A transverse-longitudinal coupled parametric guidance method, device, medium and product based on an analytical solution of an aircraft trajectory

Abstract

The present invention discloses a transverse-longitudinal coupled parameterized guidance method, device, medium, and product based on an analytical solution to an aircraft trajectory, relating to the field of aircraft guidance technology. The present invention obtains an analytical solution to the guidance cycle number, real-time terminal velocity, the motion equation for no-fly zone avoidance, and real-time trajectory planning to determine the nominal profile; determines control instructions based on the real-time motion state data and the nominal profile; assigns control instructions based on the profile tracking guidance law to obtain guidance instructions; corrects the nominal profile based on the analytical solution, and returns to the step of "obtaining the aircraft's real-time motion state data" until the number of corrections to the nominal profile equals the number of guidance cycles. By correcting the nominal profile, the present invention can improve aircraft guidance accuracy.

Description

Technical Field

[0001] The present invention relates to the field of aircraft guidance technology, and in particular to a transverse-longitudinal coupled parameterized guidance method, device, medium and product based on an analytical solution of an aircraft trajectory. Background Art

[0002] In the field of hypersonic glide vehicle (HGV) control, no-fly zone avoidance involves real-time trajectory generation using analytical trajectory design methods within the trajectory planning layer, based on a known decision path. This involves trajectory prediction, multi-stage trajectory parameterization, and tracking guidance. HGVs experience significant lateral maneuvers during no-fly zone avoidance, and their dynamics exhibit high aerodynamic characteristics, characterized by large angles of attack and large bank angles. This results in strong coupling between lateral and longitudinal motions and high nonlinearity. During the tracking guidance phase, conventional space shuttle control variable allocation methods employ a fixed angle of attack profile. Lateral and longitudinal control is achieved solely through the bank angle, with the vehicle's heading deviation adjusted by reversing the bank angle's sign. This control strategy has certain limitations for HGV penetration: First, abrupt changes occur during bank angle reversal, resulting in a large rate of bank change, making it difficult for actuators to execute and stably track the desired flight profile. Second, the specified angle of attack profile reduces the degrees of freedom in trajectory control, making it impossible to plan the vehicle's lateral maneuverability. Summary of the Invention

[0003] The purpose of the present invention is to provide a transverse-longitudinal coupled parameterized guidance method, device, medium and product based on the analytical solution of the aircraft trajectory, which can improve the aircraft guidance accuracy.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory comprises:

[0006] Obtaining the analytical solution for the guidance cycle number, real-time terminal velocity, motion equations for no-fly zone avoidance, and real-time trajectory planning; the real-time trajectory planning parameters are obtained by converting the analytical trajectory planning optimal control problem into a multi-stage profile parameter planning problem and solving it based on the no-fly zone information and the aircraft state by the upper-level path decision;

[0007] Determining a nominal cross-section according to the analytical solution; the nominal cross-section includes a drag acceleration cross-section and a lift acceleration cross-section;

[0008] Obtain real-time motion status data of the aircraft;

[0009] determining a control instruction according to the real-time motion state data and the nominal cross section; the control instruction including a lateral lift acceleration and a longitudinal lift acceleration;

[0010] Allocating control instructions according to the profile tracking guidance law to obtain guidance instructions; the guidance instructions include an angle of attack and a roll angle;

[0011] Correct the nominal profile based on the analytical solution and return to the step of "obtaining real-time motion state data of the aircraft" until the number of corrections to the nominal profile is equal to the number of guidance cycles;

[0012] Get real-time terminal speed;

[0013] Determine whether the real-time terminal velocity and the aircraft guidance velocity are equal, and obtain a determination result;

[0014] If the judgment result is no, inputting the guidance instruction into the motion equation and integrating it to obtain the guidance motion state data of the aircraft;

[0015] Using the guided motion state data as real-time motion state data, and returning to the step of "determining a control instruction according to the real-time motion state data and the nominal profile";

[0016] If the judgment result is yes, the guidance process ends.

[0017] Optionally, the angle of attack is:

[0018] Among them, α d is the angle of attack, α is the feasible angle of attack, α min is the lower bound of the feasible angle of attack, α max is the upper limit of the feasible angle of attack, L is the lift acceleration of the aircraft, and L pro is the total lift acceleration, L 1pro is the longitudinal lift acceleration, L 2pro is the lateral lift acceleration;

[0019] The tilt angle is: d =arctan2(L 2pro ,L 1pro );

[0020] The profile tracking guidance law is:

[0021]

[0022] Where D is the actual resistance acceleration, D d is the resistance acceleration command, f1 is the first feedback gain coefficient, f2 is the second feedback gain coefficient, is the corresponding reference height change rate, L1 / D pro is the drag acceleration profile; L1 / D d is the lift acceleration profile, is the rate of change of height.

[0023] Optionally, the correcting the nominal profile based on the analytical solution includes:

[0024] Determine the profile parameter of the resistance acceleration profile as the first profile parameter;

[0025] determining a profile parameter of the lift acceleration profile as a second profile parameter;

[0026] The velocity analytical prediction formula is expanded by the first order Taylor at the first profile parameter to obtain the first Taylor equation;

[0027] The analytical prediction formula of the cross-range is expanded by the first order Taylor on the second profile parameter to obtain the second Taylor equation;

[0028] Determine an analytical solution based on the first Taylor equation and the second Taylor equation;

[0029] Correcting the first profile parameter according to the first-order derivative approximation of the analytical solution to obtain the corrected first profile parameter;

[0030] determining a corrected drag acceleration profile according to the corrected first profile parameter;

[0031] Correcting the second profile parameters according to the first-order derivative approximation of the analytical solution to obtain corrected second profile parameters;

[0032] A corrected lift acceleration profile is determined according to the corrected second profile parameter.

[0033] Optionally, the first-order Taylor expansion is:

[0034]

[0035] Among them, V f is the desired terminal velocity of the aircraft, V H (x D0 ,x Df ) is the analytical expression of velocity, k 10 is the L1 / D profile parameter before correction; Δk 10 is the L1 / D profile parameter correction value; x Cf，i is the i-th path point of the terminal horizontal path, x CH (x D,i-1 ,x D,i ) is the analytical expression of the horizontal range, k 21，i is the first profile parameter of L2 profile before correction; Δk 21，i is the correction value of the first section parameter of L2; k 20，i is the second profile parameter of L2 profile before correction; Δk 20，i is the second profile parameter of the L2 profile after correction;

[0036] The profile parameters after correction are:

[0037]

[0038] Among them, k 10 ' is the L1 / D profile parameter after correction; k 21，i ' is the first profile parameter of the L2 profile after correction; k 20，i ' is the second profile parameter of the L2 profile after correction.

[0039] A computer device comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory.

[0040] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory.

[0041] A computer program product includes a computer program. When the computer program is executed by a processor, the computer program implements a transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory.

[0042] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0043] The present invention provides a transverse-longitudinal coupled parameterized guidance method, device, medium, and product based on an analytical solution for an aircraft trajectory. The method determines the nominal profile based on real-time trajectory planning parameters; determines control instructions based on real-time motion state data and the nominal profile; distributes control instructions based on a profile-tracking guidance law to obtain guidance instructions; and corrects the nominal profile based on the real-time trajectory planning parameters. This method can account for reentry glide constraints and guidance errors while satisfying the planned profile. Unlike the analytical guidance laws of traditional space shuttles, the present invention removes the constraints of a constant angle of attack or angle of attack profile, allowing for greater freedom in tracking both longitudinal and transverse profiles. This allows for efficient flight while managing the aircraft's maneuverability while avoiding multiple no-fly zones. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0045] Figure 1A flow chart of a lateral-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory provided in Example 1 of the present invention;

[0046] Figure 2 A flow chart of a lateral-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory provided in Example 2 of the present invention;

[0047] Figure 3 A schematic diagram of a reentry corridor provided in Example 2 of the present invention;

[0048] Figure 4 A velocity sensitivity-profile parameter diagram provided in Example 2 of the present invention;

[0049] Figure 5 This is a cross-range sensitivity-profile parameter diagram provided in Example 2 of the present invention;

[0050] Figure 6 This is a track deviation sensitivity-profile parameter diagram provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0052] The purpose of the present invention is to provide a transverse-longitudinal coupled parameterized guidance method, device, medium and product based on the analytical solution of the aircraft trajectory, which can improve the aircraft guidance accuracy.

[0053] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] Example 1

[0055] like Figure 1 As shown, in this embodiment, a transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory includes:

[0056] Step 101: Obtain the guidance cycle number, real-time terminal velocity, the equations of motion for no-fly zone avoidance, and the analytical solution for real-time trajectory planning. The real-time trajectory planning parameters are obtained by the upper-level path decision-making process by transforming the analytical trajectory planning optimal control problem into a multi-stage profile parameter planning problem and solving it based on the no-fly zone information and the aircraft's state.

[0057] Step 102: Determine the nominal profile based on the analytical solution. The nominal profile includes the drag acceleration profile and the lift acceleration profile.

[0058] Step 103: Acquire real-time motion status data of the aircraft.

[0059] Step 104: Determine control instructions based on the real-time motion state data and the nominal profile. The control instructions include lateral lift acceleration and longitudinal lift acceleration.

[0060] Step 105: Allocate control instructions according to the profile tracking guidance law to obtain guidance instructions. The guidance instructions include the angle of attack and the roll angle.

[0061] Step 106: Correct the nominal profile based on the analytical solution, and return to the step of "obtaining real-time motion state data of the aircraft" until the number of corrections to the nominal profile is equal to the number of guidance cycles.

[0062] Step 107: Obtain the real-time terminal speed.

[0063] Step 108: Determine whether the real-time terminal velocity and the aircraft guidance velocity are equal, and obtain a determination result.

[0064] Step 109: If the judgment result is no, the guidance instruction is input into the motion equation and integrated to obtain the guidance motion state data of the aircraft.

[0065] Step 1010: Use the guided motion state data as real-time motion state data, and return to the step of "determining control instructions based on the real-time motion state data and the nominal profile".

[0066] Step 1011: If the judgment result is yes, then the guidance process ends.

[0067] The angle of attack is:

[0068] Among them, α d is the angle of attack, α is the feasible angle of attack, α min is the lower bound of the feasible angle of attack, α max is the upper limit of the feasible angle of attack, L is the lift acceleration of the aircraft, and L pro is the total lift acceleration, L 1pro is the longitudinal lift acceleration, L 2pro is the lateral lift acceleration.

[0069] The tilt angle is: σ d =arctan2(L 2pro ,L 1pro ).

[0070] The profile tracking guidance law is:

[0071]

[0072] Where D is the actual resistance acceleration, D d is the resistance acceleration command, f1 is the first feedback gain coefficient, f2 is the second feedback gain coefficient, is the corresponding reference height change rate, L1 / D pro is the drag acceleration profile. L1 / D d is the lift acceleration profile, is the rate of change of height.

[0073] Step 106 includes:

[0074] Step 106 - 1 : Determine the profile parameters of the drag acceleration profile as first profile parameters.

[0075] Step 106 - 2 : Determine the profile parameters of the lift acceleration profile as the second profile parameters.

[0076] Step 106-3: Perform a first-order Taylor expansion on the velocity analytical prediction formula at the first profile parameter to obtain the first Taylor equation.

[0077] Step 106-4: Perform a first-order Taylor expansion on the cross-range analytical prediction formula on the second profile parameter to obtain a second Taylor equation.

[0078] Step 106 - 5 : Determine an analytical solution based on the first Taylor equation and the second Taylor equation.

[0079] Step 106 - 6 : Correct the first profile parameters according to the first-order derivative approximation of the analytical solution to obtain corrected first profile parameters.

[0080] Step 106 - 7 : Determine the corrected resistance acceleration profile according to the corrected first profile parameters.

[0081] Step 106 - 8 : Correct the second profile parameters according to the first-order derivative approximation of the analytical solution to obtain corrected second profile parameters.

[0082] Step 106 - 9 : Determine the corrected lift acceleration profile according to the corrected second profile parameters.

[0083] The first-order Taylor expansion is:

[0084]

[0085] Among them, V f is the desired terminal velocity of the aircraft, V H (x D0 ,x Df ) is the analytical expression of velocity, k 10is the L1 / D profile parameter before correction; Δk 10 is the L1 / D profile parameter correction value; x Cf，i is the i-th path point of the terminal horizontal path, x CH (x D,i-1 ,x D,i ) is the analytical expression of the horizontal range, k 21，i is the first profile parameter of L2 profile before correction; Δk 21，i is the correction value of the first section parameter of L2; k 20，i is the second profile parameter of L2 profile before correction; Δk 20，i is the second profile parameter of the L2 profile after correction.

[0086] The profile parameters after correction are:

[0087]

[0088] Among them, k 10 ' is the L1 / D profile parameter after correction; k 21，i ' is the first profile parameter of the L2 profile after correction; k 20，i ' is the second profile parameter of the L2 profile after correction.

[0089] Example 2

[0090] To generate a trajectory for a complete motion model in real time, this embodiment uses the flight profile obtained by parameterizing the trajectory as the nominal profile and tracks the flight profile using a prediction-correction closed-loop approach. First, based on the nominal profile, the required lateral and longitudinal lift accelerations are calculated in real time. The control variables, angle of attack α and bank angle σ, are allocated, and a profile-tracking guidance law is designed to jointly control lateral and longitudinal motion. Then, the terminal state is predicted based on the analytical solution of the trajectory, and the profile parameters are corrected during each guidance cycle to minimize the loss of guidance accuracy caused by profile-tracking errors. Finally, a closed-loop guidance circuit is designed to implement analytical guidance for HGVs to avoid no-fly zones. The process of determining the analytical solution is as follows: Based on the principles of perturbation theory, perturbed zero-order, first-order, and second-order linear time-varying subsystems of the motion equation are constructed to achieve decoupling of the quantities to be solved; then, the constant variation method is used to recursively solve the velocity, track angle, and cross-range of each order subsystem; for the non-integrable terms in the integration process, the high-order Gauss-Legendre quadrature formula is used to approximate them as polynomial analytical solutions, and the order of the polynomial is selected by balancing the approximation accuracy and integration efficiency; finally, the analytical solutions of the subsystems of each order are added together to obtain the analytical solution of the reentry glide trajectory.

[0091] 1. Control allocation and trajectory tracking.

[0092] Due to the strong nonlinearity of HGVs, a reasonable allocation of lateral and longitudinal flight capabilities is required to balance longitudinal glide and lateral maneuvering. The longitudinal profile must meet terminal velocity and range constraints while also satisfying the reentry glide process. The lateral profile must meet pathpoint requirements and no-fly zone avoidance requirements, keeping flight energy within a reasonable range.

[0093] The actual control variables of HGV are the angle of attack α and the roll angle σ, which need to be allocated according to the planned control profile. The L1 / D profile and the L2 profile are recorded as the nominal profile L1 / D pro and L 2pro According to the equilibrium gliding condition, ignoring the Coriolis acceleration and centrifugal acceleration caused by the rotation of the earth, the nominal profile D pro It can be calculated as follows:

[0094]

[0095] Where V is the current velocity, g and R are constants. The required longitudinal lift acceleration L of the aircraft is 1pro for:

[0096] L 1pro =D pro L1 / D pro (2).

[0097] The total lift acceleration L required by the aircraft pro for:

[0098]

[0099] The angle of attack can be obtained by solving the following equation:

[0100]

[0101] Among them, α min and α max They are the lower and upper bounds of the feasible angle of attack, which means that when the aircraft lift acceleration L can satisfy the profile L pro When the angle of attack passes L pro By reverse calculation, if the aircraft is not able to reach L pro When the angle of attack passes the upper limit of the lift acceleration L max The inverse calculation can be written as follows:

[0102]

[0103] Among them, h min is the lower bound of the aircraft altitude, C Lmax is the upper bound of the lift coefficient.

[0104] The roll angle can be obtained by solving the following equation:

[0105] σ d =arctan2(L 2pro ,L 1pro ) (6).

[0106] where arctan2(·,·) is a four-quadrant inverse tangent function.

[0107] Using formula (6), even if the aircraft cannot reach the commanded lift acceleration L pro , the required lift acceleration in both the horizontal and vertical planes will be uniformly scaled, thus avoiding the saturation of the control quantity to the greatest extent.

[0108] In addition, since the HGV needs to meet the process constraints and control constraints of the re-entry glide, a narrow and irregular re-entry corridor is formed, and real-time feedback is required to ensure that the profile is within the re-entry corridor. The present invention tracks the nominal profile D through closed-loop feedback control. pro , achieving control of longitudinal motion height and speed, matching the balanced glide constraint, thereby improving the guidance accuracy of the velocity analytical solution. Laterally, through open-loop inverse solution of the control quantity, accurate tracking of the L2 profile is achieved.

[0109] Considering the typical reentry glide process constraints, the stagnation point heat flux rate Constraint, dynamic pressure Constraints and overloads Constraints, the upper bound of the aircraft drag acceleration profile can be expressed as:

[0110]

[0111] in, are the resistance acceleration corresponding to the maximum stagnation point heat flux, maximum dynamic pressure, and maximum overload, which can be expressed as follows:

[0112]

[0113] The lower bound of the aircraft drag acceleration profile can be expressed as:

[0114]

[0115] Among them, D QEGC is the drag acceleration corresponding to the equilibrium gliding condition at zero roll angle.

[0116] Therefore, the corridor boundary shape formed by the process constraints is as follows Figure 3 shown.

[0117] Based on the guidance idea of ​​space shuttle DV profile tracking, the "feedforward + feedback" strategy is used to track L1 / D in real time. proProfile, the role of feedforward is to track the nominal profile, the role of feedback is to stabilize D pro The profile tracking error is used to approach the equilibrium gliding condition of the HGV. The profile tracking guidance law is as follows:

[0118]

[0119] Where D is the actual resistance acceleration, D d is the resistance acceleration command, f1 and f2 are the feedback gain coefficients, is the corresponding height change rate, and the calculation formula is as follows:

[0120]

[0121] Among them, h S is the height constant of the exponential atmospheric density. d Replace L1 / D pro Substituting into equations (1) to (6), we can obtain the angle of attack command and roll angle command for closed-loop tracking feedback.

[0122] The method proposed in the present invention expands the control quantity distribution method of the traditional space shuttle. In the control strategy of the space shuttle, the angle of attack profile is fixed, and the aircraft only relies on the roll angle to achieve lateral and longitudinal control, and the heading deviation of the aircraft is adjusted by reversing the sign of the roll angle. This control strategy has certain limitations for HGV penetration: on the one hand, there is a sudden change when the roll angle is reversed, resulting in a large roll angle change rate, which makes it difficult for the actuator to execute and unable to stably track the desired flight profile; on the other hand, the specified angle of attack profile reduces the degree of freedom of trajectory control and cannot plan the lateral maneuverability of the aircraft. Therefore, unlike the control strategy of the space shuttle, the present invention relaxes the restrictions on the HGV angle of attack, and through the coordination between the angle of attack and the roll angle instructions, it meets the lift acceleration requirements in the lateral and longitudinal movements at the same time, and realizes the way to avoid multiple no-fly zones with the least maneuverability.

[0123] 2. Real-time prediction and correction of trajectory profile.

[0124] Taking into account deviations in control variables such as the roll angle and angle of attack constraints, model errors, and aerodynamic errors, the HGV may need to consume additional energy through maneuvers to track the lateral and longitudinal profiles, resulting in deviations from the path points and target points. The planned L1 / D profile and L2 profile need to be corrected periodically.

[0125] According to the analytical solution of the trajectory, the required longitudinal distance x of each path point is predicted analytically D,i Downward Horizontal Stroke x Cf,i and the terminal velocity V f In each trajectory sub-segment, the profile parameter k is corrected according to the deviation of the traverse distance and terminal velocity at each path point. 10 , k21,i , k 20,i , i = 1,…, n, thus obtaining new L1 / D and L2 profiles.

[0126] First, analyze the profile parameter k 10 , k 21 , k 20 The sensitivity of the terminal range and terminal speed is used to analyze the dominant factors of each terminal state, select the reference state corresponding to the parameter correction, and design the profile correction strategy. The Morris sensitivity analysis method is used in this paper, and the results are as follows: Figure 4-Figure 6 shown.

[0127] like Figure 4-Figure 6 The dominant parameter of the terminal velocity is the profile parameter k corresponding to the L1 / D profile. 10 , that is, the speed is mainly controlled by the drag acceleration, which determines the longitudinal flight trajectory of the HGV; the dominant parameter of the terminal cross-range is the profile parameter k corresponding to the L2 profile 21,i , k 20,i , that is, the lateral range is mainly controlled by the lateral lift acceleration, which determines the lateral flight trajectory of the HGV. Therefore, when correcting the profile parameters, k 10 Correction V f , through the parameter k 21,i , k 20,i Correction x Cf,i .

[0128] Then, using the idea of ​​perturbation, the velocity V f The analytical prediction formula is based on the nominal L1 / D profile parameter k 10 Perform a first-order Taylor expansion at Cf,i The analytical prediction formula is given by the nominal L2 profile parameter k 21,i , k 20,i Perform a first-order Taylor expansion at , and correct the L2 profile of the trajectory segment according to the current position. The expansion is as follows:

[0129]

[0130] The left side of the equation is the desired terminal velocity and path point range of the aircraft, and the right side is the terminal velocity and range predicted by the analytical solution of the trajectory. The derivative can be approximated by the first-order derivative of the analytical solution. According to equation (13), the profile parameter correction Δk is obtained 10 , Δk 21,i , Δk 20,i , i = 1, ..., n. The corrected profile parameters can be written as follows:

[0131]

[0132] Set the guidance cycle and predict and correct the profile parameters in each cycle. As the distance to the target point gets closer, the trajectory prediction accuracy increases and the profile correction becomes more accurate.

[0133] 3 Real-time trajectory tracking guidance method.

[0134] Next, combining the proposed control allocation strategy and tracking guidance law, a closed-loop guidance process for avoiding no-fly zones based on analytical prediction-correction trajectory tracking is designed, as shown in the following example: Figure 2 , the guidance steps are summarized as follows:

[0135] 1) Obtain the L1 / D profile and L2 profile according to the real-time trajectory planning in Section 4.4.

[0136] 2) Calculate the lateral and longitudinal lift acceleration and drag acceleration guidance instructions (Equation (3), Equation (1)).

[0137] 3) According to the profile tracking guidance law (Equation (10)), control instructions are assigned to obtain the angle of attack and roll angle guidance instructions (Equations (4) and (6)).

[0138] 4) Integrate the original motion equations of the HGV by inputting the guidance commands.

[0139] 5) If entering the next guidance cycle, predict and correct the L1 / D profile and L2 profile parameters (Equation (14)).

[0140] 6) When the HGV speed reaches the terminal velocity, the guidance ends.

[0141] This no-fly zone avoidance trajectory tracking guidance method is an analytical prediction-correction approach that accounts for reentry glide constraints and guidance errors while satisfying the planned profile. Unlike the analytical guidance laws used in traditional space shuttles, the proposed method removes the constraints of a constant angle of attack or angle of attack profile, allowing for greater freedom in tracking both longitudinal and lateral profiles. This allows for efficient flight while managing the vehicle's maneuverability while avoiding multiple no-fly zones.

[0142] Example 3

[0143] A computer device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a lateral-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory in Example 1.

[0144] Example 4

[0145] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory in Example 1.

[0146] Example 5

[0147] A computer program product includes a computer program, which, when executed by a processor, implements the steps of a transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory in embodiment 1.

[0148] Example 6

[0149] A computer device, which may be a database. The computer device includes a processor, a memory, an input / output (I / O) interface, and a communication interface. The processor, memory, and I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device is used to store pending transactions. The I / O interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, it implements the lateral-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory in Example 1.

[0150] It should be noted that the object information (including but not limited to object device information, object personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in the present invention are all information and data authorized by the object or fully authorized by all parties, and the collection, use and processing of relevant data must comply with the relevant laws, regulations and standards of relevant countries and regions.

[0151] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The databases involved in the various embodiments provided by the present invention may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided by the present invention may be, but are not limited to, general-purpose processors, central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), programmable logic devices (PLDs), data processing logic devices based on quantum computing, and the like.

[0152] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0153] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A lateral-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory, characterized in that: include: Obtain analytical solutions for guidance cycle number, real-time terminal velocity, equations of motion for no-fly zone avoidance, and real-time trajectory planning; The analytical solution of the real-time trajectory planning is obtained by converting the analytical trajectory planning optimal control problem into a multi-stage profile parameter planning problem and solving it according to the no-fly zone information and the state of the aircraft by the upper-level path decision; Determining a nominal cross-section according to the analytical solution; the nominal cross-section includes a drag acceleration cross-section and a lift acceleration cross-section; Obtain real-time motion status data of the aircraft; determining a control instruction according to the real-time motion state data and the nominal cross section; the control instruction including a lateral lift acceleration and a longitudinal lift acceleration; Allocating control instructions according to the profile tracking guidance law to obtain guidance instructions; the guidance instructions include an angle of attack and a roll angle; Correct the nominal profile based on the analytical solution and return to step "obtaining real-time motion state data of the aircraft" until the number of corrections to the nominal profile equals the number of guidance cycles; Get real-time terminal speed; Determine whether the real-time terminal velocity and the aircraft guidance velocity are equal, and obtain a determination result; If the judgment result is no, inputting the guidance instruction into the motion equation and integrating it to obtain the guidance motion state data of the aircraft; Using the guided motion state data as real-time motion state data, and returning to the step of "determining a control instruction according to the real-time motion state data and the nominal profile"; If the judgment result is yes, then the guidance process ends; The method of correcting the nominal profile based on the analytical solution includes: Determine the profile parameter of the resistance acceleration profile as the first profile parameter; determining a profile parameter of the lift acceleration profile as a second profile parameter; The velocity analytical prediction formula is expanded by the first order Taylor at the first profile parameter to obtain the first Taylor equation; The analytical prediction formula of the cross-range is expanded by the first order Taylor on the second profile parameter to obtain the second Taylor equation; Determine an analytical solution based on the first Taylor equation and the second Taylor equation; Correcting the first profile parameter according to the first-order derivative approximation of the analytical solution to obtain the corrected first profile parameter; determining a corrected drag acceleration profile according to the corrected first profile parameter; Correcting the second profile parameters according to the first-order derivative approximation of the analytical solution to obtain corrected second profile parameters; determining a corrected lift acceleration profile according to the corrected second profile parameter; The first-order Taylor expansion is: Among them, V f is the desired terminal velocity of the aircraft, V H (x D0 ,x Df ) is the analytical expression of velocity, k 10 is the L1 / D profile parameter before correction; Δk 10 is the L1 / D profile parameter correction value; x Cf,i is the i-th path point of the terminal horizontal path, x CH (x D,i-1 ,x D,i ) is the analytical expression of the horizontal range, k 21，i is the first profile parameter of L2 profile before correction; Δk 21，i k is the correction value of the first section parameter of L2; 20，i is the second profile parameter of L2 profile before correction; Δk 20，i is the correction value of the second profile parameter of L2 profile; The profile parameters after correction are: Among them, k 10 ′ is the L1 / D profile parameter after correction; k 21,i ′ is the first profile parameter of the L2 profile after correction; k 20，i ′ is the second profile parameter of the L2 profile after correction.

2. A transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory according to claim 1, characterized in that: The angle of attack is: Among them, α d is the angle of attack, α is the feasible angle of attack, α min is the lower bound of the feasible angle of attack, α max is the upper limit of the feasible angle of attack, L is the lift acceleration of the aircraft, and L pro is the total lift acceleration, L 1pro is the longitudinal lift acceleration, L 2pro is the lateral lift acceleration; The tilt angle is: d =arctan2(L 2pro ,L 1pro ); The profile tracking guidance law is: Where D is the actual resistance acceleration, D d is the resistance acceleration command, f1 is the first feedback gain coefficient, f2 is the second feedback gain coefficient, is the corresponding reference height change rate, L1 / D pro is the drag acceleration profile; L1 / D d is the lift acceleration profile, is the rate of change of height.

3. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement a lateral-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory according to any one of claims 1 to 2.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it realizes a transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory according to any one of claims 1 to 2.

5. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, it realizes a transverse-longitudinal coupled parameterized guidance method based on an analytical solution of an aircraft trajectory according to any one of claims 1 to 2.

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