Aircraft optimal recovery trajectory design method based on Bezier shape function

Abstract

The invention provides an aircraft optimal recovery trajectory design method based on a Bezier shape function, and relates to the technical field of aircraft automatic control. The method comprises the following steps: S1, acquiring state parameters of an aircraft in real time and setting the state parameters as initial state constraints; s2, defining an end point state and setting an end point state constraint; s3, constructing a composite constraint function; s4, based on the initial state constraint and the end point state constraint, adopting a Bezier curve to calculate initial Bezier curve parameters, and generating an initial trajectory; and S5, iteratively optimizing the Bezier curve parameters by taking the initial Bezier curve parameters as an optimization initial value and taking the flight time minimization as an optimization index, and verifying the feasibility of the recovery trajectory by using a kinetic model, and finally generating an optimal recovery trajectory. According to the method, the calculation efficiency and the trajectory optimality are balanced, the real-time performance and reliability of boundary protection control are improved, and it is ensured that the aircraft can rapidly recover stable flight within the safe envelope boundary.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automatic control of aircraft, and particularly to a method for designing optimal recovery trajectory of aircraft based on Bezier shape function. BACKGROUND

[0002] With the continuous improvement of the maneuverability of aircraft, the risk of high-maneuvering platforms such as fighter aircraft approaching the boundary of the safety envelope is increasingly prominent, and dynamic boundary protection and emergency recovery control have become a key technical requirement of flight control system. When the aircraft approaches the boundary of the safety envelope, a recovery trajectory that takes into account the smoothness, strict dynamic constraints and time optimality needs to be generated within milliseconds. Traditional rule-based protection strategies often cause secondary instability due to trajectory oscillation, while offline pre-planning methods cannot adapt to the state mutation of the aircraft under extreme maneuvering or sudden disturbance.

[0003] Currently, the main trajectory generation methods include polynomial interpolation, spline curve and optimal control method. Although the polynomial interpolation is simple to calculate, it is difficult to meet the high-order dynamic constraints, and the strong coupling and nonlinear characteristics of the aircraft are not fully considered, resulting in inherent defects in the generated trajectory in terms of acceleration continuity and control input feasibility; although the spline curve can ensure the continuity of curvature, the local control characteristics of the spline curve lead to the need to reconstruct all parameters for local adjustment of the trajectory, which is computationally redundant and difficult to meet the real-time requirements under sudden working conditions.

[0004] Therefore, there is an urgent need for a smooth optimal trajectory planning method that can quickly respond, generate online, and strictly meet complex flight dynamics and state constraints, effectively balance the optimality and feasibility of the trajectory under the premise of ensuring computational efficiency, and ultimately achieve reliable, smooth and rapid autonomous recovery control of the aircraft near the safety envelope boundary. SUMMARY

[0005] The purpose of the present application is to provide a method for designing optimal recovery trajectory of aircraft based on Bezier shape function, which solves the technical problem that the prior art is difficult to quickly generate a recovery trajectory that takes into account smoothness, dynamic constraints and optimality when the aircraft approaches the boundary of the safety envelope. By realizing fast trajectory optimization under complex constraints, the present application effectively balances computational efficiency and trajectory optimality, significantly improves the real-time performance and reliability of boundary protection control, ensures that the aircraft can quickly recover to stable flight within the safety envelope boundary, and reduces the risk of control oscillation.

[0006] To achieve the above purpose, the present application provides a method for designing optimal recovery trajectory of aircraft based on Bezier shape function, which is executed after receiving a boundary protection instruction, comprising the following steps: Step S1, real-time acquisition of state parameters of the aircraft and setting as initial state constraints; Step S2, defining the terminal state and setting the terminal state constraint; Step S3, constructing the composite constraint function; Step S4, based on the initial state constraint and the terminal state constraint, calculating the initial Bezier curve parameters using the Bezier curve to generate the initial trajectory; Step S5, taking the initial Bezier curve parameters as the optimization initial value, minimizing the flight time as the optimization index, iteratively optimizing the Bezier curve parameters, and verifying the feasibility of the recovery trajectory using the dynamics model to finally generate the optimal recovery trajectory.

[0007] Preferably, in step S1, the initial state constraint includes the initial position, the initial speed, the initial flight path pitch angle and the initial flight path yaw angle.

[0008] Preferably, in step S2, the terminal state is defined as the steady state at a certain safety distance from the upper boundary and the lower boundary of the safety envelope; the terminal state constraint includes the terminal height constraint, the terminal attitude and speed constraint, and the terminal velocity vector constraint.

[0009] Preferably, in step S3, the composite constraint function includes the initial state constraint, the terminal state constraint, the height boundary constraint, the speed boundary constraint, the overload constraint, and the state quantity constraint.

[0010] Preferably, in step S4, a three-dimensional trajectory parameterization method is used to describe each axial trajectory by an independent Bezier curve, and the order of the initial trajectory is set to 3 to calculate the initial Bezier curve parameters; the initial Bezier curve parameters include the initial control point coordinates of each axial trajectory.

[0011] Preferably, step S5 specifically includes: Step S501, taking the initial Bezier curve parameters as the optimization initial value, minimizing the flight time as the optimization index, and converting the trajectory optimization problem into a nonlinear programming problem of the Bezier curve parameters; Step S502, iteratively solving the nonlinear programming problem of the Bezier curve parameters using a numerical optimization algorithm; in each iteration, a candidate trajectory is generated according to the current Bezier curve parameters and the flight time; Step S503, using the dynamics model to perform reverse calculation on the candidate trajectory, and calculating the corresponding aircraft state quantities according to the three-dimensional trajectory; Step S504, comparing the calculated aircraft state quantities with the composite constraint function to determine whether they meet the dynamics constraints and the state constraints, and verifying the feasibility of the candidate trajectory; Step S505, repeating steps S502 to S504 until the maximum number of iterations is reached, and outputting the time-optimal and dynamically feasible aircraft optimal recovery trajectory sequence, i.e., the optimal recovery trajectory of the aircraft.

[0012] Preferably, the numerical optimization algorithm in step S5 is IPOPT.

[0013] Preferably, the numerical optimization algorithm in step S5 is SNOPT.

[0014] An aircraft safety envelope boundary protection controller adopts the above-mentioned aircraft optimal recovery trajectory design method based on Bezier shape function, comprising: A state acquisition module is configured to acquire state parameters of the aircraft in real time. A constraint calculation module is configured to construct a composite constraint function. A Bezier trajectory generator is configured to calculate initial control point coordinates of an initial trajectory based on a Bezier curve. An optimization solving module is integrated with a numerical optimization algorithm and is configured to perform iterative optimization with flight time minimization as an optimization index. A dynamics verification unit is configured with an F-16 aircraft aerodynamic parameter database and is configured to verify the feasibility of the recovery trajectory.

[0015] Preferably, the optimization solving module adopts an adaptive step strategy, comprising: When a constraint conflict is detected, the order of the Bezier curve is automatically adjusted. According to the convergence speed of the optimization process, the step size of the optimization iteration is dynamically adjusted. A maximum iteration number threshold is set to prevent the optimization process from diverging.

[0016] Therefore, the present application adopts the above-mentioned aircraft optimal recovery trajectory design method based on Bezier shape function, and has the following beneficial technical effects: (1) The present application introduces Bezier curve into the field of aircraft trajectory planning, converts the recovery trajectory planning problem into a parameter optimization problem of Bezier curve, uses its endpoint interpolation characteristics and convex hull properties to construct an optimal recovery trajectory that meets the end state constraint, and realizes the rapid generation of a time-optimal smooth recovery trajectory while strictly meeting various constraints.

[0017] (2) The method of the present application improves the real-time performance and reliability of trajectory planning, can adapt to different flight states, effectively avoids trajectory oscillation problem, ensures that the aircraft can quickly and smoothly recover to a safe flight state when approaching the safety envelope boundary, and reduces the calculation complexity through parameter optimization, thereby providing an efficient and feasible solution for aircraft boundary protection control. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 The flowchart of the aircraft optimal recovery trajectory design method based on Bezier shape function of the present application; Figure 2is the simulation result of the optimal recovery trajectory planning of the aircraft fast climb according to the application, the height of the upper boundary is 3500m; Figure 3 is the simulation result of the optimal recovery trajectory planning of the aircraft fast climb according to the application, the height of the upper boundary is 3500m. DETAILED DESCRIPTION

[0019] The technical solutions of the application are further described below with reference to the drawings and examples.

[0020] Unless otherwise defined, the technical terms or scientific terms used in the application shall have the usual meanings understood by those skilled in the art to which the application belongs.

[0021] Example 1 As shown in Figure 1 , a Bezier shape function-based aircraft optimal recovery trajectory design method is executed after receiving a boundary protection change-out instruction, including the following steps: Step S1, real-time acquisition of the state parameters of the aircraft and setting as initial state constraints.

[0022] The initial state constraints include initial position , initial speed , initial track pitch angle and initial track yaw angle .

[0023] Initial position constraint: ; Wherein, , , respectively represent the position coordinates of the aircraft in the three-axis coordinate system at the initial time , , , ; represents the -axis coordinate of the initial position of the aircraft; represents the -axis coordinate of the initial position of the aircraft; represents the -axis coordinate of the initial position of the aircraft.

[0024] Initial speed vector constraint (kinematics constraint): According to the speed , initial track pitch angle and initial track yaw angle , the position derivative (i.e. speed component) constraint at the initial time is: ; wherein, denotes the initial time instant the aircraft is in a velocity component in the axis direction; denotes the initial time instant the aircraft is in a velocity component in the axis direction; denotes the initial time instant the aircraft is in a velocity component in the axis direction.

[0025] In the trajectory generation method based on Bezier curves (as claimed in claim 5), the above-mentioned physical constraints are usually converted into geometric constraints of the control points, (i.e. the 0th control point of the Bezier curve) is directly equal to the initial position, and the specific expression is: ; wherein, denotes the transpose.

[0026] Step S2, define the terminal state and set the terminal state constraint.

[0027] The embodiment defines the terminal state as the steady flight state at the 500m height from the upper boundary and the lower boundary of the safety envelope, thereby obtaining the position and attitude constraints of the terminal state of the recovery trajectory, denoted as the terminal position , the terminal velocity , the terminal flight path pitch angle and the terminal yaw angle . The terminal state constraint includes the terminal height constraint, the terminal attitude and velocity constraint and the terminal velocity vector constraint.

[0028] Terminal height constraint (position constraint): according to different recovery directions, the target height is calculated as follows: ; wherein, denotes the upper boundary safety height of the safety envelope; denotes the lower boundary safety height of the safety envelope; denotes the safety redundancy distance.

[0029] Terminal attitude and velocity constraint (steady flight condition): since steady flight is required, the terminal flight path pitch angle must be forced to be zero, and the specific expression is: ; wherein, denotes the flight speed of the aircraft at the trajectory terminal time instant ; denotes the flight speed of the aircraft at the trajectory terminal time instant azimuth of the position.

[0030] End velocity vector constraint (kinematic constraint): Substitute the above level flight condition into the velocity decomposition formula ( , ), to obtain the position derivative constraint at the end time. This is a key formula for constraining the direction of the tangent at the end of the Bezier curve in the optimization algorithm, and the specific expression is: ; wherein, denotes the velocity component of the aircraft in the direction of the x-axis at the end time of the trajectory; denotes the velocity component of the aircraft in the direction of the y-axis at the end time of the trajectory; denotes the velocity component of the aircraft in the direction of the z-axis at the end time of the trajectory. denotes the velocity component of the aircraft in the direction of the x-axis at the end time of the trajectory; denotes the velocity component of the aircraft in the direction of the y-axis at the end time of the trajectory; denotes the velocity component of the aircraft in the direction of the z-axis at the end time of the trajectory.

[0031] Step S3, constructing a composite constraint function.

[0032] The composite constraint function includes initial state constraints, end state constraints, height boundary constraints, velocity boundary constraints, overload constraints, and state quantity constraints.

[0033] The specific expression of the height boundary constraint is: ; wherein, denotes the flight altitude; denotes the minimum value of the allowable flight altitude; denotes the maximum value of the allowable flight altitude.

[0034] The specific expression of the velocity boundary constraint is: ; wherein, denotes the flight velocity; denotes the minimum value of the allowable flight velocity; denotes the maximum value of the allowable flight velocity.

[0035] The specific expression of the overload constraint is: ; wherein, denotes the overload; denotes the lift; denotes the drag; denotes the maximum value of the allowable overload.

[0036] ​​​​The specific expression of the state quantity constraint is: ; ; ; ; wherein, represents an angle of attack; represents a roll angle; represents a sideslip angle; represents a thrust; represents a minimum value allowed for the thrust; represents a maximum value allowed for the thrust; represents a minimum value allowed for the angle of attack; represents a maximum value allowed for the angle of attack; represents a minimum value allowed for the roll angle; represents a maximum value allowed for the roll angle; represents a minimum value allowed for the sideslip angle; represents a maximum value allowed for the sideslip angle.

[0037] The difference between the constrained quantity and the boundary value is integrated into a composite constraint function , and the specific expression is: ; wherein, represents an actual value of the thrust; represents a time step number of trajectory discretization; represents a zero vector.

[0038] Step S4: based on the initial state constraint and the end state constraint, an initial Bezier curve parameter is calculated by using a Bezier curve to generate an initial trajectory.

[0039] In this embodiment, a three-dimensional trajectory parameterization method is used, each axial trajectory is described by an independent Bezier curve, and the order of the initial trajectory is set to 3 to calculate the initial Bezier curve parameter; the initial Bezier curve parameter includes the initial control point coordinates of each axial trajectory.

[0040] The time required for the aircraft to fly from the initial state to the end state is defined as the flight time, and the initial flight time is calculated based on the initial state of the aircraft, and the specific expression is: ; wherein, represents an estimated value of the initial flight time; represents a norm of a vector.

[0041] The basis functions of a third-order Bézier curve are calculated using the following expression: ; ; ; in, This represents the basis functions for calculating Bézier curves; The parameter variables representing the Bézier curve; Represents the control point matrix of a Bézier curve; , , These represent the third-order Bézier curves in... axis, axis, Basis functions in the axial direction; , , These represent the third-order Bézier curves in... axis, axis, The first derivative of the basis functions along the axial direction; , , These represent the third-order Bézier curves in... axis, axis, The second derivative of the basis functions in the axial direction.

[0042] The initial control point coordinates for each axis trajectory are calculated from the initial flight time and basis functions. Taking the axis as an example, the specific expression is: ; ; ; ; in, Represents a third-order Bézier curve The first control point in the axial direction; Indicates the initial state of the aircraft Axis position coordinates; Represents a third-order Bézier curve The second control point in the axial direction; Indicates the initial time. Velocity components in the axial direction; express The total number of control points for the Bézier curve in the axial direction; Represents a third-order Bézier curve The third control point in the axial direction; representing the end time velocity component in the axis direction; representing the end of the aircraft axis position coordinates; representing the 3rd order Bezier curve the 4th control point in the axis direction.

[0043] According to the initial control point coordinates and the basis function, an initial trajectory is generated, and the specific expression is: ; wherein, , , respectively represent axis, axis, axis direction initial trajectory position sequence; , , respectively represent axis, axis, axis direction Bezier curve initial control point matrix; , , respectively represent axis, axis, axis position derivative estimate; , , respectively represent axis, axis, axis basis function matrix; represent order unit matrix.

[0044] Step S5, taking the initial Bezier curve parameters as the optimization initial value, taking the flight time minimization as the optimization index, iteratively optimizing the Bezier curve parameters, and verifying the feasibility of the recovery trajectory by using the dynamics model, and finally generating the optimal recovery trajectory. Specifically includes: Step S501, taking the initial Bezier curve parameters as the optimization initial value, taking the flight time minimization as the optimization index, converting the trajectory optimization problem into a nonlinear programming problem of the Bezier curve parameters, and the specific expression is: ; wherein, representing the initial value vector of the nonlinear programming; representing the total number of control points of the axis direction Bezier curve; representing the total number of control points of the axis direction Bezier curve; This means taking the 3rd row to the 4th row of the matrix. Row matrix index; This means taking the 3rd row to the 4th row of the matrix. Row matrix index; This means taking the 3rd row to the 4th row of the matrix. Row matrix index.

[0045] Step S502: The nonlinear programming problem of Bézier curve parameters is solved iteratively using a numerical optimization algorithm; in each iteration, candidate trajectories are generated based on the current Bézier curve parameters and flight time.

[0046] Numerical optimization algorithms employ IPOPT (internal point method) or SNOPT (sequential quadratic programming method).

[0047] Step S503: Using the dynamic model, perform reverse calculation on the candidate trajectory and solve the corresponding aircraft state variables based on the three-dimensional trajectory.

[0048] The parameters of the dynamic model are set to the actual data of the maneuvering aircraft, including fuselage mass, reference wing area, aerodynamic database (lift and drag coefficient table), and engine thrust model.

[0049] The coordinates of the control points along each axis are calculated based on the control quantity sequence obtained from the optimization solution (i.e., the parameters of the intermediate control points of the Bézier curve). Taking the axis as an example, the trajectory coordinates are generated using Bernstein basis functions, and the specific expression is as follows: ; in, Indicates the Bézier curve in terms of parameters corresponding Axial position coordinates; This indicates the order of the Bézier curve, which is set to 3 in this embodiment; express The first axial direction Bézier curve Coordinates of control points; Represents the binomial coefficient; This represents the first part of the Bernstein basis functions; This represents the second part of the Bernstein basis functions.

[0050] The coordinates of the control points are calculated based on the control quantity sequence. Taking the axis as an example, the specific expression is: ; ; ; ; ; in, express Control point matrix of Bézier curves in the axial direction; This represents the result obtained from the nonlinear programming optimization solution. The matrix of optimal solutions along the axial direction; express The 3rd line to the 4th line OK; express The first line; express The second line; Indicates the flight time of the candidate trajectory; express The OK; express The OK.

[0051] The coordinates of the three-dimensional trajectory points are obtained from the coordinates of the control points. Taking the axis as an example, the specific expression is: ; ; ; ; ; in, express The coordinates of the trajectory points along the axis; express Normalized velocity components of the trajectory along the axis; express The basis function matrix of the Bézier curve along the axial direction; express The first derivative matrix of the basis functions of the Bézier curve in the axial direction; express Normalized acceleration components of the trajectory in the axial direction; express The second derivative matrix of the basis functions of the Bézier curve in the axial direction; express The actual velocity components of the trajectory along the axial direction; express The true acceleration components of the trajectory in the axial direction.

[0052] Step S504: Compare the calculated aircraft state variables with the composite constraint function to determine whether the constraints are satisfied and verify the feasibility of the candidate trajectory.

[0053] If satisfied, i.e. If this indicates that the candidate trajectory is feasible, then the flight time of this candidate trajectory is calculated. That is, the objective function The value. (To be) Compared with the current optimal flight time found in previous iterations If a comparison is made, Then let And record the Bézier curve parameters of this candidate trajectory; if , It remains unchanged.

[0054] If not satisfied, that is If the candidate trajectory is deemed infeasible, it is discarded and a new candidate trajectory is generated.

[0055] Step S505: Repeat steps S502 to S504 until the maximum number of iterations is reached, and output the aircraft's optimal recovery trajectory sequence that is both time-optimal and dynamically feasible, i.e., the aircraft's optimal recovery trajectory.

[0056] This embodiment simulates the optimal recovery trajectory planning for rapid aircraft climb, with the upper boundary height set at 3500m. The simulation results are as follows: Figure 2 As shown, the optimal recovery trajectory generated by the method in this embodiment demonstrates how the aircraft smoothly, quickly, and automatically recovers from a dangerous state near the upper boundary, eventually stabilizing in level flight at a height of 500 meters (3000 meters) below the upper boundary. This proves that the method in this embodiment can effectively handle boundary protection problems near the upper limit.

[0057] This embodiment simulates the optimal recovery trajectory planning for a rapid descent of an aircraft, with the lower boundary height set at 5200m. The simulation results are as follows: Figure 3 As shown, the optimal recovery trajectory generated by the method in this embodiment demonstrates how an aircraft is pulled up from a dive and smoothly recovers to a level flight state 500 meters above the lower boundary (i.e., 5700 meters above the ground). This proves that the method in this embodiment can effectively handle boundary protection problems close to the lower limit (more dangerous, preventing a collision with the ground).

[0058] An aircraft safety envelope boundary protection controller, employing the aforementioned aircraft optimal recovery trajectory design method based on Bezier functions, includes: The status acquisition module is used to acquire the status parameters of the aircraft in real time.

[0059] The constraint calculation module is used to construct composite constraint functions.

[0060] A Bezier trajectory generator used to calculate the coordinates of the initial control points for an initial trajectory based on a Bezier curve.

[0061] The optimization solution module integrates numerical optimization algorithms such as IPOPT or SNOPT for iterative optimization with minimizing flight time as the optimization metric.

[0062] The optimization solution module employs an adaptive step-size strategy, including: (1) When a constraint conflict is detected, the order of the Bézier curve is automatically adjusted.

[0063] (2) Adjust the step size of the optimization iteration dynamically according to the convergence speed of the optimization process.

[0064] (3) Set a maximum iteration threshold to prevent the optimization process from diverging.

[0065] The dynamics verification unit is equipped with an F-16 aircraft aerodynamic parameter database to verify the feasibility of trajectory recovery.

[0066] Therefore, the present invention adopts the above-mentioned aircraft optimal recovery trajectory design method based on Bezier function, which solves the technical problem of existing technology that it is difficult to quickly generate a recovery trajectory that takes into account smoothness, dynamic constraints and optimality when the aircraft approaches the safety envelope boundary. By realizing fast trajectory optimization under complex constraints, it effectively balances computational efficiency and trajectory optimality, improves the real-time performance and reliability of boundary protection control, ensures that the aircraft can quickly recover stable flight within the safety envelope boundary, and reduces the risk of control oscillation.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for designing the optimal recovery trajectory of an aircraft based on Bezier functions, characterized in that, Upon receiving the boundary protection changeout instruction, the following steps are executed: Step S1: Acquire the aircraft's state parameters in real time and set them as initial state constraints; Step S2: Define the endpoint state and set endpoint state constraints; Step S3: Construct composite constraint functions; Step S4: Based on the initial state constraints and the final state constraints, calculate the initial Bézier curve parameters using Bézier curves to generate the initial trajectory; Step S5: Using the initial Bézier curve parameters as the initial optimization values ​​and minimizing the flight time as the optimization index, iteratively optimize the Bézier curve parameters, and use the dynamic model to verify the feasibility of the recovery trajectory, and finally generate the optimal recovery trajectory.

2. The method for designing the optimal recovery trajectory of an aircraft based on Bezier functions according to claim 1, characterized in that, In step S1, the initial state constraints include the initial position, initial velocity, initial trajectory pitch angle, and initial trajectory yaw angle.

3. The method for designing the optimal recovery trajectory of an aircraft based on Bezier functions according to claim 1, characterized in that, In step S2, the endpoint state is defined as the level flight state at a certain safe distance from the upper and lower boundaries of the safety envelope; the endpoint state constraints include endpoint altitude constraints, endpoint attitude and velocity constraints, and endpoint velocity vector constraints.

4. The method for designing the optimal recovery trajectory of an aircraft based on Bezier functions according to claim 1, characterized in that, In step S3, the composite constraint function includes initial state constraints, final state constraints, height boundary constraints, velocity boundary constraints, overload constraints, and state quantity constraints.

5. The method for designing the optimal recovery trajectory of an aircraft based on Bezier functions according to claim 1, characterized in that, In step S4, a three-dimensional trajectory parameterization method is used to describe the trajectory of each axis through independent Bézier curves, and the order of the initial trajectory is set to 3 to calculate the initial Bézier curve parameters; the initial Bézier curve parameters include the coordinates of the initial control points of each axis trajectory.

6. The method for designing the optimal recovery trajectory of an aircraft based on a Bezier function according to claim 1, characterized in that, Step S5 specifically includes: Step S501: Using the initial Bézier curve parameters as the initial optimization values ​​and minimizing flight time as the optimization index, the trajectory optimization problem is transformed into a nonlinear programming problem for the Bézier curve parameters. Step S502: The nonlinear programming problem of the Bézier curve parameters is solved iteratively using a numerical optimization algorithm; in each iteration, candidate trajectories are generated based on the current Bézier curve parameters and flight time. Step S503: Using the dynamic model, perform reverse calculation on the candidate trajectory and calculate the corresponding aircraft state variables based on the three-dimensional trajectory. Step S504: Compare the calculated aircraft state variables with the composite constraint function to determine whether they meet the dynamic constraints and state constraints, and verify the feasibility of the candidate trajectory. Step S505: Repeat steps S502 to S504 until the maximum number of iterations is reached, and output the aircraft's optimal recovery trajectory sequence that is both time-optimal and dynamically feasible, i.e., the aircraft's optimal recovery trajectory.

7. The method for designing the optimal recovery trajectory of an aircraft based on a Bezier function according to claim 6, characterized in that, The numerical optimization algorithm in step S5 is IPOPT.

8. The method for designing the optimal recovery trajectory of an aircraft based on a Bezier function according to claim 6, characterized in that, The numerical optimization algorithm in step S5 is SNOPT.

9. An aircraft safety envelope boundary protection controller, used to implement the method as described in any one of claims 1-8, characterized in that, include: The status acquisition module is used to acquire the status parameters of the aircraft in real time; The constraint calculation module is used to construct composite constraint functions; A Bézier trajectory generator for calculating the coordinates of initial control points based on a Bézier curve; The optimization solution module integrates numerical optimization algorithms for iterative optimization with minimization of flight time as the optimization metric. The dynamics verification unit is equipped with an F-16 aircraft aerodynamic parameter database to verify the feasibility of trajectory recovery.

10. A spacecraft safety envelope boundary protection controller according to claim 9, characterized in that, The optimization solution module employs an adaptive step-size strategy, including: When a constraint conflict is detected, the order of the Bézier curve is automatically adjusted. The step size of the optimization iteration is dynamically adjusted according to the convergence speed of the optimization process. Set a maximum iteration threshold to prevent the optimization process from diverging.

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