A trajectory planning method for a morphing aircraft in a discrete morphing mode

Abstract

This invention proposes a trajectory planning method for deformable aircraft in discrete deformable mode, belonging to the field of aircraft guidance and control technology. Based on dynamic equations, this method establishes a trajectory planning model for the deformable aircraft in discrete deformable mode, which is a mixed-integer optimal control problem. This mixed-integer optimal control problem is transformed into multiple continuous optimal control problems within the continuous range [0,1]. These problems are then linearized and discretized near a reference trajectory starting from the current position of the deformable aircraft, resulting in a convex discretized trajectory planning model. The discretized trajectory planning model is solved; if the solution converges, the solution is converted into a solution to the mixed-integer optimal control problem to obtain the trajectory planning result of the deformable aircraft. This invention can improve the efficiency and accuracy of trajectory planning for deformable aircraft in discrete deformable mode and has high application value.

Description

Technical Field

[0001] This invention belongs to the field of aircraft guidance and control technology, and specifically relates to a trajectory planning method for deformable aircraft in discrete deformation mode. Background Technology

[0002] A morphing aircraft is an aircraft that, through changes in its partial or overall shape parameters, produces better aerodynamic efficiency and handling performance, enabling more maneuverable flight trajectories, altitudes, and speeds, improving its adaptability to the environment and missions, and maintaining optimal efficiency and performance in various flight environments.

[0003] Reentry trajectory planning for morphing aircraft is a crucial step for their efficient and reliable mission completion, demanding high real-time performance, multiple constraints, and high precision. Morphing aircraft can operate in two modes: continuous and discrete. Continuous morphing involves a spatially continuous deformation range, such as a sweep angle that can arbitrarily range from 30° to 60°. Discrete morphing involves a spatially discrete deformation range, where the sweep angle is selected from elements in the set {30°, 45°, 60°}. Existing trajectory planning methods primarily address continuous morphing modes, with limited research on discrete morphing modes. Compared to continuous morphing modes, optimization in discrete modes loses gradient information, significantly increasing the difficulty and time required for solving the problem. Therefore, researching trajectory planning for morphing aircraft in discrete morphing modes to improve the accuracy and real-time performance of trajectory planning algorithms is of great significance. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a trajectory planning method for deformable aircraft in discrete deformation modes. This invention can improve the efficiency and accuracy of trajectory planning for deformable aircraft in discrete deformation modes and has high application value.

[0005] This invention proposes a trajectory planning method for a deformable aircraft in discrete deformable mode, comprising:

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

[0007] Based on the aforementioned dynamic equations, a trajectory planning model for the deformable aircraft is established, which is a mixed integer optimal control problem.

[0008] The mixed integer optimal control problem is transformed into multiple continuous optimal control problems in the range [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, resulting in a convex discretized trajectory planning model.

[0010] If the solution to the discretized trajectory planning model converges, the solution 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 dynamic equation is expressed as follows:

[0012] (1)

[0013] Among them, state variables These are the aircraft's distance from the Earth's center, longitude, latitude, speed, trajectory inclination, and trajectory deflection; control variables. These represent the angle of attack, the angle of inclination, and the deformation coefficient, respectively, where the deformation coefficient... Corresponding to aircraft Different deformation amounts; These represent lift and drag, respectively. These represent the lift coefficient and drag coefficient, respectively. Indicates air density; Indicates the reference area of ​​the aircraft; Ma represents the Mach number; It represents the acceleration due to gravity.

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

[0015] 1) The process constraints for the morphing aircraft during flight are established as follows:

[0016] (2)

[0017] in, The heat flow rate coefficient, These represent the maximum values ​​of aircraft overload, heat flux, and dynamic pressure, respectively.

[0018] 2) Construct the performance optimization target, expressed as follows:

[0019] (3)

[0020] in, These are index coefficients, all of which are positive numbers. It reflects the accumulation of the aircraft's heat flux rate during flight. It reflects the smoothness of angle of attack and roll angle during flight;

[0021] 3) Based on the results of steps 1) and 2), and combined with the dynamic equations, a trajectory planning model for the deformable aircraft under discrete deformation mode is established, expressed as follows:

[0022] (4)

[0023] in, The simplified version of equation (3) is obtained as follows: Indicates the flight deadline; For aircraft state variables, The equation is simplified from equation (1) and represents the dynamic equation. , which is simplified from equation (3), represents the process constraint; These are continuous control parameters, including angle of attack and roll angle. It is the set of values ​​for continuous control quantities; The variable is an integer, representing the deformation coefficient; The set of values ​​for discrete control variables, including A discrete control quantity;

[0024] These represent the aircraft state variables, the aircraft continuous control variables, and the aircraft discrete control variables, respectively. Indicates inequality constraints; This indicates an integral-type indicator.

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

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

[0027] Among them, the integer variables of the trajectory planning model Converting to several {0,1} binary variables, the mixed integer optimal control problem shown in equation (4) is equivalent to:

[0028] (5)

[0029] in, Integer variable The resulting binary variable {0,1};

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

[0031] Converting the binary variable {0,1} to a continuous variable [0,1] transforms the problem shown in equation (5) into:

[0032] (6)

[0033] in, Integer variable The transformed continuous variable is [0,1]. for The set of possible values ​​for .

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

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

[0036] Among them, the dynamic equation Linearize near the reference trajectory:

[0037] (7)

[0038] in, Represent any variable The value on the reference trajectory; It indicates the deviation of the aircraft's state from the reference state; Indicates aircraft control quantity Relative to reference control value Deviation; Represents the [0,1] control quantity Relative to the reference [0,1] control value Deviation;

[0039] Process constraints Linearize near the reference trajectory:

[0040] (8)

[0041] Linearize the performance metrics around the reference trajectory:

[0042] (9)

[0043] 2) Discretize the linearized kinetic equations, process constraints, and performance indices from step 1);

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

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

[0046] (10)

[0047] in, Indicates the first The deviation of the aircraft state from the reference state at each discrete point; Indicates the first The aircraft control quantity at each discrete point Relative to reference control value Deviation; Indicates the first The control quantity at a discrete point [0,1] Relative to the reference [0,1] control value deviation, This represents the time interval between two adjacent discrete points;

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

[0049] (11)

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

[0051] (12)

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

[0053] (13).

[0054] In one specific embodiment of the present invention, the method further includes:

[0055] 1) Solve the optimal control problem as shown in equation (13) to obtain the deviation of the aircraft state from the reference state at each discrete point. And the deviation of the aircraft control quantity from the reference control quantity ;

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

[0057] (14)

[0058] in, This is the convergence threshold;

[0059] If equation (14) is satisfied, it means that the solution to the optimal control problem shown in equation (6) has converged, and proceed to step 3); if not, proceed to step 2).

[0060] 2) Use the solution obtained in step 1) to update the state and control variables of the reference trajectory, as shown in the following expression:

[0061] (15)

[0062] in, Indicates the first The updated state variables of the reference trajectory at each discrete point They represent the first The control quantity of the updated reference trajectory at each discrete point;

[0063] Then, then, will Each as a new Then, the continuous optimal control problem is linearized and discretized again;

[0064] 3) Use the summation and rounding rules to convert the solution obtained in step 1) into a solution to the original mixed integer optimal control problem, as follows:

[0065] make Indicates the first The j-th dimension {0, 1} variable at each discrete time point, where the value of i ranges from... The range of values ​​for j is ;

[0066] make Indicates the first The j-th dimension auxiliary variable for each discrete point is calculated as follows:

[0067] (16)

[0068] Then the integer variable solution of the mixed integer optimal control problem shown in equation (5) for:

[0069] (17)

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

[0071] (18)

[0072] in, Indicates the first A discrete point;

[0073] The final trajectory planning results include: For the sequence of aircraft state variables, This is the sequence of continuous control parameters for the aircraft. It is a sequence of discrete control variables for the aircraft.

[0074] The features and beneficial effects of this invention are as follows:

[0075] (1) This invention is applicable to deformable aircraft in discrete deformation mode and effectively solves the problem of gradient information disappearing in the process of solving trajectory planning problem in discrete deformation mode.

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

[0077] (3) This invention realizes the rapid solution of the trajectory planning problem of deformable aircraft under discrete deformation mode, and improves the accuracy and efficiency of online trajectory planning of deformable aircraft. Attached Figure Description

[0078] Figure 1 This is an overall flowchart 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 This is a flight trajectory curve of a deformable aircraft in a specific embodiment of the present invention;

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

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

[0082] Figure 5 This is an intermediate variable in the solution process of a specific embodiment of the present invention. Curve graph showing changes over time;

[0083] Figure 6 This is an intermediate variable in the solution process of a specific embodiment of the present invention. Curve graph showing changes over time;

[0084] Figure 7 This is a graph showing the change of deformation parameters of a deformable aircraft over time in a specific embodiment of the present invention. Detailed Implementation

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

[0086] This invention proposes a trajectory planning method for a deformable aircraft in discrete deformable mode, comprising:

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

[0088] Based on the aforementioned dynamic equations, a trajectory planning model for the deformable aircraft is established, which is a mixed integer optimal control problem.

[0089] The mixed integer optimal control problem is transformed into multiple continuous optimal control problems in the range [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, resulting in a convex discretized trajectory planning model.

[0091] If the solution to the discretized trajectory planning model converges, the solution 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 for a deformable aircraft in discrete deformation mode is as follows: Figure 1 As shown, it includes the following steps:

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

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

[0095] (1)

[0096] Among them, state variables These are the aircraft's distance from the Earth's center, longitude, latitude, speed, trajectory inclination, and trajectory deflection; control variables. These represent the angle of attack, the angle of inclination, and the deformation coefficient, respectively, where the deformation coefficient can be taken as... Corresponding to aircraft Different deformation amounts; These represent lift and drag, respectively. These represent the lift coefficient and drag coefficient, respectively. Indicates air density; Indicates the reference area of ​​the aircraft; Ma represents the Mach number; It represents the acceleration due to gravity.

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

[0098] In this embodiment, the reference trajectory starts from the current position of the aircraft, adopts an appropriate constant control quantity based on experience, and uses certain latitude and longitude conditions or flight time as the termination condition of the reference trajectory.

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

[0100] 3-1) The process constraints for the morphing aircraft during flight are established as follows:

[0101] (2)

[0102] in, The heat flow rate coefficient, These represent the maximum values ​​of aircraft overload, heat flux, and dynamic pressure, respectively.

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

[0104] To ensure flight stability and safety, this embodiment uses minimum cumulative heat flux and minimum cumulative rate of change of control quantity as performance optimization objectives, expressed as follows:

[0105]

[0106] in, These are the indicator coefficients. These two coefficients are selected independently based on flight performance requirements and must be positive numbers. It reflects the accumulation of the aircraft's heat flux rate during flight. This reflects the smoothness of angle of attack and bank angle during flight. In one specific embodiment of the invention, .

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

[0108] In this embodiment, the dynamic equations, process constraints, and indices are simplified to obtain the trajectory planning model expression for the deformable aircraft in discrete deformation mode as follows:

[0109] (4)

[0110] Equation (4) is a mixed integer optimal control problem, where, The result is obtained by rearranging and simplifying equation (3). Indicates the flight deadline; For aircraft state variables, , which is simplified from equation (1) and represents the dynamic equation; The simplified form of equation (3) represents the process constraint. These are continuous control parameters, including angle of attack and roll angle. It is the set of values ​​for continuous control quantities; This is an integer variable, representing the deformation coefficient in this embodiment; The set of values ​​for discrete control variables, including A discrete control quantity, in a specific embodiment of the present invention The value is 2. In this embodiment, These represent different sweep angle values, specifically 30 degrees and 60 degrees.

[0111] in, These represent the aircraft state variables, the aircraft continuous control variables, and the aircraft discrete control variables, respectively. Indicates inequality constraints; This indicates an integral-type indicator.

[0112] 4) Transform the trajectory planning model established in step 3) into multiple continuous optimal control problems within the continuous range [0,1]; the specific steps are as follows:

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

[0114] In this embodiment, the integer variables in the mixed-integer optimal control problem obtained in step 3) are... Converting it to several binary variables {0,1}, the original problem shown in equation (4) is equivalent to:

[0115] (5)

[0116] in, Integer variable The resulting binary variable {0,1}.

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

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

[0119] (6)

[0120] in, Integer variable The resulting [0,1] continuous variable for The set of possible values ​​for .

[0121] 5) Linearize and discretize the dynamic equations, process constraints, and performance indices around 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 dynamic equations, process constraints, and performance indicators.

[0123] The dynamic equation Linearize near the reference trajectory:

[0124] (7)

[0125] in, Represent any variable The value on the reference trajectory; It indicates the deviation of the aircraft's state from the reference state; Indicates aircraft control quantity Relative to reference control value Deviation; The [0,1] control quantity in expression (6) Relative to the reference [0,1] control value The deviation.

[0126] Process constraints Linearize near the reference trajectory:

[0127] (8)

[0128] Linearize the performance metrics around the reference trajectory:

[0129] (9)

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

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

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

[0133] (10)

[0134] in, Indicates the first The deviation of the aircraft state from the reference state at each discrete point; Indicates the first The aircraft control quantity at each discrete point Relative to reference control value Deviation; Indicates the first The [0,1] control quantity in equation (6) at each discrete point Relative to the reference [0,1] control value deviation, It represents the time interval between two adjacent discrete points.

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

[0136] (11)

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

[0138] (12)

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

[0140] (13)

[0141] 6) Solve the optimal control problem obtained in step 5) using an optimization solver to obtain the deviation of the aircraft state from the reference state at each discrete point. The deviation of the aircraft control quantity from the reference control quantity ,in Indicates the first A discrete point.

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

[0143] (14)

[0144] in, The convergence threshold is set to 0.005 in this embodiment. If equation (14) is satisfied, it means that the solution to the optimal control problem shown in equation (6) has converged, and proceed to step 8); if not, proceed to step 7).

[0145] 7) Use the solution obtained in step 6) to update the state and control variables of the reference trajectory, as shown in the following expression:

[0146] (15)

[0147] in, This represents the state variable of the updated reference trajectory at the i-th discrete point. These represent the control quantities of the updated reference trajectory at the i-th discrete point.

[0148] Then, Each as a new Return to step 5).

[0149] 8) Use the summation and rounding rules to convert the solution obtained in step 6) into a solution to the original mixed integer optimal control problem, as follows:

[0150] definition Indicates the first The j-th dimension {0, 1} variable at each discrete time point, where the value of i ranges from... The range of values ​​for j is ;

[0151] definition Indicates the first The j-th dimension auxiliary variable for each discrete point is calculated as follows:

[0152] (16)

[0153] Then the integer variable solution of the mixed integer optimal control problem shown in equation (5) for:

[0154] (17)

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

[0156] (18)

[0157] in, Indicates the first Discrete points. Combining the above solution steps, the final trajectory planning result is obtained, where step 6) yields... The sequence of aircraft state variables obtained from trajectory planning, obtained in step 6). The sequence of continuous control variables for the aircraft obtained from trajectory planning, obtained in step 8). The discrete control sequence of the aircraft is obtained from trajectory planning.

[0158] The following simulation using Matlab further illustrates the process of the method described in this embodiment. In a specific implementation of the simulation, the initial altitude, longitude, latitude, speed, trajectory inclination angle, and trajectory deflection angle of the aircraft are set as follows: The longitude and latitude of the aircraft's final position are respectively The aircraft's termination altitude range is The aircraft's final velocity is The aircraft has two aerodynamic modes, and the deformation coefficient can take two values: {1, 2}. The reference area of ​​the aircraft is set as... The total number of discrete points selected is Optimize performance parameters The convergence criterion is: The average CPU time was 3.0 seconds after 100 simulations, demonstrating that fast trajectory planning can be achieved.

[0159] Figure 2 This is a flight trajectory curve of a deformable aircraft in a specific embodiment of the present invention. For example... Figure 2 As shown, using the method described in this embodiment, the aircraft can reach a predetermined latitude and longitude position, and the position at the time of the aircraft's termination strictly satisfies... Requirements. Figure 3 This is a graph showing the change in altitude of a deformable aircraft over time in a specific embodiment of the present invention. Figure 3 As shown, the aircraft's altitude first rises and then falls during flight, and the altitude at the time of termination is 32.000 km, which meets the termination altitude range. Figure 4 This is a graph showing the speed of a deformable aircraft over time in a specific embodiment of the present invention. Figure 4 As shown, the speed of the aircraft continuously decreases during flight, and the final speed of the aircraft is 2000.0 m / s, which meets the termination speed range. Figure 5 This is an intermediate variable in the solution process of a specific embodiment of the present invention. Curve showing changes over time. Figure 6 This is an intermediate variable in the solution process of a specific embodiment of the present invention. Curve showing changes over time. Figure 7 This is a graph showing the change of deformation parameters of a deformable aircraft over time in a specific embodiment of the present invention. Figures 5-7 This demonstrates how the continuous optimal solution obtained in step 6) is ultimately transformed into the solution of the problem shown in equation (4) based on the summation and rounding rules.

Claims

1. A trajectory planning method for a deformable aircraft in discrete deformation mode, characterized in that, include: Construct the dynamic equations of a deformable aircraft in discrete deformation mode; Based on the aforementioned dynamic equations, a trajectory planning model for the deformable aircraft is established, which is a mixed integer optimal control problem. The mixed integer optimal control problem is transformed into multiple continuous optimal control problems in the range [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, resulting in a convex discretized trajectory planning model. If the solution to the discretized trajectory planning model converges, the solution is converted into a solution to the mixed integer optimal control problem to obtain the trajectory planning result of the deformable aircraft. The dynamic equation is expressed as follows: （1） Among them, state variables These are the aircraft's distance from the Earth's center, longitude, latitude, speed, trajectory inclination, and trajectory deflection; control variables. These represent the angle of attack, the angle of inclination, and the deformation coefficient, respectively, where the deformation coefficient... Corresponding to aircraft Different deformation amounts; These represent lift and drag, respectively. These represent the lift coefficient and drag coefficient, respectively. Indicates air density; Indicates the reference area of ​​the aircraft; Ma represents the Mach number; Represents gravitational acceleration; The establishment of the trajectory planning model for the deformable aircraft includes: 1) The process constraints for the morphing aircraft during flight are established as follows: （2） wherein, is the heat flux coefficient, respectively denote the maximum values of the aircraft overload, heat flux, dynamic pressure; 2) Construct the performance optimization target, expressed as follows: （3） wherein, are positive numbers, reflects the accumulation of the heat flux rate of the aircraft during flight, reflects the smoothness of the angle of attack and the angle of sideslip during flight; 3) Based on the results of steps 1) and 2), and combined with the dynamic equations, a trajectory planning model for the deformable aircraft in discrete deformation mode is established, expressed as follows: （4） in, The simplified version of equation (3) is obtained as follows: Indicates the flight deadline; For aircraft state variables, The equation is simplified from equation (1) and represents the dynamic equation. , which is simplified from equation (3), represents the process constraint; These are continuous control parameters, including angle of attack and roll angle. It is the set of values ​​for continuous control quantities; The variable is an integer, representing the deformation coefficient; The set of values ​​for discrete control variables, including A discrete control quantity; These represent the aircraft state variables, the aircraft continuous control variables, and the aircraft discrete control variables, respectively. Indicates inequality constraints; Indicates an integral-type indicator; The process of transforming the mixed-integer optimal control problem into multiple continuous optimal control problems in the range [0,1] includes: 1) The trajectory planning model is equivalently transformed into a mixed integer optimal control problem with multiple {0,1} binary variables; where the integer variables of the trajectory planning model are converted to a number of {0, 1} binary variables, the mixed integer optimal control problem as shown in equation (4) is equivalent to: （5） wherein, is an integer variable a {0,1} binary variable resulting from the conversion 2) The mixed integer optimal control problem of multiple {0,1} binary variables obtained in step 1) is transformed into the optimal control problem of multiple [0,1] continuous variables; Converting the binary variable {0,1} to a continuous variable [0,1] transforms the problem shown in equation (5) into: （6） wherein, is an integer variable a [0,1] continuous variable, is a set of values.

2. The method of claim 1, wherein, The obtained convex discretized trajectory planning model includes: 1) Linearize the dynamic equations, process constraints, and performance indicators; where the dynamics equation Linearization around the reference trajectory: （7） in, Represent any variable The value on the reference trajectory; It indicates the deviation of the aircraft's state from the reference state; Indicates aircraft control quantity Relative to reference control value Deviation; Represents the [0,1] control quantity Relative to the reference [0,1] control value Deviation; Constraining the process Linearization around a reference trajectory: （8） Linearize the performance metrics around the reference trajectory: （9） 2) Discretize the linearized kinetic equations, process constraints, and performance indices from step 1); Let i represent the ith discrete point, and let N represent the total number of discrete points ; The discretized result of the dynamic equation after linearization in step 1) is as follows: （10） in, Indicates the first The deviation of the aircraft state from the reference state at each discrete point; Indicates the first The aircraft control quantity at each discrete point Relative to reference control value Deviation; Indicates the first The control quantity at a discrete point [0,1] Relative to the reference [0,1] control value deviation, This represents the time interval between two adjacent discrete points; The process constraint discretization result after linearization in step 1) is as follows: （11） The discretized results of the performance index after linearization in step 1) are as follows: （12） 3) Based on the results of steps 1) and 2), the optimal control problem expression after linearization and discretization is as follows: （13）。 3. The method of claim 2, wherein, The method further includes: 1) Solve the optimal control problem as shown in equation (13) to obtain the deviation of the aircraft state from the reference state at each discrete point. And the deviation of the aircraft control quantity from the reference control quantity ; Then use the following formula to determine whether the solution converges: （14） wherein is a convergence threshold; If equation (14) is satisfied, it means that the solution to the optimal control problem shown in equation (6) has converged, and proceed to step 3); if not, proceed to step 2). 2) Use the solution obtained in step 1) to update the state and control variables of the reference trajectory, as shown in the following expression: （15） in, Indicates the first The updated state variables of the reference trajectory at each discrete point They represent the first The control quantity of the updated reference trajectory at each discrete point; Then, the are respectively regarded as new , the linearization and discretization of the continuous optimal control problem are performed again; 3) Use the summation and rounding rules to convert the solution obtained in step 1) into a solution to the original mixed integer optimal control problem, as follows: Let denote the {0,1} variable of the jth dimension at the ith discrete time point, where i ranges from 1 to N and j ranges from 1 to J. ;​​ Let denote the jth auxiliary variable of the ith discrete point, which is computed as follows: ​ （16） then the integer variable solution of the mixed integer optimal control problem as shown in equation (5) is: （17） The integer variable solution to the mixed-integer optimal control problem shown in equation (4) is calculated as follows: （18） in, Indicates the first A discrete point; The resulting trajectory planning result finally includes: is a sequence of aircraft state quantities, is a sequence of aircraft continuous control quantities, is a sequence of aircraft discrete control quantities.

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