A method for optimizing reentry trajectories of morphing aircraft

Abstract

The present application belongs to the technical field of trajectory optimization of morphing aircraft, and specifically discloses a reentry trajectory optimization method of morphing aircraft, comprising: establishing a reentry dynamics model and a multi-constraint condition model of the morphing aircraft; constructing a minimum drag coefficient configuration-Mach number profile and a reentry height flight corridor, and converting the trajectory optimization problem of the morphing aircraft into a trajectory optimization problem with a fixed aerodynamic shape; performing dimensionless, linearization and discretization processing on the reentry dynamics model, and introducing a control quantity transformation, so as to convert the trajectory optimization problem into a standard second-order cone programming problem; using a primal-dual interior point method to discretely solve the second-order cone programming problem, so as to obtain an optimal reentry trajectory satisfying all constraint conditions, and complete the reentry trajectory optimization method of the morphing aircraft. The present application avoids calculating the configuration parameter derivative in the trajectory optimization, and solves the problem that the derivative information of the configuration parameter cannot be obtained from the aerodynamic data.

Description

Technical Field

[0001] This invention belongs to the field of trajectory optimization technology for variable configuration aircraft, and specifically relates to a method for optimizing the reentry trajectory of a variable configuration aircraft. Background Technology

[0002] Traditional fixed-configuration aircraft are typically designed for specific missions and exhibit good performance under limited operating conditions, but their singular aerodynamic shape cannot adapt to the complex mission requirements spanning multiple airspaces and speed ranges. In contrast, variable-configuration aircraft can dynamically adjust configuration parameters (such as wing sweep angle and span) according to mission requirements, maintaining superior aerodynamic performance within the flight envelope. However, the configuration switching process of variable-configuration aircraft significantly affects its aerodynamic performance and is tightly coupled with trajectory optimization. Existing trajectory optimization methods typically use configuration parameters as decision variables for joint trajectory-configuration optimization, requiring derivative information of aerodynamic data with respect to configuration parameters. Due to the high cost of high-precision aerodynamic calculations, only a small amount of discrete aerodynamic data for typical configurations is usually available during the feasibility study and early ballistic design stages, making it difficult to provide derivative information. This makes it challenging to effectively combine configuration switching and trajectory optimization under limited configuration aerodynamic data conditions. Summary of the Invention

[0003] The purpose of this invention is to solve the problem that aerodynamic data is not available for the derivative information of configuration parameters, and to propose a method for optimizing the reentry trajectory of a variable configuration aircraft.

[0004] The technical solution of this invention is: a method for optimizing the reentry trajectory of a variable-configuration aircraft, comprising the following steps: Establish a reentry dynamics model and a multi-constraint model for a variable-configuration aircraft; By constructing the minimum drag coefficient configuration-Mach number profile and reentry altitude flight corridor, the trajectory optimization problem of variable configuration aircraft is transformed into a trajectory optimization problem with a fixed aerodynamic shape; The reentry dynamics model is dimensionless, linearized, and discretized. Control variables are introduced to transform the multi-constraint model into a constraint of the rate of change of the tilt angle, and the trajectory optimization problem with a fixed aerodynamic shape is transformed into a standard second-order cone programming problem. The original dual interior point method is used to discretize and solve the second-order cone programming problem, obtaining the optimal reentry trajectory that satisfies all constraints, thus completing the reentry trajectory optimization method for variable configuration aircraft.

[0005] As a preferred option, the dynamic equations of the variable configuration aircraft are:

[0006]

[0007]

[0008] in, , and Indicates the geocentric distance, longitude, and latitude of the variable-configuration aircraft; This indicates the Mach number of a variable-configuration aircraft. , and Indicates the track angle, heading angle, and roll angle; and This represents the lift and drag of a variable-configuration aircraft. Indicates the mass of a variable-configuration aircraft; This represents gravity plus Mach number; Represents the sine function. Represents the cosine function. Represents the tangent function; and The lift and drag coefficients of a variable-configuration aircraft are represented by the Mach number. Configuration and attack angle Joint decision; Indicates the reference area; This indicates the atmospheric density at the altitude of the variable-configuration aircraft.

[0009] As a preferred option, multi-constraint models include: Aircraft stagnation point heat flux density constraint:

[0010] in, This represents the heat flux density at the stagnation point of the aircraft. This indicates the maximum heat flux density at the stagnation point of the aircraft; Indicates the heat flux coefficient; Indicates atmospheric density; This indicates the Mach number of a variable-configuration aircraft. Dynamic pressure constraint:

[0011] in, Indicates dynamic pressure; Indicates the maximum dynamic pressure; Pneumatic overload constraint:

[0012] in, Indicates pneumatic overload; Indicates the maximum pneumatic overload value; and This represents the lift and drag of a variable-configuration aircraft. Indicates the mass of a variable-configuration aircraft; This represents gravity plus Mach number; Access equilibrium gliding equation constraints:

[0013] in, Indicates the tilt angle; Indicates the geocentric distance of a variable-configuration aircraft; This represents the cosine function.

[0014] As a preferred option, the minimum drag coefficient configuration is a function of the Mach number profile. Specifically:

[0015] in, This represents the target minimum drag coefficient. Indicates configuration, The Mach number is represented by the drag coefficient-Mach number profile when the configuration-Mach number profile that optimizes a certain performance index is determined. and lift coefficient-Mach number profile The unique determination transforms the trajectory optimization problem of the variable configuration aircraft into a trajectory optimization problem with a fixed aerodynamic shape. As a preferred option, the lower boundary of the reentry altitude flight corridor for:

[0016] in, Indicates reference altitude. This represents a logarithmic function with the natural constant as its base. Indicates reference air pressure. The Mach number represents the variable configuration aircraft. This indicates the maximum dynamic pressure. Indicates the reference area. Indicates the optimal lift coefficient. This represents the optimal drag coefficient. Indicates the mass of a variable-configuration aircraft. This represents gravity plus Mach number. Indicates the maximum pneumatic overload. Indicates the heat flux coefficient. Indicates the maximum heat flux density; Upper boundary of the re-entry altitude flight corridor for:

[0017] in, Indicates the reference distance from the Earth's center.

[0018] As a preferred approach, the reentry dynamics model is dimensionless, linearized, and discretized, and a control variable is introduced to transform the multi-constraint model into a constraint on the rate of change of the tilt angle. This method, which transforms the trajectory optimization problem into a standard second-order cone programming problem, is as follows: Determine the relationship between the dimensionless Mach number, the dimensionless geocentric distance, and the dimensionless energy; Based on the relationship between dimensionless Mach number, dimensionless geocentric distance, and dimensionless energy, as well as three assumptions, the reentry dynamics model is reduced in order to obtain the reduced-order state dynamics equations for the modified configuration aircraft. By introducing the rate of change of the roll angle as a control variable, the constraints of the stagnation point heat flux density, dynamic pressure, aerodynamic overload, and quasi-equilibrium gliding equation are transformed into constraints on the rate of change of the roll angle. A first-order Taylor expansion is performed on the non-convex terms in the reduced-order variable-configuration aircraft state dynamics equation to obtain a linearized variable-configuration aircraft state dynamics equation, and a credibility region constraint is introduced to ensure the effectiveness of the linearized region. The linearized state dynamics equations of the variable configuration aircraft are discretized using the trapezoidal integral method to obtain the state update equations for each segment, thus constructing a standard second-order cone programming problem.

[0019] As a preferred option, the three assumptions are: the trajectory during flight satisfies... The variable-configuration aircraft exhibits minimal altitude change relative to range change during reentry, satisfying the requirement... The flight altitude of the aircraft relative to the Earth's radius satisfies ; Indicates the angular velocity of the trajectory. Indicates the track angle; The state dynamics equations for a reduced-order variable-configuration aircraft are:

[0020] in, and Indicates the longitude and latitude angles of a variable-configuration aircraft. and Indicates the heading angle and the heel angle. and This represents the lift coefficient and drag coefficient of a variable configuration aircraft.

[0021] Preferably, the constraint regarding the rate of change of the tilt angle is:

[0022]

[0023] Indicated by energy The tilt angle is the independent variable. Indicates energy The maximum roll angle allowed when simultaneously satisfying the stagnation point heat flux density constraint, dynamic pressure constraint, and aerodynamic overload constraint of the aircraft; This represents the initial roll angle under the assumption of quasi-equilibrium gliding; This represents the terminal roll angle under the assumption of entry equilibrium gliding; Indicates the initial altitude of the aircraft; This indicates the initial energy of the aircraft; Indicates the terminal altitude of the aircraft; This indicates the terminal energy of the aircraft.

[0024] As a preferred option, the reduced-order variable configuration aircraft's state dynamics equations are:

[0025] in, Indicates the energy of the aircraft; Represents the state vector with respect to the spacecraft energy. The derivative; Represents state variables, Indicates longitude angle, Indicates latitude angle, Indicates the heading angle. Indicates the tilt angle; Indicates the energy of the aircraft The rate of change of the tilt angle is the control variable. This represents the control input allocation matrix; This represents the nonlinear drift term of the system. Indicates the lift coefficient. Indicates the drag coefficient. Indicates the lift-to-drag ratio. Indicates dimensionless velocity; For nonlinear drift terms In the Reference state of the next iteration Performing a first-order Taylor expansion, we obtain the linearized state dynamics equations for the variable-configuration aircraft:

[0026] in, Represents the nonlinear drift term Relative to state variables The Jacobian matrix; This represents the affine offset term after linearization; To ensure the effectiveness of linearization, the optimal state variable must be in the first position. Within a finite neighborhood of the reference state in the next iteration, a trust region constraint is introduced:

[0027] in, This indicates taking the absolute value of each component of the vector; This represents the radius vector of the trust region, used to constrain the state variables in this iteration relative to the reference state. The deviation range; It represents the four-dimensional real space.

[0028] As a preferred approach, the method of discretizing the linearized state dynamics equations of the variable configuration aircraft using the trapezoidal integral method to obtain the state update equations for each segment, and constructing the standard second-order cone programming problem, is as follows: energy range Uniformly discretized _ sub-intervals, _ total _ The discrete node, the first The discrete nodes are represented as follows:

[0029] in, Represents the initial energy. Indicates terminal energy. Indicates the first Energy of discrete nodes This represents the energy step size between adjacent discrete nodes; Definition of the first The state variables and control variables at each discrete node are as follows:

[0030] in, Indicates the first The state vector at each energy node. Indicates the first Control inputs at each energy node; The linearized state-dynamic equations of the variable-configuration aircraft are discretized using the trapezoidal integral method to obtain the first... The node and the first State update equations between nodes:

[0031]

[0032] in, and Representing two adjacent discrete nodes respectively and The state vector at that location; and These represent the control inputs at two adjacent discrete nodes, respectively. Indicates the first During the next iteration, at node Affine offset term at the location; Indicates the first During the next iteration, at node Affine offset term at the location; and Representing the discretized state vector and the state vector respectively and The corresponding coefficient matrix; and They represent the discretized result and the control input, respectively. and The corresponding coefficient matrix; express identity matrix; and They represent the first During the next iteration, at node and Jacobian matrix at the location; Let be a constant matrix, then... ; All state update constraints are uniformly represented as a set of linear constraints:

[0033] in, This represents the optimization decision vector composed of all discrete node state variables and control variables; This represents the overall constraint coefficient matrix formed by concatenating the coefficient matrices corresponding to the state update equations of each discrete interval in blocks; Represents the terms on the right-hand side of each discrete interval The overall constant vector formed by sequentially stacking is combined with the reentry altitude flight corridor constraint, the rate of change of the roll angle constraint, and the confidence region constraint to construct a standard second-order cone programming problem.

[0034] The beneficial effects of this invention are: 1. This invention transforms a variable configuration aircraft model into an equivalent fixed configuration aircraft model by using a minimum drag coefficient configuration profile, thereby avoiding dependence on the derivatives of configuration parameters and overcoming the problem of missing aerodynamic data during configuration switching.

[0035] 2. This invention constructs a standard second-order cone optimization problem and solves it using the primal dual interior point method. This approach can reduce the solution time and improve the solution efficiency while ensuring high optimization accuracy, and it has the potential for real-time optimization. Attached Figure Description

[0036] Figure 1 The diagram shows a flowchart of a reentry trajectory optimization method for a variable configuration aircraft provided in Example 1.

[0037] Figure 2 The figure shown is a schematic diagram of the external shape of the variable configuration aircraft provided in Example 1.

[0038] Figure 3 The figure shows the lift coefficient-Mach number curves for the three fixed configurations provided in Example 1.

[0039] Figure 4 The figure shows the drag coefficient-Mach number curves for the three fixed configurations provided in Example 1.

[0040] Figure 5 The diagram shown is a schematic of the fixed configuration 1 H-Ma flight corridor provided in Embodiment 1.

[0041] Figure 6 The diagram shown is a schematic of the fixed configuration 2 H-Ma flight corridor provided in Embodiment 1.

[0042] Figure 7 The diagram shown is a schematic of the fixed configuration 3 H-Ma flight corridor provided in Embodiment 1.

[0043] Figure 8 The figure shown is a cross-sectional view of the minimum drag coefficient configuration provided in Example 1.

[0044] Figure 9 The figure shows the lift coefficient corresponding to the minimum drag coefficient configuration profile provided in Example 1.

[0045] Figure 10 The figure shows the drag coefficient corresponding to the minimum drag coefficient configuration profile provided in Example 1.

[0046] Figure 11 The image shows the H-Ma flight corridor with the minimum drag coefficient configuration provided in Example 1.

[0047] Figure 12 The figure shows the latitude and longitude of all reentry trajectories in the solution results provided in Example 2.

[0048] Figure 13 The figure shows the height-Mach number curves of all reentry trajectories in the solution results provided in Example 2.

[0049] Figure 14 The figure shows the track angle-Mach number curves of all reentry trajectories in the solution results provided in Example 2.

[0050] Figure 15 The figure shows the tilt angle-Mach number curves of all reentry trajectories in the solution results provided in Example 2. Detailed Implementation

[0051] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, and are not intended to limit the scope of the invention.

[0052] Example 1: like Figure 1 As shown, a method for optimizing the reentry trajectory of a variable-configuration aircraft includes the following steps: S1. Establish the reentry dynamics model and multi-constraint model of the variable configuration aircraft; S2. Construct the minimum drag coefficient configuration-Mach number profile and reentry altitude flight corridor to transform the trajectory optimization problem of variable configuration aircraft into a trajectory optimization problem with a fixed aerodynamic shape; S3. The reentry dynamics model is dimensionless, linearized, and discretized, and a control variable is introduced to transform the multi-constraint model into a constraint of the rate of change of the tilt angle, thus transforming the trajectory optimization problem with a fixed aerodynamic shape into a standard second-order cone programming problem. S4. The original dual interior point method is used to discretize and solve the second-order cone programming problem to obtain the optimal reentry trajectory that satisfies all constraints, thus completing the reentry trajectory optimization method for variable configuration aircraft.

[0053] In this embodiment, step S1 specifically includes the following steps: Variable configuration aircraft shape like Figure 2 As shown, for the various typical configurations of a variable-configuration aircraft, the motion of the aircraft's center of mass follows the same kinematic equations, the basic form of which is:

[0054] in, These represent the geocentric distance, longitude, and latitude of the aircraft, respectively. Indicates the Mach number of the aircraft; These represent the track angle, heading angle, and roll angle, respectively. and These represent the lift and drag of an aircraft, respectively. For the mass of the aircraft; This is gravity plus the Mach number.

[0055] lift of aircraft and resistance Calculated using the following formula:

[0056]

[0057] in, and These are the lift coefficient and drag coefficient of an aircraft, respectively, determined by the Mach number. configuration Angle of attack Joint decision; This is a reference area; It is the atmospheric density at the altitude of the aircraft.

[0058] In this embodiment of the invention, three fixed configurations are taken as examples. The constrained form of the stagnation point heat flux density of the aircraft is as follows:

[0059] in, The heat flux coefficient is... Atmospheric density, This represents the flight Mach number.

[0060] The dynamic pressure constraint is expressed as:

[0061] The aerodynamic overload constraint forms are as follows:

[0062] The entry equilibrium gliding equation constraints are as follows:

[0063] The angle-of-attack-Mach number profile of the reentry vehicle is designed as follows:

[0064] in, , These are the initial and terminal angles of attack, respectively. The initial Mach number for the angle of attack transition. To end the Mach number.

[0065] Based on the aforementioned preset angle of attack-Mach number profile, the relationship between the lift coefficient and drag coefficient of the three fixed configurations in this application embodiment as a function of Mach number is shown in Figures 3 and 4, respectively.

[0066] Under standard atmospheric conditions, atmospheric density decreases exponentially with altitude, as expressed by the following basic expression:

[0067] in For reference height, For reference air pressure.

[0068] Based on a pre-defined angle-of-attack-Mach number profile, the aerodynamic parameters of an aircraft with the same configuration can be uniquely determined relative to the Mach number, thereby transforming various path constraints into upper and lower boundaries relative to the Mach number. The corresponding altitude boundary is expressed as follows:

[0069]

[0070] In this embodiment of the invention, three fixed configurations of the H-Ma flight corridor, such as Figure 5 , Figure 6 As shown in Figure 7.

[0071] In this embodiment, step S2 specifically includes the following steps: Based on the preset angle of attack-Mach number profile, and according to the target minimum drag coefficient Selecting the optimal configuration at each Mach number, the minimum drag coefficient configuration-Mach number profile function. The expression is as follows:

[0072] When the configuration-Mach number profile that optimizes a certain performance index is determined, the drag coefficient-Mach number profile is... and lift coefficient-Mach number profile The unique determination transforms the trajectory optimization problem of a variable configuration aircraft into a trajectory optimization problem with a fixed aerodynamic shape. The configuration parameters are set as functions of the Mach number rather than optimization decision variables, thus avoiding the calculation of the derivatives of the configuration parameters in trajectory optimization.

[0073] The expression for the altitude flight corridor at the minimum drag coefficient configuration-Mach number profile can be derived from the optimal drag coefficient. and optimal lift coefficient The only certainty: The final lower boundary of the flight corridor is:

[0074] in, Indicates reference altitude. This represents a logarithmic function with the natural constant as its base. Indicates reference air pressure. The Mach number represents the variable configuration aircraft. This indicates the maximum dynamic pressure. Indicates the reference area. Indicates the optimal lift coefficient. This represents the optimal drag coefficient. Indicates the mass of a variable-configuration aircraft. This represents gravity plus Mach number. Indicates the maximum pneumatic overload. Indicates the heat flux coefficient. Indicates the maximum heat flux density; The expression for the upper boundary of the flight corridor is:

[0075] in, Indicates the reference distance from the Earth's center.

[0076] Three configurations are known The corresponding aerodynamic coefficient, let This allows us to obtain the minimum drag coefficient configuration-Mach number profile function under the minimum drag coefficient index. Its expression is:

[0077] Figure 8 shows the drag coefficient variation curves of three typical configurations at different Mach numbers, and marks the configuration switching points, i.e., the intersection points of the drag coefficient curves of each configuration. The figure uses a dual vertical axis design, with the right side representing the span-to-length ratio and the left side representing the drag coefficient, and the horizontal axis representing the Mach number. As can be seen from the figure, under the strategy of optimizing for the minimum drag coefficient, the optimal configuration of the aircraft will be dynamically adjusted with the change of Mach number. Therefore, the minimum drag coefficient configuration-Mach number profile function under the minimum drag coefficient index can be obtained. for:

[0078] Based on the minimum drag coefficient configuration-Mach number profile function, the Mach number profiles of the lift coefficient and drag coefficient of the optimal configuration can be obtained, as shown below. Figure 9 and Figure 10 As shown.

[0079] Figure 11 The figure illustrates the H-V flight corridor under the minimum drag coefficient configuration profile. Three types of path constraints are also plotted: overload, heat flux density, and dynamic pressure, as well as the entry equilibrium gliding condition constraint. It can be seen that throughout the entire Mach number range, the maximum overload constraint remains at the top, becoming the dominant limiting factor at the lower boundary.

[0080] In this embodiment, step S3 transforms the trajectory optimization problem of a variable configuration aircraft into a fixed configuration trajectory optimization problem with time-varying aerodynamic parameters based on the variation law of lift coefficient and drag coefficient with Mach number. The specific method for constructing a standard second-order cone programming problem by performing model order reduction, dimensionless transformation, and linearization on the motion equations, and introducing control variable transformation, is as follows: To improve optimization efficiency and reduce computational complexity, this embodiment of the invention reduces the order of the aircraft's motion equations based on the following three assumptions.

[0081] Assuming the trajectory fluctuations during flight are small, satisfying , This represents the angular velocity of the flight path; it is assumed that the change in altitude of the aircraft during the reentry phase is minimal relative to the change in range, therefore Assuming the aircraft's flight altitude is relatively small compared to the Earth's radius. .

[0082] Define the following dimensionless variables: Dimensionless Mach number:

[0083] Dimensionless geocentric distance:

[0084] Dimensionless energy:

[0085] in, The standard gravity plus the Mach number, For the Earth's radius, For the aircraft's Mach number, This is the distance from the Earth's center to the aircraft.

[0086] According to the definition of dimensionless energy, the Mach number... It can be calculated using the following relationship:

[0087] and These are the directional overloads of lift and drag, respectively, expressed as:

[0088]

[0089] Based on the above three model assumptions, the motion equations of the aircraft can be simplified, improving the efficiency of trajectory optimization.

[0090] The simplified formula for calculating Mach number is:

[0091] Based on the access equilibrium assumption, normalized lift The relationship with the flight Mach number is as follows:

[0092] Similarly, normalized drag plus Mach number The formula is:

[0093] By differentiating the dimensionless energy expression, we can obtain

[0094] From this we can obtain

[0095] Based on the above simplification, the reduced-order equations of motion for the aircraft can be expressed as:

[0096] in, and Indicates the longitude and latitude angles of a variable-configuration aircraft. and Indicates the heading angle and the heel angle. and This represents the lift coefficient and drag coefficient of the variable configuration aircraft. To avoid sudden jumps in the roll angle during optimization, which could lead to an uneven trajectory, this embodiment of the invention introduces the rate of change of the roll angle with energy as a control variable, namely:

[0097] Constraints such as altitude, dynamic pressure, heat flux density, and overload in the flight path cannot be directly applied to the reduced-order state equations. Based on the aforementioned assumptions, these constraints can be transformed through variable relationships in the energy domain and uniformly expressed as upper and lower bounds for the roll angle:

[0098] in, In energy The maximum allowable tilt angle when the constraints of heat flow, dynamic pressure, and overload are met.

[0099] The expression for the downslope angle under the smooth gliding assumption can be obtained as follows:

[0100] When the dimensionless height is at its minimum, the tilt angle reaches its maximum value, and the expression for the maximum tilt angle can be obtained as follows:

[0101] In addition, to satisfy the boundary conditions, the dip angles at the beginning and end points must meet the following requirements:

[0102] in, Indicated by energy The tilt angle is the independent variable. Indicates energy The maximum roll angle allowed when simultaneously satisfying the stagnation point heat flux density constraint, dynamic pressure constraint, and aerodynamic overload constraint of the aircraft; This represents the initial roll angle under the assumption of quasi-equilibrium gliding; This represents the terminal roll angle under the assumption of entry equilibrium gliding; Indicates the initial altitude of the aircraft; This indicates the initial energy of the aircraft; Indicates the terminal altitude of the aircraft; This indicates the terminal energy of the aircraft.

[0103] The reduced-order state dynamics of the aircraft can be written in the following form:

[0104] in, Indicates the energy of the aircraft; Represents the state vector with respect to energy The derivative; Represents state variables, Indicates longitude angle, Indicates latitude angle, Indicates the heading angle. Indicates the tilt angle; Indicated by energy The rate of change of the tilt angle is the control variable. This represents the control input allocation matrix. (Vector) The nonlinear drift term of the system is expressed as follows:

[0105] in, Indicates the lift coefficient. Indicates the drag coefficient. Indicates the lift-to-drag ratio. This indicates a dimensionless velocity.

[0106] To obtain the convex optimization solution structure, for At the last iteration point Performing a first-order Taylor expansion, we obtain the linearized model:

[0107] in: Represents nonlinear terms Relative to state variables The Jacobian matrix; This represents the affine offset term after linearization.

[0108] To ensure the effectiveness of the linearized region, the optimization state variable must be in the first position. Within a finite neighborhood of the reference state in the next iteration, a trust region constraint is introduced:

[0109] in, This indicates taking the absolute value of each component of the vector; This represents the radius vector of the trust region, used to constrain the state variables in this iteration relative to the reference state. The deviation range; It represents the four-dimensional real space.

[0110] energy range Uniformly discretized _ sub-intervals, _ total _ Point, record the first Each node is , Represents the initial energy. Indicates terminal energy. Represents the energy step size between adjacent discrete nodes; define the first... The state variables and control variables at each discrete node are as follows:

[0111] in, Indicates the first The state vector at each energy node. Indicates the first Control inputs at each energy node.

[0112] The trapezoidal integral method is used to discretize the linearized state dynamics equations of the variable configuration aircraft, resulting in the... The node and the first State update equations between nodes:

[0113]

[0114] in, and Representing two adjacent discrete nodes respectively and The state vector at that location; and These represent the control inputs at two adjacent discrete nodes, respectively. Indicates the first During the next iteration, at node Affine offset term at the location; Indicates the first During the next iteration, at node Affine offset term at the location; and Representing the discretized state vector and the state vector respectively and The corresponding coefficient matrix; and They represent the discretized result and the control input, respectively. and The corresponding coefficient matrix; express identity matrix; and They represent the first During the next iteration, at node and Jacobian matrix at the location; Let be a constant matrix, then... ; All state update constraints are uniformly represented as a set of linear constraints:

[0115] in, This represents the optimization decision vector composed of all discrete node state variables and control variables; This represents the overall constraint coefficient matrix formed by concatenating the coefficient matrices corresponding to the state update equations of each discrete interval in blocks; Represents the terms on the right-hand side of each discrete interval The overall constant vector formed by sequentially stacking is combined with the reentry altitude flight corridor constraint, the rate of change of the roll angle constraint, and the confidence region constraint to construct a standard second-order cone programming problem.

[0116] In this embodiment, step S4, which uses the primal dual interior point method to solve the above-mentioned second-order cone optimization problem, is as follows: The primal dual interior point method is used to solve the optimal trajectory under the above constraints. This method guarantees that, within an acceptable accuracy range, the optimal trajectory solution satisfying the constraints is obtained. The above solution process can be solved using the GPOPS toolbox. Example 2: Based on Example 1, this embodiment of the invention sets the mass of the aircraft to be... The reference area is The technical effects of the reentry trajectory optimization method for variable configuration aircraft proposed in this invention will be explained.

[0117] The initial conditions for the aircraft are set as follows: initial Mach number of 2300 m / s, aircraft located at latitude and longitude (0°, 0°), heading angle of 90°, and roll angle of 15°. The terminal conditions are set as follows: final Mach number of 1000 m / s, heading angle not fixed, and roll angle of 15°. During flight, the process constraints and control constraints of the aircraft include: maximum heat flux density of 1000 kW / m², maximum dynamic pressure of 100 kPa, maximum overload of 3, maximum roll angle of 90°, and minimum roll angle of 0°. Let the objective function be... ,in The sample variance of the control variable is used to describe the smoothness of the control variable. The corresponding weighting factors are used. The number of iterations is 7, and the number of discrete points is 40. Multiple trajectories are solved between the final latitudes of -16.5° and 16.5°.

[0118] Simulation results are as follows Figure 12 , Figure 13 , Figure 14 and Figure 15 As shown in Figure 12, the maximum range trajectory distribution under the minimum drag coefficient configuration strategy is illustrated, covering a longitude range of 0°–16.5°. The endpoint latitude exhibits a "rise then fall" trend, peaking at approximately 9° around 7.5°. Figure 13 shows the corresponding Mach number-altitude trajectory. All trajectories are located within the flight corridor, satisfying constraints such as thermal flux, dynamic pressure, and overload to ensure flight safety. Figure 14 shows that the absolute value of the track angle is less than 1.2°, confirming the validity of the zero track angle assumption. Figure 15 shows that the roll angle control consistently satisfies the constraints.

[0119] Example 3: Based on Example 1, this embodiment of the invention provides a reentry trajectory optimization system for a variable configuration aircraft, which can be used to implement the reentry trajectory optimization method for a variable configuration aircraft as described in the foregoing embodiments. The system includes: The first module is used to establish the reentry dynamics model and multi-constraint model of the variable configuration aircraft. The second module is used to construct the minimum drag coefficient configuration-Mach number profile and reentry altitude flight corridor, transforming the trajectory optimization problem of variable configuration aircraft into a trajectory optimization problem with a fixed aerodynamic shape. The third module is used to perform dimensionless, linearized and discretized processing on the reentry dynamics model, and introduce control variables to transform the multi-constraint model into a constraint of the rate of change of the tilt angle, and transform the trajectory optimization problem with a fixed aerodynamic shape into a standard second-order cone programming problem. The fourth module is used to discretize and solve the second-order cone programming problem using the primal dual interior point method, obtain the optimal reentry trajectory that satisfies all constraints, and complete the reentry trajectory optimization method for variable configuration aircraft.

[0120] According to embodiments of the present invention, the present invention also provides an electronic device, a readable storage medium, and a computer program product.

[0121] In an exemplary embodiment, the electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the variable configuration aircraft reentry trajectory optimization method as described in Embodiment 1 above.

[0122] In an exemplary embodiment, the readable storage medium may be a non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the reentry trajectory optimization method for a variable-configuration aircraft according to Embodiment 1 above.

[0123] In an exemplary embodiment, the computer program product includes a computer program that, when executed by a processor, implements the reentry trajectory optimization method for variable configuration aircraft as described in Embodiment 1 above.

[0124] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0125] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0126] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0127] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with embodiments of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0128] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact via communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other. Servers can be cloud servers, servers in distributed systems, or servers incorporating blockchain technology.

[0129] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for optimizing the reentry trajectory of a variable-configuration aircraft, characterized in that, Includes the following steps: Establish a reentry dynamics model and a multi-constraint model for a variable-configuration aircraft; By constructing the minimum drag coefficient configuration-Mach number profile and reentry altitude flight corridor, the trajectory optimization problem of variable configuration aircraft is transformed into a trajectory optimization problem with a fixed aerodynamic shape; The reentry dynamics model is dimensionless, linearized, and discretized. Control variables are introduced to transform the multi-constraint model into a constraint of the rate of change of the tilt angle, and the trajectory optimization problem with a fixed aerodynamic shape is transformed into a standard second-order cone programming problem. The original dual interior point method is used to discretize and solve the second-order cone programming problem, obtaining the optimal reentry trajectory that satisfies all constraints, thus completing the reentry trajectory optimization method for variable configuration aircraft.

2. The reentry trajectory optimization method for variable configuration aircraft according to claim 1, characterized in that, The dynamic equations of a variable-configuration aircraft are: in, , and Indicates the geocentric distance, longitude, and latitude of the variable-configuration aircraft; This indicates the Mach number of a variable-configuration aircraft. , and Indicates the track angle, heading angle, and roll angle; and This represents the lift and drag of a variable-configuration aircraft. Indicates the mass of a variable-configuration aircraft; This represents gravity plus Mach number; Represents the sine function. Represents the cosine function. Represents the tangent function; and The lift and drag coefficients of a variable-configuration aircraft are represented by the Mach number. Configuration and attack angle Joint decision; Indicates the reference area; This indicates the atmospheric density at the altitude of the variable-configuration aircraft.

3. The reentry trajectory optimization method for variable configuration aircraft according to claim 1, characterized in that, Multi-constraint models include: Aircraft stagnation point heat flux density constraint: in, This represents the heat flux density at the stagnation point of the aircraft. This indicates the maximum heat flux density at the stagnation point of the aircraft; Indicates the heat flux coefficient; Indicates atmospheric density; This indicates the Mach number of a variable-configuration aircraft. Dynamic pressure constraint: in, Indicates dynamic pressure; Indicates the maximum dynamic pressure; Pneumatic overload constraint: in, Indicates pneumatic overload; Indicates the maximum pneumatic overload value; and This represents the lift and drag of a variable-configuration aircraft. Indicates the mass of a variable-configuration aircraft; This represents gravity plus Mach number; Access equilibrium gliding equation constraints: in, Indicates the tilt angle; Indicates the geocentric distance of a variable-configuration aircraft; This represents the cosine function.

4. The reentry trajectory optimization method for variable configuration aircraft according to claim 1, characterized in that, Minimum drag coefficient configuration - a function of Mach number profile Specifically: in, This represents the target minimum drag coefficient. Indicates configuration, The Mach number is represented by the drag coefficient-Mach number profile when the configuration-Mach number profile that optimizes a certain performance index is determined. and lift coefficient-Mach number profile The unique determination transforms the trajectory optimization problem of the variable configuration aircraft into a trajectory optimization problem with a fixed aerodynamic shape.

5. The reentry trajectory optimization method for variable configuration aircraft according to claim 4, characterized in that, Lower boundary of the re-entry altitude flight corridor for: in, Indicates reference altitude. This represents a logarithmic function with the natural constant as its base. Indicates reference air pressure. The Mach number represents the variable configuration aircraft. This indicates the maximum dynamic pressure. Indicates the reference area. Indicates the optimal lift coefficient. This represents the optimal drag coefficient. Indicates the mass of a variable-configuration aircraft. This represents gravity plus the Mach number. This indicates the maximum pneumatic overload. Indicates the heat flux coefficient. Indicates the maximum heat flux density; Upper boundary of the re-entry altitude flight corridor for: in, Indicates the reference distance from the Earth's center.

6. The reentry trajectory optimization method for variable configuration aircraft according to claim 5, characterized in that, The method of making the reentry dynamics model dimensionless, linearized, and discretized, and introducing control variables to transform the multi-constraint model into a constraint of the rate of change of the tilt angle, and transforming the trajectory optimization problem into a standard second-order cone programming problem, is as follows: Determine the relationship between the dimensionless Mach number, the dimensionless geocentric distance, and the dimensionless energy; Based on the relationship between dimensionless Mach number, dimensionless geocentric distance, and dimensionless energy, as well as three assumptions, the reentry dynamics model is reduced in order to obtain the reduced-order state dynamics equations for the modified configuration aircraft. By introducing the rate of change of the roll angle as a control variable, the constraints of the stagnation point heat flux density, dynamic pressure, aerodynamic overload, and quasi-equilibrium gliding equation are transformed into constraints on the rate of change of the roll angle. A first-order Taylor expansion is performed on the non-convex terms in the reduced-order variable-configuration aircraft state dynamics equation to obtain a linearized variable-configuration aircraft state dynamics equation, and a credibility region constraint is introduced to ensure the effectiveness of the linearized region. The linearized state dynamics equations of the variable configuration aircraft are discretized using the trapezoidal integral method to obtain the state update equations for each segment, thus constructing a standard second-order cone programming problem.

7. The reentry trajectory optimization method for variable configuration aircraft according to claim 6, characterized in that, The three assumptions are: the trajectory during flight satisfies... The variable-configuration aircraft exhibits minimal altitude change relative to range change during reentry, satisfying the requirement... ; The flight altitude of the aircraft relative to the Earth's radius satisfies ; Indicates the angular velocity of the trajectory. Indicates the track angle; The state dynamics equations for a reduced-order variable-configuration aircraft are: in, and Indicates the longitude and latitude angles of a variable-configuration aircraft. and Indicates the heading angle and the heel angle. and This represents the lift coefficient and drag coefficient of a variable configuration aircraft.

8. The reentry trajectory optimization method for variable configuration aircraft according to claim 6, characterized in that, The constraint on the rate of change of the tilt angle is: Indicated by energy The tilt angle is the independent variable. Indicates energy The maximum roll angle allowed when simultaneously satisfying the stagnation point heat flux density constraint, dynamic pressure constraint, and aerodynamic overload constraint of the aircraft; This represents the initial roll angle under the assumption of quasi-equilibrium gliding; This represents the terminal roll angle under the assumption of entry equilibrium gliding; Indicates the initial altitude of the aircraft; This indicates the initial energy of the aircraft; Indicates the terminal altitude of the aircraft; This indicates the terminal energy of the aircraft.

9. The reentry trajectory optimization method for variable configuration aircraft according to claim 6, characterized in that, The state dynamics equations for a reduced-order variable-configuration aircraft are: in, Indicates the energy of the aircraft; The state vector represents the state vector with respect to the spacecraft energy. The derivative; Represents state variables, Indicates longitude angle, Indicates latitude angle, Indicates the heading angle. Indicates the tilt angle; Indicates the energy of the aircraft The rate of change of the tilt angle is the control variable. This represents the control input allocation matrix; This represents the nonlinear drift term of the system. Indicates the lift coefficient. Indicates the drag coefficient. Indicates the lift-to-drag ratio. Indicates dimensionless velocity; For nonlinear drift terms In the Reference state of the next iteration Performing a first-order Taylor expansion, we obtain the linearized state dynamics equations for the variable-configuration aircraft: in, Represents the nonlinear drift term Relative to state variables Jacobian matrix; This represents the affine offset term after linearization; To ensure the effectiveness of linearization, the optimal state variable must be in the first position. Within a finite neighborhood of the reference state in the next iteration, a trust region constraint is introduced: in, This indicates taking the absolute value of each component of the vector; This represents the radius vector of the trust region, used to constrain the state variables in this iteration relative to the reference state. Deviation range; It represents the four-dimensional real space.

10. The reentry trajectory optimization method for a variable-configuration aircraft according to claim 9, characterized in that, The method of discretizing the linearized state dynamics equations of a variable-configuration aircraft using the trapezoidal integral method to obtain the state update equations for each segment, and constructing a standard second-order cone programming problem, is as follows: energy range Uniformly discretized _ sub-intervals, _ total _ The discrete node, the first The discrete nodes are represented as follows: in, Represents the initial energy. Indicates terminal energy. Indicates the first Energy of discrete nodes This represents the energy step size between adjacent discrete nodes; Definition of the first The state variables and control variables at each discrete node are as follows: in, Indicates the first The state vector at each energy node. Indicates the first Control inputs at each energy node; The linearized state-dynamic equations of the variable-configuration aircraft are discretized using the trapezoidal integral method to obtain the first... The node and the first State update equations between nodes: in, and Representing two adjacent discrete nodes respectively and The state vector at that location; and These represent the control inputs at two adjacent discrete nodes, respectively. Indicates the first During the next iteration, at node Affine offset term at the location; Indicates the first During the next iteration, at node Affine offset term at the location; and Representing the discretized state vector and the state vector respectively and The corresponding coefficient matrix; and Representing the discretized result and the control input respectively and The corresponding coefficient matrix; express identity matrix; and They represent the first During the next iteration, at node and Jacobian matrix at the location; Let be a constant matrix, then... ; All state update constraints are uniformly represented as a set of linear constraints: in, This represents the optimization decision vector composed of all discrete node state variables and control variables; This represents the overall constraint coefficient matrix formed by concatenating the coefficient matrices corresponding to the state update equations of each discrete interval in blocks; This represents the right-hand side terms of each discrete interval. The overall constant vector formed by sequentially stacking is combined with the reentry altitude flight corridor constraint, the rate of change of the roll angle constraint, and the confidence region constraint to construct a standard second-order cone programming problem.

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