(t),u(t),μ(t)) around the reference trajectory:

[0040]

[0041] Linearize the performance metric around a reference trajectory:

[0042]

[0043] 2) discretizing the linearized kinetic equations, process constraints, and performance indicators in step 1);

[0044] Let i represent the i-th discrete point, and the total number of discrete points is N;

[0045] The discretization result of the dynamic equation after linearization in step 1) is as follows:

[0046]

[0047] Among them, δx i represents the deviation of the aircraft state at the i-th discrete point relative to the reference state; δu i represents the control value u of the aircraft at the ith discrete point i Relative to the reference control Deviation of μi Represents the i-th discrete point [0,1] Control quantity μ i Relative to reference [0,1] Control volume Deviation, T represents the time interval between two adjacent discrete points;

[0048] The discretization result of the process constraint after linearization in step 1) is as follows:

[0049]

[0050] The discretization results of the performance indicators after linearization in step 1) are as follows:

[0051]

[0052] 3) Based on the results of steps 1) and 2), the optimal control problem expression after linearization and discretization is as follows:

[0053]

[0054] In a specific embodiment of the present invention, the method further comprises:

[0055] 1) Solve the optimal control problem shown in equation (13) to obtain the deviation δx of the aircraft state at each discrete point relative to the reference state: i And the deviation of the aircraft control quantity relative to the reference control quantity δu i ,δμ i ;

[0056] Then use the following formula to determine whether the solution converges:

[0057]

[0058] Among them, β>0 is the convergence threshold;

[0059] If equation (14) is satisfied, it means that the solution of the optimal control problem shown in equation (6) converges, and the process goes to step 3); if not, the process goes to step 2);

[0060] 2) Use the solution obtained in step 1) to update the state and control amount of the reference trajectory. The expression is as follows:

[0061]

[0062] Among them, x new,i * represents the state of the updated reference trajectory at the i-th discrete point, u new,i * ,μ new,i * They represent the control amount of the updated reference trajectory at the i-th discrete point respectively;

[0063] Then, then, x new,i* ,u new,i * ,μ new,i * As new x i * ,u i * ,μ i * , re-linearize and discretize the continuous optimal control problem;

[0064] 3) The solution obtained in step 1) is converted into the solution of the original mixed integer optimal control problem using the summation rounding rule, as follows:

[0065] Let ω j,i represents the j-th dimension {0, 1} variable at the i-th discrete time point, where the value range of i is i=1,...,N and the value range of j is j=1,...,n w ;

[0066] make Represents the j-th dimension auxiliary variable of the i-th discrete point. The calculation expression is as follows:

[0067]

[0068] Then the integer variable solution ω of the mixed integer optimal control problem is as shown in equation (5): j (i) is:

[0069]

[0070] The integer variable solution of the mixed integer optimal control problem shown in equation (4) is calculated as:

[0071] ε i =ε j ifω j,i =1 (18)

[0072] Among them, i represents the i-th discrete point;

[0073] The final trajectory planning results include: is the sequence of aircraft state quantities, is the continuous control sequence of the aircraft, is the sequence of discrete control quantities of the aircraft.

[0074] The characteristics and beneficial effects of the present invention are:

[0075] (1) The present invention is suitable for a deformable aircraft in a discrete deformation mode, and effectively solves the difficulty of gradient information disappearance in the process of solving the trajectory planning problem in the discrete deformation mode.

[0076] (2) The present invention constructs a trajectory planning model for a deformable aircraft under a discrete deformation mode, and transforms this mixed integer optimal control problem into a continuous optimal control problem. Then, the continuous solution obtained from the continuous optimal control problem is transformed into a discrete solution of the original integer problem by using the summation and rounding criterion.

[0077] (3) The present invention realizes the rapid solution of the trajectory planning problem of the deformable aircraft under the discrete deformation mode, and improves the accuracy and efficiency of the online trajectory planning of the deformable aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is an overall flow chart of a trajectory planning method for a deformable aircraft in a discrete deformation mode according to an embodiment of the present invention;

[0079] Figure 2 is a flight trajectory curve diagram of a deformable aircraft in a specific embodiment of the present invention;

[0080] Figure 3 is a graph showing the change in height of a deformed aircraft over time in a specific embodiment of the present invention;

[0081] Figure 4 is a graph showing the speed of a deformable aircraft changing with time in a specific embodiment of the present invention;

[0082] Figure 5 is a graph showing the change of the intermediate variable μ over time during the solution process in a specific embodiment of the present invention;

[0083] Figure 6 is a graph showing the change of the intermediate variable ω over time during the solution process in a specific embodiment of the present invention;

[0084] Figure 7 It is a curve diagram of the deformation parameters of a deformable aircraft changing with time in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0085] The present invention proposes a trajectory planning method for a deformable aircraft in a discrete deformation mode, and the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0086] An embodiment of the present invention provides a trajectory planning method for a deformable aircraft in a discrete deformation mode, comprising:

[0087] Construct the dynamic equations of the deformable aircraft under discrete deformation mode;

[0088] Based on the dynamic equations, a trajectory planning model of the deformable aircraft is established, wherein the model is a mixed integer optimal control problem;

[0089] Convert the mixed integer optimal control problem into a plurality of continuous optimal control problems in the range of [0,1];

[0090] The continuous optimal control problem is linearized and discretized near a preset reference trajectory starting from the current position of the deformable aircraft to obtain a convex discretized trajectory planning model;

[0091] The discretized trajectory planning model is solved, and if the solution result converges, the solution result is converted into a solution to the mixed integer optimal control problem to obtain the trajectory planning result of the deformable aircraft.

[0092] In a specific embodiment of the present invention, the trajectory planning method of a deformable aircraft in a discrete deformation mode has the following overall process: Figure 1 As shown, the following steps are included:

[0093] 1) Construct the dynamic equations of the deformable aircraft under discrete deformation mode.

[0094] In this embodiment, the dynamic equation of the deformable aircraft in the discrete deformation mode is expressed as follows:

[0095]

[0096] Among them, the state variables r, λ, φ, V, θ, σ are the distance from the center of the earth, longitude, latitude, speed, ballistic inclination, and ballistic deviation of the aircraft respectively; the control variables α, ν, k represent the angle of attack, roll angle, and deformation coefficient respectively, where the deformation coefficient can be k = 1, 2, ..., n w Corresponding to aircraft n w different deformations; L, D represent lift and drag respectively; C L ,C D They represent lift coefficient and drag coefficient respectively; ρ represents air density; S ref represents the reference area of ​​the aircraft; Ma represents the Mach number; g represents the acceleration due to gravity.

[0097] 2) Based on the dynamic equation obtained in step 1), a reference trajectory of the deformable aircraft is established with the current position as the starting point.

[0098] In this embodiment, the reference trajectory takes the current position of the aircraft as the starting point, adopts a suitable constant control amount based on experience, and takes a certain latitude and longitude condition or flight time as the termination condition of the reference trajectory.

[0099] 3) Based on the result of step 1), a trajectory planning model of the deformable aircraft in discrete deformation mode is established. The model is a mixed integer optimal control problem. The specific steps are as follows:

[0100] 3-1) Establish the process constraints of the deformable aircraft during flight as follows:

[0101]

[0102] Among them, k q is the heat flow coefficient, n max ,q max ,p max They represent the maximum values ​​of vehicle overload, heat flow and dynamic pressure respectively.

[0103] 3-2) Establish performance optimization goals.

[0104] In order to ensure the stability and safety of flight, this embodiment takes the minimum heat flux accumulation and the minimum control amount change rate accumulation as the performance optimization goals, and the expressions are as follows:

[0105]

[0106] Among them, C1 and C2 are index coefficients, which are selected according to the flight performance requirements and are required to be positive numbers. C1 reflects the accumulation of the heat flow rate of the aircraft during the flight, and C2 reflects the smoothness of the angle of attack and the roll angle during the flight. In a specific embodiment of the present invention, C1 = 1e-7, C2 = 0.1.

[0107] 3-3) Based on the results of steps 3-1) and 3-2), combined with the dynamic equation established in step 1), a trajectory planning model for the deformable aircraft in discrete deformation mode is established.

[0108] In this embodiment, the dynamic equations, process constraints and indicators are simplified, and the trajectory planning model expression of the deformable aircraft in the discrete deformation mode is obtained as follows:

[0109]

[0110] Formula (4) is a mixed integer optimal control problem, where By simplifying formula (3), we can get: f represents the flight cut-off time; x(t) is the state of the aircraft, The formula (1) is simplified and represents the dynamic equation; 0≤c(x(t),u(t),ε(t)), which is simplified and represents the process constraint; u(t) is the continuous control variable, including the angle of attack and the roll angle, is a set of continuous control value; ε(t) is an integer variable, which represents the deformation coefficient in this embodiment; is a set of discrete control values, including n w discrete control quantities, in a specific embodiment of the present invention, n w is 2. In this embodiment, ε1 ,ε 2 Represents different sweep angle values, 30deg and 60deg respectively.

[0111] Among them, x, u, ε represent the aircraft state quantity, aircraft continuous control quantity, and aircraft discrete control quantity respectively; c represents the inequality constraint; Φ represents the integral index.

[0112] 4) Convert the trajectory planning model established in step 3) into a continuous optimal control problem in multiple continuous [0,1] ranges; the specific steps are as follows:

[0113] 4-1) Convert the trajectory planning model established in step 3) into a mixed integer optimal control problem with multiple {0,1} binary variables.

[0114] In this embodiment, the integer variable ε(t) in the mixed integer optimal control problem obtained in step 3) is converted into a number of {0,1} binary variables, and the original problem shown in formula (4) is equivalent to:

[0115]

[0116] Among them, ω(t) is a {0,1} binary variable converted from the integer variable ε(t).

[0117] 4-2) Convert the mixed integer optimal control problem of multiple {0,1} binary variables obtained in step 4-1) into an optimal control problem of multiple [0,1] continuous variables.

[0118] In this embodiment, the {0,1} binary variable is converted to a [0,1] continuous variable, and the problem shown in formula (5) is converted to:

[0119]

[0120] Among them, μ(t) is a [0,1] continuous variable converted from the integer variable ω(t), and Λ is the value set of μ(t).

[0121] 5) Linearize and discretize the dynamic equations, process constraints, and performance indicators near the reference trajectory obtained in step 2) to obtain a convex discretized trajectory planning model, and add trust region constraints; the specific steps are as follows:

[0122] 5-1) Linearize the kinetic equations, process constraints, and performance indicators.

[0123] The kinetic equation Linearize about a reference trajectory:

[0124]

[0125] Among them, κ* represents the value of any variable κ on the reference trajectory; δx represents the deviation of the aircraft state relative to the reference state; δu represents the deviation of the aircraft control quantity u relative to the reference control quantity u*; δμ represents the deviation of the [0,1] control quantity μ in equation (6) relative to the reference [0,1] control quantity μ*.

[0126] Linearize the process constraint 0≤c(x(t),u(t),μ(t)) around the reference trajectory:

[0127]

[0128] Linearize the performance metric around a reference trajectory:

[0129]

[0130] 5-2) Discretize the linearized kinetic equations, process constraints, and performance indicators in step 5-1).

[0131] Let i represent the i-th discrete point, and the total number of discrete points is N. In this embodiment, a larger N will increase the solution time of the algorithm, and a smaller N will cause insufficient accuracy in solving the planning problem. In this embodiment, N is 100.

[0132] The discretization result of the dynamic equation after linearization in step 5-1) is as follows:

[0133]

[0134] Among them, δx i represents the deviation of the aircraft state at the i-th discrete point relative to the reference state; δu i represents the control value u of the aircraft at the ith discrete point i Relative to the reference control Deviation of δμ i represents the [0,1] control quantity μ in equation (6) at the ith discrete point i Control amount relative to reference [0,1] The deviation of , T represents the time interval between two adjacent discrete points.

[0135] The discretization result of the process constraint after linearization in step 5-1) is as follows:

[0136]

[0137] The discretization results of the performance indicators after linearization in step 5-1) are as follows:

[0138]

[0139] 5-3) Based on the results of steps 5-1) and 5-2), the optimal control problem expression after linearization and discretization is as follows:

[0140]

[0141] 6) Use the optimization solver to solve the optimal control problem obtained in step 5) and obtain the deviation δx of the aircraft state at each discrete point relative to the reference state i , the deviation of the aircraft control quantity relative to the reference control quantity δu i ,δμ i , where i represents the i-th discrete point.

[0142] Then use the following formula to determine whether the solution converges:

[0143]

[0144] Wherein, β>0 is the convergence threshold, and in this embodiment, it is 0.005. If equation (14) is satisfied, it means that the solution of the optimal control problem shown in equation (6) converges, and the process goes to step 8); if not, the process goes to step 7).

[0145] 7) Using the solution obtained in step 6), the state and control amount of the reference trajectory are updated. The expression is as follows:

[0146]

[0147] Among them, x new,i * represents the state of the updated reference trajectory at the i-th discrete point, u new,i * ,μ new,i * They respectively represent the control amount of the updated reference trajectory at the i-th discrete point.

[0148] Then, x new,i * ,u new,i * ,μ new,i * As new x i * ,u i * ,μ i * , return to step 5).

[0149] 8) The solution obtained in step 6) is converted into the solution of the original mixed integer optimal control problem using the summation rounding rule, as follows:

[0150] Definitionj,i represents the j-th dimension {0, 1} variable at the i-th discrete time point, where the value range of i is i=1,...,N and the value range of j is j=1,...,n w ;

[0151] definition Represents the j-th dimension auxiliary variable of the i-th discrete point, and its calculation expression is as follows:

[0152]

[0153] Then the integer variable solution ω of the mixed integer optimal control problem is as shown in equation (5): j (i) is:

[0154]

[0155] The integer variable solution of the mixed integer optimal control problem shown in equation (4) is calculated as:

[0156] ε i =ε j ifω j,i =1 (18)

[0157] Where i represents the i-th discrete point. Combining the above solution steps, the result of trajectory planning is finally obtained, where step 6) is the sequence of aircraft state quantities obtained by trajectory planning, and step 6) is the continuous control sequence of the aircraft obtained by trajectory planning, and the one obtained in step 8) The sequence of discrete control variables for the aircraft obtained for trajectory planning.

[0158] The following is a simulation using Matlab to further illustrate the process of the method described in this embodiment. In a simulation of a specific implementation of the present invention, the initial altitude, longitude, latitude, speed, ballistic inclination, and ballistic deviation of the aircraft are set to 51km, 0deg, 0deg, 5000m / s, 0deg, 90deg, respectively. The longitude and latitude of the aircraft's final position are 31deg, 10deg, respectively. The aircraft's final altitude range is [30, 32]km. The aircraft's final speed is 2000m / s. The aircraft has two aerodynamic modes, and the deformation coefficient can take two values ​​of {1, 2}. Set the aircraft reference area to 1m 2 , select the total number of discrete points as N = 100, optimize the performance index parameters C1 = 1e-7, C2 = 0.1, and the convergence judgment condition is β = 0.005. After 100 simulations, the average CPU time is 3.0s, which can achieve fast trajectory planning.

[0159] Figure 2FIG. 1 is a graph showing the flight trajectory of a deformed aircraft in a specific embodiment of the present invention. Figure 2 As shown, by adopting the method described in this embodiment, the aircraft can reach the predetermined longitude and latitude position, and the position of the aircraft at the termination time strictly meets the requirements of 31deg, 10deg. Figure 3 FIG. 1 is a graph showing the change in height of a deformable aircraft over time in a specific embodiment of the present invention. Figure 3 As shown, the altitude of the aircraft first rises and then falls during the flight. The altitude of the aircraft at the termination moment is 32.000km, which meets the termination altitude range. Figure 4 FIG. 1 is a graph showing the speed of a deformable aircraft changing over time in a specific embodiment of the present invention. Figure 4 As shown, the speed of the aircraft has been decreasing during the flight, and the final speed of the aircraft is 2000.0 m / s, which meets the final speed range. Figure 5 It is a graph showing the change of the intermediate variable μ with time during the solution process in a specific embodiment of the present invention. Figure 6 It is a curve diagram of the change of the intermediate variable ω over time during the solution process in a specific embodiment of the present invention. Figure 7 It is a curve diagram of the deformation parameters of a deformable aircraft changing with time in a specific embodiment of the present invention. Figure 5-Figure 7 It is shown that the continuous optimal solution obtained in step 6) is finally transformed into the solution of the problem shown in formula (4) based on the summation rounding rule.

Claims

1. A trajectory planning method for a deformable aircraft in a discrete deformation mode, characterized in that: include: Construct the dynamic equations of the deformable aircraft under discrete deformation mode; Based on the dynamic equations, a trajectory planning model of the deformable aircraft is established, wherein the model is a mixed integer optimal control problem; Convert the mixed integer optimal control problem into a plurality of continuous optimal control problems in the range of [0,1]; The continuous optimal control problem is linearized and discretized near a preset reference trajectory starting from the current position of the deformable aircraft to obtain a convex discretized trajectory planning model; The discretized trajectory planning model is solved, and if the solution result converges, the solution result is converted into a solution to the mixed integer optimal control problem to obtain the trajectory planning result of the deformable aircraft.

2. The method according to claim 1, characterized in that: The kinetic equation is expressed as follows: Among them, the state variables r, λ, φ, V, θ, σ are the distance from the center of the earth, longitude, latitude, speed, ballistic inclination, and ballistic deviation of the aircraft respectively; the control variables α, ν, k represent the angle of attack, roll angle, and deformation coefficient respectively, where the deformation coefficient k = 1, 2, ..., n w Corresponding to aircraft n w different deformations; L, D represent lift and drag respectively; C L ,C D They represent lift coefficient and drag coefficient respectively; ρ represents air density; S ref represents the reference area of ​​the aircraft; Ma represents the Mach number; g represents the acceleration due to gravity.

3. The method according to claim 2, characterized in that The step of establishing a trajectory planning model for the deformable aircraft comprises: 1) Establish the process constraints of the deformable aircraft during flight as follows: Among them, k q is the heat flow coefficient, n max ,q max ,p max They represent the maximum values ​​of vehicle overload, heat flow, and dynamic pressure respectively; 2) Construct performance optimization goals, the expression is as follows: Among them, C1 and C2 are index coefficients, both of which are positive numbers. C1 reflects the accumulation of the heat flux rate of the aircraft during the flight, and C2 reflects the smoothness of the angle of attack and the roll angle during the flight. 3) Based on the results of steps 1) and 2), combined with the dynamic equation, the trajectory planning model of the deformable aircraft in the discrete deformation mode is established, and the expression is as follows: in, Simplified from formula (3), t f represents the flight cut-off time; x(t) is the state of the aircraft, Simplified from formula (1), it represents the dynamic equation; 0≤c(x(t),u(t),ε(t)), simplified from formula (3), it represents the process constraint; u(t) is the continuous control variable, including the angle of attack and the roll angle, is a set of continuous control value; ε(t) is an integer variable, indicating the deformation coefficient; is a set of discrete control values, including n w Discrete control quantity; x, u, ε represent the vehicle state quantity, vehicle continuous control quantity, and vehicle discrete control quantity respectively; c represents the inequality constraint; Φ represents the integral index.

4. The method according to claim 3, characterized in that The step of converting the mixed integer optimal control problem into a plurality of continuous optimal control problems in the range of [0,1] comprises: 1) The trajectory planning model is equivalently converted into a mixed integer optimal control problem with multiple {0,1} binary variables; Among them, the integer variable ε(t) of the trajectory planning model is converted into several {0,1} binary variables, then the mixed integer optimal control problem shown in formula (4) is equivalent to: Among them, ω(t) is a binary variable {0,1} obtained by converting the integer variable ε(t); 2) converting the mixed integer optimal control problem of multiple {0,1} binary variables obtained in step 1) into the optimal control problem of multiple [0,1] continuous variables; Among them, the {0,1} binary variable is converted to a [0,1] continuous variable, and the problem shown in formula (5) is transformed into: Among them, μ(t) is the [0,1] continuous variable obtained by converting the integer variable ω(t), and Λ is the value set of μ(t).

5. The method according to claim 4, characterized in that The convex discretized trajectory planning model includes: 1) Linearize the kinetic equations, process constraints, and performance indicators; The kinetic equation Linearize about a reference trajectory: Among them, κ * represents the value of any variable κ on the reference trajectory; δx represents the deviation of the aircraft state relative to the reference state; δu represents the deviation of the aircraft control quantity u relative to the reference control quantity u*; δμ represents [0,1] The control quantity μ is relative to the reference [0,1] Deviation of the control quantity μ*; Linearize the process constraint 0≤c(x(t),u(t),μ(t)) around the reference trajectory: Linearize the performance metric around a reference trajectory: 2) discretizing the linearized kinetic equations, process constraints, and performance indicators in step 1); Let i represent the i-th discrete point, and the total number of discrete points is N; The discretization result of the dynamic equation after linearization in step 1) is as follows: Among them, δx i represents the deviation of the aircraft state at the i-th discrete point relative to the reference state; δu i represents the control value u of the aircraft at the ith discrete point i Relative to the reference control Deviation of δμ i Represents the i-th discrete point [0,1] Control quantity μ i Relative to reference [0,1] Control volume Deviation, T represents the time interval between two adjacent discrete points; The discretization result of the process constraint after linearization in step 1) is as follows: The discretization results of the performance indicators after linearization in step 1) are as follows: 3) Based on the results of steps 1) and 2), the optimal control problem expression after linearization and discretization is as follows:

6. The method according to claim 5, characterized in that The method further comprises: 1) Solve the optimal control problem shown in equation (13) to obtain the deviation δx of the aircraft state at each discrete point relative to the reference state: i And the deviation of the aircraft control quantity relative to the reference control quantity δu i ,δμ i ; Then use the following formula to determine whether the solution converges: Among them, β>0 is the convergence threshold; If equation (14) is satisfied, it means that the solution of the optimal control problem shown in equation (6) converges, and the process goes to step 3); if not, the process goes to step 2); 2) Use the solution obtained in step 1) to update the state and control amount of the reference trajectory. The expression is as follows: Among them, x new,i * represents the state of the updated reference trajectory at the i-th discrete point, u new,i * ,μ new,i * They represent the control amount of the updated reference trajectory at the i-th discrete point respectively; Then, then, x new,i * ,u new,i * ,μ new,i * As new x i * ,u i * ,μ i * , re-linearize and discretize the continuous optimal control problem; 3) The solution obtained in step 1) is converted into the solution of the original mixed integer optimal control problem using the summation rounding rule, as follows: Let ω j,i represents the j-th dimension {0, 1} variable at the i-th discrete time point, where the value range of i is i=1,...,N and the value range of j is j=1,...,n w ; make Represents the j-th dimension auxiliary variable of the i-th discrete point. The calculation expression is as follows: Then the integer variable solution ω of the mixed integer optimal control problem is as shown in equation (5): j (i) is: The integer variable solution of the mixed integer optimal control problem shown in equation (4) is calculated as: e i =e j if oh j,i =1 (18) Among them, i represents the i-th discrete point; The final trajectory planning results include: is the sequence of aircraft state quantities, is the continuous control sequence of the aircraft, is the sequence of discrete control quantities of the aircraft.

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