A near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints

Abstract

The application provides a near-analytical gliding trajectory planning method considering space-time full state constraints, and belongs to the field of aircraft control, and comprises the following steps: constructing a resistance acceleration profile model by considering terminal height, speed, local ballistic inclination, flight range and flight time constraints; constructing a flight range and time analytical prediction model according to the profile model, and then obtaining a reference profile based on a profile parameter correction algorithm; tracking the reference profile to obtain longitudinal trajectory parameters and flight time; according to the longitudinal trajectory parameters, a lateral planning method based on a heading adjustment / retention algorithm is used to obtain a lateral trajectory satisfying terminal position and track yaw angle constraints; considering lateral large maneuvering conditions, a terminal position and flight time deviation correction method is designed, the trajectory is corrected by iteratively updating the target flight range and flight time in an outer loop until the terminal accuracy requirement is met, and the flight trajectory is output. The method has high accuracy and calculation efficiency, and can quickly predict the flight capability boundary.

Description

Technical Field

[0001] This invention belongs to the field of aircraft control technology, specifically relating to a near-analytical gliding trajectory planning method that considers spatiotemporal full-state constraints. Background Technology

[0002] As a key technology for hypersonic glide vehicles, rapid trajectory planning is an important means to improve their flight autonomy, mission adaptability, and intelligence. However, the complex and ever-changing near-space flight environment, the high lift-to-drag ratio aerodynamic shape, hypersonic flight characteristics, and typical combat missions mean that hypersonic glide flight faces various complex constraints and mission conditions, posing significant challenges to glide trajectory planning. In recent years, with the emergence of the concept of cooperative operations, the operational requirements for simultaneous or staggered target arrival have placed stringent demands on the flight time control capabilities of aircraft. Furthermore, the emergence of operational requirements such as all-round multi-angle saturation attacks, cooperative encirclement, and formation networking means that aircraft must not only meet the conditions of simultaneous / sequential arrival but also satisfy different incident azimuth and landing angle constraints to achieve spatiotemporal coordination. At this point, the glide trajectory planning problem evolves into a strongly coupled, fast-time-varying, multi-constraint nonlinear programming problem with constraints on typical processes, time, and terminal states, further narrowing the feasible region of trajectory planning and increasing the difficulty of rapid trajectory planning. However, there are few existing literatures on rapid gliding trajectory planning methods that simultaneously consider the above constraints. The main research hotspots include two aspects: rapid gliding trajectory planning methods and trajectory planning and guidance methods that consider time and angle constraints.

[0003] Currently, rapid trajectory planning methods for the gliding phase mainly include methods based on standard trajectories, methods based on the equilibrium gliding assumption, and methods based on prediction and correction. Among these, the drag acceleration profile-based method, as a type of standard trajectory-based method, is widely used in reentry gliding trajectory design and guidance missions due to its high applicability and computational accuracy, leading to classic methods such as Space Shuttle reentry guidance and Evolved Acceleration Guidance Logic for Entry (EAGLE). However, none of these methods take into account flight time and terminal angle constraints.

[0004] In recent years, based on the methods mentioned above, some scholars have studied rapid planning and guidance methods for gliding trajectories considering time and angle constraints, using methods such as standard profile design, prediction correction, and sequential convex optimization. However, these methods generally employ numerical integration for range and time prediction, or generate trajectories based on numerical optimization algorithms, resulting in long computation times. Furthermore, most methods divide the reentry trajectory into multiple stages for design, and the selection of segment points greatly limits the maneuverability and adjustment capabilities of gliding flight, thus limiting the range of time and angle adjustments. Summary of the Invention

[0005] To improve the time and angle adjustment range, task applicability, and computational efficiency of the planning algorithm, this invention provides a near-analytical gliding trajectory planning method that considers spatiotemporal full-state constraints.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints includes the following steps: Considering the constraints of terminal altitude, speed, local ballistic inclination, range and flight time, a two-parameter drag acceleration profile model with corridor boundary interpolation is constructed. Based on the aforementioned two-parameter drag-acceleration profile model, a range prediction model and a time prediction model for the aircraft are constructed. Based on the predicted range and time, the parameters of the two-parameter drag acceleration profile model are corrected to obtain the two-parameter drag acceleration profile. The two-parameter drag acceleration profile is tracked to obtain longitudinal trajectory parameters and tilt angle command amplitude. and flight time deviation; Two-stage lateral planning based on heading adjustment / maintenance: based on longitudinal trajectory parameters and roll angle command amplitude. The tilt reversal point is solved iteratively. The lateral trajectory parameters and the tilt angle command symbol are obtained. and terminal location parameters; Calculate the terminal position deviation based on the terminal position parameters and the target trajectory yaw angle. And determine the sign of the terminal position deviation. ; according to , And update the target range and flight time based on flight time deviation; Based on the updated target range and flight time, the longitudinal and lateral flight trajectories are continuously corrected through outer loop iterations until the terminal accuracy requirements are met, at which point the flight trajectory and roll angle commands are output. .

[0007] The near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints provided by this invention has the following beneficial effects: (1) The reference drag acceleration profile of the present invention is obtained based on the two-parameter interpolation of the corridor boundary. Therefore, it can maximize the range of range and flight time adjustment under the condition of satisfying the process constraints. At the same time, it is easy to quickly quantify the adjustable range. The fitting of the corridor boundary achieves high accuracy with a small polynomial order, which reduces the computational cost and complexity of the method. In addition, the transition section is designed as a cubic polynomial function, which can ensure the continuity, smoothness and easy tracking of the reference profile, and can realize the application of terminal altitude, speed, local ballistic inclination angle range and flight time constraints.

[0008] (2) The two-stage lateral planning algorithm based on heading adjustment / holding has high control accuracy of terminal position and track yaw angle and a large heading adjustment range. It can also realize the rapid quantification of the adjustable range of terminal track yaw angle, which can provide a reference for collaborative task planning and online allocation.

[0009] (3) Due to the adoption of profile analytical prediction correction design and improved outer loop correction strategy, the proposed method has high control accuracy of time and terminal full state constraints, as well as high computational efficiency, and can quickly predict the flight capability boundary. Attached Figure Description

[0010] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a schematic diagram of the DE cross section; Figure 2 This is a schematic diagram illustrating the course adjustment pattern. Figure 3 This is a schematic diagram of lateral planning; Figure 4 This is a schematic diagram of a large lateral maneuver trajectory; Figure 5 A flowchart of the near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints provided by the present invention; Figure 6 A preliminary diagram of flight capability boundaries; Figure 7 A preliminary diagram of the terminal track yaw angle adjustable capability boundary; Figure 8 These are the simulation result curves corresponding to different constraint conditions. Detailed Implementation

[0012] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0013] To improve the task applicability and computational efficiency of planning algorithms, this invention studies a rapid planning method for reentry gliding trajectories considering time and full-state constraints. This method divides the gliding trajectory into longitudinal trajectory planning and lateral planning. In the longitudinal trajectory planning part, a two-parameter drag acceleration profile model in the form of corridor boundary interpolation is first designed. Then, analytical prediction expressions for flight time and range considering the influence of Earth's rotation are derived. Subsequently, the profile design is achieved by correcting the profile parameters, simultaneously satisfying the constraints of terminal altitude, velocity, local ballistic tilt angle, range, and flight time. Lateral planning employs a strategy combining an iterative one-time tilt reversal point with a heading angle error corridor to satisfy the constraints of terminal position and track yaw angle. Furthermore, for large-scale lateral maneuvers, a target range and flight time correction strategy considering longitudinal and lateral coupled motion is further designed, completing the generation of a three-degree-of-freedom gliding trajectory. Finally, the effectiveness, applicability, and speed of the method are verified using the reentry gliding of a CAV-H as an example.

[0014] This method divides the gliding trajectory planning problem into longitudinal trajectory planning and lateral planning. In the longitudinal trajectory planning part, firstly, a two-parameter drag acceleration profile model in the form of corridor boundary interpolation is designed; secondly, analytical prediction expressions for time and range considering the influence of Earth's rotation are derived, improving the speed and accuracy of the prediction algorithm. Then, the profile design is completed by correcting the dual profile parameters, simultaneously satisfying terminal energy, range, time, and local ballistic inclination constraints. Lateral planning is implemented by a combination of heading adjustment / holding algorithms to meet terminal position and track yaw angle constraints. Based on this, for cases with large-scale lateral maneuvers, a target range and time correction strategy considering the coupling of longitudinal and lateral motions is designed, completing the generation of a three-degree-of-freedom gliding trajectory. Finally, a simulation was conducted using CAV-H reentry gliding as an example to verify the effectiveness and multi-task applicability of the proposed method. Compared with existing methods, the proposed method has higher control accuracy under time and terminal full-state constraints, a larger time and heading adjustable range, and higher computational efficiency due to the adoption of profile analytical prediction correction design and improved outer loop correction strategy. It can quickly predict the flight capability boundary.

[0015] First, the gliding trajectory planning problem is described.

[0016] 1. Aircraft motion model Assuming the Earth is a rotating sphere, establish a dimensionless, three-degree-of-freedom equation of motion for the center of mass, with energy as the independent variable: (1) The left side of equation (1) consists of dimensionless state quantities. For dimensionless energy The derivative; The dimensionless distance to the geocenter. For dimensionless velocity, Longitude of the Earth's core It is the geocentric latitude; For the local ballistic inclination angle, The yaw angle of the track. The tilt angle is given. The dimensionless lift acceleration is also given. Drag acceleration The calculation formula is: (2) In equation (2), For the mass of the aircraft, For the Earth's radius, For aerodynamic reference area, , These are the lift and drag coefficients, respectively; atmospheric density. Unified adoption of the index model Perform calculations. Flight altitude; , and , These are the Coriolis acceleration and the entrainment acceleration corresponding to the Earth's rotation, respectively.

[0017] 2. Aircraft constraint model During reentry gliding, in order to ensure that the aircraft reaches the mid-to-terminal handover point safely and accurately, it needs to meet the corresponding process constraints, control constraints, and terminal constraints. The corresponding constraint models are given below.

[0018] 2.1 Process Constraints Process constraints mainly include heat flux, dynamic pressure, overload, and equilibrium glide conditions. Among these, heat flux... Dynamic pressure Overload The hard constraints that must be satisfied during flight are represented by the following constraint model: (3) In the formula, The heat flux density coefficient, , as well as These are heat flux density, dynamic pressure, and peak overload, respectively. Furthermore, to limit the skipping of the gliding trajectory and improve trajectory control, equilibrium gliding conditions are added as process constraints: (4) In the formula, To balance the gliding tilt angle, this invention uses a uniform 0°. Compared to the previous constraints, the balancing gliding condition is a "soft constraint" and does not need to be strictly satisfied.

[0019] To facilitate subsequent profile design, energy Perform normalization, that is, let , , , Let the initial and terminal energies be the reentry energies, respectively. Then, the constraints in equations (3) and (4) can be transformed into drag acceleration. and The functional relationship is: (5) In the formula, , Let be the average glide distance from the Earth's center. Therefore, the boundary of the DE reentry corridor can be obtained as: (6) In the formula, , These are the upper and lower boundaries of the re-entry corridor, respectively.

[0020] Therefore, the process constraints in equations (3) and (4) can be transformed into drag acceleration corridor constraints: (7) 2.2 Control Constraints Control the angle of attack and tilt angle The constraint on the control variable mainly limits its amplitude, that is: (8) In the formula, , , , These are the upper and lower limits for the angle of attack and the heel angle, respectively.

[0021] Taking into account both range capability and heat protection requirements, the angle of attack profile is preset as follows: (9) In the formula, , These are the maximum angle of attack and the maximum lift-to-drag ratio angle of attack, respectively. and These are the piecewise parameters of the angle-of-attack curve.

[0022] 2.3 Terminal Constraints The terminal constraints of the gliding phase include terminal altitude, speed, longitude, latitude, local ballistic inclination, track yaw angle, heading angle deviation, and flight time constraints, i.e., full spatiotemporal constraints: (10) In the formula, For the terminal's line of sight angle, , , , , , , and These are the corresponding terminal constraint values.

[0023] Considering that the method of this invention is based on the drag acceleration-energy profile, it is necessary to transform the terminal constraints in equation (10). Specifically, the terminal height and velocity constraints can be transformed into: (11) Terminal latitude and longitude constraints can be converted into flight range constraints: (12) In the formula, , These are the constraint values ​​for drag acceleration and range.

[0024] Based on this, the present invention proposes a near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints. According to different trajectory characteristics, the reentry gliding trajectory can be divided into an initial descent segment and a gliding segment. In the initial descent segment, due to the relatively high flight altitude and small aerodynamic forces, effective control of the aircraft is difficult; therefore, a constant roll angle is adopted for this segment. Perform open-loop control when the drag acceleration Then, the flight transitions to the gliding phase. The sign of the constant roll angle is determined based on the initial and terminal heading constraints, the specific method of which will be discussed later in the section on lateral planning method design.

[0025] The gliding phase employs a rapid trajectory planning method based on drag acceleration-energy profiles. This involves first planning the longitudinal drag acceleration profile to obtain the roll angle magnitude, and then determining the sign of the roll angle through lateral planning. The longitudinal trajectory planning includes parametric design of the drag acceleration profile and analytical prediction and correction of range and flight time. Lateral planning is achieved through a combination of algorithms for heading adjustment, heading maintenance, and terminal position correction. Furthermore, a target range and flight time correction strategy considering the coupled longitudinal and lateral motions was designed, thus completing the generation of a three-degree-of-freedom gliding trajectory.

[0026] Step 1: Longitudinal Trajectory Planning The purpose of longitudinal trajectory planning is to determine a reference trajectory that satisfies process constraints, altitude, speed, range, flight time, and local ballistic inclination constraints. To this end, a two-parameter drag acceleration profile model with corridor boundary interpolation was first designed, and analytical prediction expressions for flight time and range considering the effects of Earth's rotation were derived. Then, profile design and longitudinal trajectory planning were achieved through profile parameter correction.

[0027] Step 1.1, Drag Acceleration-Energy Corridor Fitting To facilitate the parametric design of the subsequent drag acceleration profile, it is necessary to fit the upper and lower boundaries of the reentry corridor. The upper boundary of the corridor consists of heat flux, dynamic pressure, and overload constraints; based on the curve shape, it can be fitted as a four-segment quadratic curve. (13) In the formula, To fit the upper boundary of the corridor, For energy, For normalized energy, and These are the initial normalized energy for reentry and the terminal normalized energy for reentry, respectively. , , These represent the normalized energy at the inflection points of the corridor's upper boundary. Furthermore, to ensure the continuity and smoothness of the corridor boundary, cubic polynomial curves are introduced between each segment of the corridor's upper boundary for transition. Simultaneously, the fitted corridor should be located within the original corridor to ensure flight safety.

[0028] The lower boundary of the corridor is a gliding equilibrium constraint. Based on the curve shape, it can be fitted as a quadratic curve: (14) In the formula, To fit the lower boundary of the corridor, The normalized energy at the lower boundary segment point. , , These are the coefficients of the fitted polynomial, where... .

[0029] Figure 1 By comparing the shapes of the actual corridor boundary and the fitted corridor boundary, it can be seen that the fitted corridor basically coincides with the actual corridor, and the fitting accuracy is high. In fact, considering that the shape of the reentry corridor is only related to the overall parameters of the aircraft and the preset angle of attack profile, once the two are determined, fitting can be performed based on the corridor shape. This approach has good adaptability and reliability.

[0030] Step 1.2, Parametric Design of Drag Acceleration Profile As mentioned earlier, the purpose of longitudinal trajectory planning during the gliding phase is to design drag acceleration profiles within the reentry corridor. This is to meet the constraints of terminal energy, range, time, and local ballistic inclination. Considering these constraints, the drag acceleration profile can be designed as a piecewise polynomial with dual interpolation parameters, allowing the profile parameters to be solved based on the satisfied range and time constraints.

[0031] Based on the analysis of flight dynamics characteristics, it can be seen that when the aircraft moves along the upper boundary of the corridor... During flight, a minimum range trajectory will be generated, and the corresponding flight time will also be at its minimum; when the aircraft travels along the lower boundary of the corridor... During flight, a maximum range trajectory will be generated, corresponding to a maximum flight time. Therefore, it is possible to... , The internal interpolation method is used to design the reference drag acceleration profile, which can ensure the safe flight of the aircraft within the reentry corridor, while maximizing the range of range and flight time adjustment.

[0032] like Figure 1 As shown, the reference drag acceleration profile The design is in five-segment form, and the specific expression is as follows: (15) In the formula, , These are the interpolation coefficients for the undetermined profile, used to ensure that the drag acceleration profile remains within the corridor. , Constraints should be satisfied (16) also, The normalized energy at the slip point. , , , This is the normalized energy at the preset segmentation points. and The adjustment segment is obtained by interpolating the upper and lower boundaries of the corridor; , , For the transition section, its polynomial coefficients , , , ( The continuity of the designed profile can be determined by the function values ​​at the left and right endpoints and the continuity condition of the first derivative, so as to ensure the continuity and smoothness of the designed profile.

[0033] The following example uses terminal drag acceleration and local ballistic tilt angle constraints to illustrate the algorithm for applying endpoint constraints to solve polynomial coefficients.

[0034] First, the transition coefficient , , , It is possible , The conditions for the continuity and differentiability of the function at a given point are determined. Among them, The constraints at the location are (17) In the formula, The constraint on the rate of change of terminal drag acceleration can be expressed as follows: , , The function, specifically the method is as follows: Drag acceleration right The derivative can be expressed as (18) in, This is the local trajectory inclination constraint value at the terminal. This is the terminal flight speed constraint value. This is the terminal drag acceleration constraint value. r The distance from the Earth's center. V This refers to flight speed.

[0035] In the formula, the expressions for the derivatives of each term are: (19) in, It is a high constant; This refers to the local trajectory inclination angle.

[0036] Substituting equation (19) into equation (18), we get: (20) Substituting the terminal constraint values ​​of each state variable into formula (20), we can obtain... (twenty one) Therefore, it can be based on The continuous and differentiable conditions of the drag acceleration profile are determined to complete the application of terminal energy and local velocity tilt angle constraints.

[0037] Preset normalized energy point , , , and constraint values , Once determined, refer to the drag acceleration profile. Only with parameters , The two are related and can be determined by range and flight time constraints. Therefore, a reference drag-acceleration profile is designed. This design can simultaneously meet the constraints of process, terminal energy, local ballistic inclination, range, and flight time. Designing the drag acceleration profile as an analytical polynomial is a relatively traditional method, but the profile designed in this invention is obtained by interpolation of the corridor boundary, thus maximizing the range and flight time adjustment range while satisfying process constraints. Furthermore, the transition section is designed as a cubic polynomial function, ensuring the continuity and smoothness of the reference profile and facilitating tracking.

[0038] Step 1.3, Flight Time Analysis and Prediction When performing trajectory planning based on the drag-acceleration profile method, it is necessary to predict the range and flight time corresponding to the entire profile. Define the range. Let be the length of the trajectory projected onto the Earth's surface as a three-dimensional trajectory. Then, the derivatives of the range and energy with respect to time are: (twenty two) In the formula, An additional factor affecting the Earth's rotation. , The dimensionless angular velocity of Earth's rotation. The latitude of the Earth's core. This is the yaw angle of the flight path.

[0039] Considering the Earth's rotation, and assuming the local trajectory inclination is small, that is... Then the derivatives of the flight distance and flight time with respect to normalized energy are: (twenty three) In the formula, To increase drag acceleration, , .

[0040] Considering Since it is a small amount, it can be approximated as a function of normalized energy. Linear functions: (twenty four) In the formula: (25) In the formula, , For the starting point and the corresponding terminal state When the flight path is near a great circle, In It can be determined from the initial target line of sight angle Approximate representation. Therefore, the coefficients... , All parameters are known. It can be represented as A linear function.

[0041] make Integrating equation (23) yields the range and flight time corresponding to the reference drag acceleration profile, as shown in the following expression: (26) In the formula, .

[0042] The right side of the above equation is about the normalized energy. By deriving the antiderivative of the integral of the function, analytical prediction formulas for the flight distance and time can be obtained. Since... For about Since the piecewise quadratic and cubic polynomials are given, we only need to derive the general form of the quadratic and cubic polynomials, find their corresponding antiderivatives, and sum the integral results of each segment to obtain the analytical prediction results of the total flight time and range. The specific algorithm is given below.

[0043] (1) Flight range prediction Assuming normalized energy range Inside, and It satisfies the following quadratic function relationship: (27) Through analytical derivation, the range prediction function can be obtained as follows: (28) In the formula, , , , , are the coefficients of the quadratic function in its general form. Intermediate variables for finding the roots of a quadratic equation. .

[0044] Assuming normalized energy range Inside, and Satisfying the following cubic function relationship (29) Through analytical derivation, the range prediction function can be obtained as follows: (30) In the formula, For the equation The solution can be obtained by using the quadratic formula, without the need for numerical methods. , , , These are the coefficients of the cubic function in its general form.

[0045] (2) Time prediction like and The quadratic function relationship satisfying equation (27) can be analytically derived to obtain the flight time prediction formula as follows: (31) In the formula: (32) In the formula, , , , , To solve for intermediate quantities.

[0046] like and The cubic function relationship satisfying equation (29) can be analytically derived to obtain the following flight time prediction formula: (33) In the formula: (34) In the formula, , , , The coefficients of the transformed equation are... The solution can be calculated using the quadratic formula, without the need for numerical methods.

[0047] Equations (28), (30), (31), and (33) are all related to the initial normalized energy at a certain stage. Terminal normalized energy and the profile function of that segment The parsing expression. Therefore, once given , The flight distance and flight time of each segment can be predicted using the above analytical formula. By summing the calculation results of each segment, the predicted flight time and flight distance of the entire profile can be obtained.

[0048] The above method avoids using numerical integration to predict flight distance and time, thus achieving higher computational efficiency. Secondly, compared to traditional piecewise linear profiles, the analytical prediction formula is derived for quadratic and cubic polynomial profiles, expanding the form of the profile function. Simultaneously, it can compensate for prediction errors in flight distance and time caused by Earth's rotation, resulting in higher prediction accuracy. Furthermore, due to the assumptions made in the derivation process... , Therefore, the predicted range and time have a certain error, which can be corrected by a small number of subsequent outer loop iterations.

[0049] (3) Correction algorithm As mentioned earlier, the flight range Flight time Based solely on drag acceleration profile parameters , Therefore, it satisfies the following functional relationship: (35) In the formula, and These are the profile parameters for flight distance and flight time, respectively. , Analytical functions.

[0050] Based on the drag acceleration profile, simultaneously analyze the parameters of two profiles. , Perform correction: (36) Then equation (36) can be expressed as about , A system of two nonlinear equations: (37) In the formula: , .

[0051] The above system of two linear equations can be solved using Newton's iteration method, due to the flight distance ,time The proposed algorithm uses the analytical formulas (28), (30), (31), and (33) from step 1.3 for prediction. Compared with the method of prediction using numerical integration, the computational efficiency of the proposed algorithm is significantly improved.

[0052] Step 2: Generation of Side Angle Amplitude Command Once the reference drag acceleration-energy profile is determined, the tilt angle command amplitude can be obtained by tracking this profile. Taking the second derivative of drag acceleration with respect to energy, we can obtain: (38) In the formula: (39) In the formula, For drag acceleration, For lift acceleration, a b are intermediate variables. This is the second derivative of the actual drag acceleration with respect to energy. Let velocity be the first derivative with respect to energy. , , These are the drag coefficient, the first derivative of the drag coefficient with respect to energy, and the second derivative, respectively.

[0053] Design the second-order stage Tracking: (40) In the formula, The damping coefficient is... The natural frequency. Substituting equation (40) into equation (38), we obtain the tilt angle command amplitude as: (41) In the formula, , Reference drag acceleration energy The first and second derivatives can be obtained through a reference profile. right The derivative is obtained by transformation; Actual resistance acceleration energy The first derivative.

[0054] Step 3, Lateral Planning The purpose of lateral planning is to determine the sign of the roll angle to control the lateral motion of the aircraft, thereby satisfying the terminal position and yaw angle constraints. To this end, the lateral planning method of this invention consists of two parts: 1) an iterative algorithm for the reversal point based on a single roll reversal; and 2) a traditional heading angle error corridor design. The iterative roll reversal point occurs in the initial phase of gliding flight, mainly used for large-scale heading adjustments to meet the terminal track yaw angle constraints. The heading angle error corridor acts in the later phase of flight, mainly used to meet the terminal position and heading angle error constraints. Finally, by analyzing the mechanism of this planning method, a quantification of the adjustable range of the terminal track yaw angle and a method for determining the initial roll angle sign are presented.

[0055] (1) Lateral reduced-order motion model Considering the Earth's rotation, assume Then, the reduced-order lateral motion equation can be obtained by deriving equation (1): (42) In the formula, .

[0056] definition: (43) Then we have: (44) In the formula, , , , All can be tracked Therefore, by integrating the above equations of motion, the state variables at the terminal energy point can be predicted quickly. , , This facilitates iterative calculations for subsequent lateral planning.

[0057] (2) Lateral planning considering terminal track yaw angle constraints To simultaneously meet the terminal trajectory yaw angle and position constraints, a comprehensive trade-off and utilization of lateral maneuverability are necessary to achieve incident azimuth adjustment and ensure terminal position accuracy. Considering that the flight speed gradually decreases during unpowered gliding, the lateral maneuverability also gradually decreases with flight time. Therefore, if... Figure 2 As shown, in the initial gliding phase, the aircraft needs to perform certain lateral maneuvers to bring its real-time line-of-sight angle close to the desired incident azimuth angle, thereby achieving a wide range of adjustments to the incident heading and trajectory. In the subsequent phase, a lateral planning method based on the heading angle error corridor is mainly used to control the aircraft to fly along the desired incident azimuth angle to the target area, while ensuring high terminal position accuracy. Based on the above analysis, lateral planning can be divided into a heading adjustment phase and a heading maintenance and terminal position correction phase. The heading adjustment phase is used to adjust the aircraft to point towards the target at the desired incident azimuth angle, while the heading maintenance phase is used to control the track yaw angle to gradually approach the incident azimuth angle.

[0058] To achieve the above objectives, Figure 3 A schematic diagram of the lateral planning is provided. The heading-maintaining segment employs a heading angle error corridor control method, while the heading-adjusting segment is achieved by adjusting the roll reversal point. [Settings are missing from the original text.] Define the normalized energy corresponding to the tilt reversal point. As for the change in heading, it can be seen from theoretical analysis and numerical simulation that... and The relationship exhibits a monotonic change because the timing of the first roll reversal determines the change in the aircraft's incident azimuth relative to the target. The later the roll reversal, the greater the distance the aircraft travels in a lateral maneuver in one direction, resulting in a greater change in azimuth relative to the target, and consequently, a greater change in the final heading. The larger the value, the more it can be solved iteratively using the secant method. To meet the terminal track yaw angle constraint requirements, the lateral planning method is given below.

[0059] First, the sign of the heel angle during the heading adjustment segment can be determined by the following formula: (45) in, The initial tilt angle sign, Normalized energy for entering the heading angle error corridor; when At that time, the sign of the heel angle is determined by the heading angle error corridor, and the corresponding heel reversal logic is as follows: (46) In the formula, The sign of the tilt angle at the previous moment. For heading angle error, The heading angle error corridor boundary can be designed as a piecewise linear function of velocity.

[0060] Based on this, the tilt reversal point can be solved iteratively. To satisfy the terminal track yaw angle constraint, the specific steps are as follows: (1) Let j = 0, the tilt reversal point is ; (2) Substituting the reduced-order lateral motion equation into equation (42) and integrating, we obtain the terminal track yaw angle deviation as follows: ,set up To determine the iteration error limit, check if the following condition is true: (47) If true, terminate the calculation and output the result. Otherwise, proceed to (3); in, The initial value is the tilt reversal point. As a constraint on the yaw angle of the terminal track; (3) Let the tilting reversal point be Returning to step (2), the obtained terminal track yaw angle deviation is If the accuracy requirements are met, the calculation terminates and the output is given. Otherwise, proceed to (4); in, This is the normalized energy increment.

[0061] (4) Calculate the partial derivatives: (48) Update the tilt reversal point: (49) (5) Order j = j+ 1. Transfer to (2).

[0062] It is worth noting that, in order to ensure the feasibility of the obtained roll reversal point and that the ship can enter the heading angle error corridor after the reversal, the roll reversal point must meet the following conditions. ,in, The maximum rollover energy can be determined based on the lateral maneuverability before and after the rollover, and is taken as [value missing]. Furthermore, to ensure the terminal track yaw angle meets accuracy requirements, the width of the final segment of the heading angle error corridor should be less than [a certain value]. .

[0063] (3) Quantification of the adjustable range of track yaw angle and algorithm for determining the initial tilt direction As mentioned above, and The relationship is monotonically changing; therefore, for a reentry trajectory with a fixed drag acceleration profile, there are two extreme ground trajectories, such as... Figure 2 As shown. When When, corresponding to Figure 2 Case 1, Follow It increases with the increase of, when hour, Reaching the maximum value ;when When, corresponding to Figure 2 Case 2, Follow As it increases, it decreases, when hour, Reaching the minimum value Therefore, for the initial tilt angle Cases with different symbols, and They all follow a monotonic relationship.

[0064] Based on the above analysis, we can further provide the terminal trajectory yaw angle under certain conditions for the drag acceleration profile. Adjustable range and initial tilt angle direction The specific algorithm is as follows: (1) Let , The lateral reduced-order motion equation of integral (42) yields the terminal heading angle. ; (2) Let , Integrating the reduced-order lateral motion equation of equation (42), we can obtain the terminal heading angle. ; (3) Determine The adjustment range is ; (4) Determine the direction of the initial tilt angle .

[0065] It is worth noting that the above mechanism analysis and algorithm are all based on the initial heading angle. The case of pointing towards a target point can generally be discussed in the same way. The above algorithm can be further used to allocate the incident azimuth angles of each aircraft and determine the initial tilt angle direction of each aircraft in cooperative missions.

[0066] The trajectory planning method proposed in this invention will be further explained below.

[0067] Considering that large lateral maneuvers increase the actual range, using the great circle length between the reentry point and the target point as the target range will result in some deviation. Furthermore, the derivation of the analytical prediction formulas for range and time introduces a zero-tilt assumption, leading to a discrepancy between the predicted and actual values. Therefore, this invention borrows from the EAGLE algorithm, using multiple iterations between longitudinal trajectory planning and lateral planning to correct the target range and flight time, thus satisfying all process and terminal constraints. However, for cases with large lateral maneuvers, simply using the difference in great circle length to correct the trajectory arc length is insufficient.

[0068] like Figure 4 As shown, let the azimuth angle between the reentry point and the target be... Great circle range is The length of the great circle arc between the trajectory terminal and the reentry point is The distance between the trajectory terminal and the target point is .when and When the deviation is large, Therefore, the accuracy of correcting the target range solely through the deviation of the large circular arc length is insufficient, a point also evident from numerous numerical simulations. Thus, a more precise method should be employed. As a correction to the target range. However, due to Using this as a correction factor would cause the target range to increase continuously, making it impossible for the trajectory terminal to converge to the vicinity of the target point. Therefore, it is necessary to determine the relative positional relationship between the trajectory terminal and the target point. The symbol is given below, and the method for determining it is described below.

[0069] Let the first The longitudinal path of the trajectory obtained in the next iteration is ,but: (50) In the formula, , The azimuth angle between the trajectory terminal and the reentry point. The azimuth angle between the target point and the reentry point.

[0070] Combination Figure 4 From (a) and (b), we can see that The symbol and terminal point position and target track yaw angle Related: (1) When hour, ; (2) When hour, ; therefore, The symbol can be represented by the following formula. (51) In the formula, The great circle distance between the reentry point and the target point. For the first The longitudinal path of the trajectory obtained in the next iteration is .

[0071] In addition, to reduce the number of corrections to the target range and improve the convergence speed of the algorithm, a maneuvering coefficient is introduced during the planning process to correct the initial target range. The specific process is as follows: Figure 5 As shown, assuming the maneuverability coefficient is... The basic steps for gliding trajectory planning are as follows: (1) Let =0, , ,in, and For the first The target range and flight time constraints for each step; (2) Based on the constraints of range and flight time, parameters are simultaneously adjusted according to the drag acceleration profile. , After correction, a reference profile can be obtained. ; (3) For the reference section Perform tracking to obtain longitudinal trajectory parameters and tilt angle amplitude commands. and flight time ; (4) Based on the terminal position and the yaw angle constraint, iteratively solve for the roll angle reversal point. The lateral trajectory parameters and the tilt angle command symbol are obtained. and terminal location parameters; (5) Calculate the deviation based on the terminal position parameters , ; (6) Update the target range to Target flight time ; This is the total flight time constraint value; (7) Judgment Check if the condition is met. If it is met, the algorithm ends and outputs the flight trajectory; otherwise, Repeat steps (2)-(7); where, This is the convergence error limit.

[0072] It is worth noting that the above trajectory generation method obtains longitudinal trajectory parameters through profile tracking and uses them as input to the lateral reduced-order equation, which improves the accuracy of lateral trajectory prediction and command iteration solution. Then, the target range and time are corrected by the terminal parameters obtained by lateral planning, avoiding the ballistic integration process of the outer loop and significantly improving the computational efficiency of the planning algorithm.

[0073] Example 1 The planning method provided by the present invention will be simulated and analyzed through specific embodiments below.

[0074] Simulation conditions Using the American general aviation aircraft CAV-H as the simulation object, the initial and terminal state constraints are set as follows: =80km, =6500m / s, =0°; =25km, =2000m / s, =-2°; Process constraints are set as follows: , , The preset angle-of-attack profile is shown in equation (9), and the relevant parameters are set as follows: , , , The heading angle error corridor parameters are set as follows: , , , The preset parameters for the drag acceleration profile are: =2 m / s 2 , , , , The control constraints are: =80°, =5°, =5°, all simulations were performed on a desktop computer equipped with an Intel Core i7-8700 3.20GHz Intel processor, and the simulation environment was the Visual Studio 2017 platform.

[0075] Rapid Prediction Simulation of Flight Capability Boundaries The following section conducts a rapid predictive simulation of flight capability boundaries to demonstrate the advantages of the proposed planning method in rapidly quantifying the range of range, flight time, and heading adjustments. First, a simulation quantifies the adjustment range of range and flight time. Based on the simulation conditions described above, parameters are adjusted in increments of 0.01. and In respectively The simulation is performed by iterating through the data and using analytical prediction formulas for range and flight time. Each prediction takes approximately 1 ms, and the resulting range and flight time adjustment range are as follows: Figure 6 As shown. Figure 6 (a) represents the time adjustment range. Figure 6 (b) is the range of flight adjustments. Figure 6 (c) represents the time-range. Figure 6 (d) is the DE profile under the fixed range condition.

[0076] Depend on Figure 6 From (a) and (b), we can see that the profile parameters It has a strong ability to adjust its range because, given a fixed initial and terminal energy, the range is only related to the drag acceleration profile. The corresponding adjustment segment has a larger adjustable range of drag acceleration, thus a larger range of range adjustment; in contrast, the profile parameters It has a stronger ability to adjust flight time because flight time is related to both drag acceleration and flight speed, and the parameters... The corresponding adjustment segment has a lower flight speed, thus allowing for greater time adjustment capabilities. Figure 6 (c) It can be seen that the coverage of the range and flight time is approximately a rhombus. The time adjustment range corresponding to the ranges at both ends is smaller, and the closer the range is to the middle, the larger the corresponding time adjustment range is. Secondly, as shown in the figure, the range adjustment range of the aircraft is approximately [2800, 8900] km, and the time adjustment range is approximately [680, 2000] s. If the target range is given, the time adjustment range can be quickly determined according to the figure, thus providing a reference for determining the coordination time in collaborative tasks. Figure 6 (d) gives the voyage distance At a range of 6392.7 km, the drag acceleration profiles corresponding to the maximum and minimum flight times are as follows: the maximum flight time is 1596 s, the minimum flight time is 1322 s, and the time adjustment range is 274 s.

[0077] Secondly, a rapid predictive simulation of the terminal trajectory yaw angle adjustment capability is conducted based on the proposed lateral planning algorithm. The reentry point longitude is set. ,latitude The yaw angle of the track is =140°, Longitude of the target point ,latitude Total voyage Other simulation conditions are the same as in Section 3.1. The lateral planning algorithm is used to perform quantitative simulation of the adjustable range of the terminal trajectory yaw angle. The simulation takes about 200ms. , The corresponding simulation result curves are as follows Figure 7 As shown. Figure 7 (a) is the yaw angle curve of the track. Figure 7 (b) is the ground track.

[0078] Depend on Figure 7 (a) It can be seen that the extreme values ​​of the terminal track yaw angle are respectively , Angle adjustable range This indicates that the proposed lateral planning algorithm has a strong ability to adjust the heading. Combined with... Figure 7 (b) It can be seen that, Corresponding initial tilt angle sign Therefore Before the roll reversal, the aircraft gradually decreases speed and moves towards the northeast of the target, gradually increasing the target's azimuth angle. After the roll reversal, the aircraft gradually turns towards the target point and enters the heading angle error corridor in the terminal phase until it hits the target.

[0079] The above results show that the designed parameterized drag acceleration profile has a large range of range and flight time adjustment, and the lateral planning algorithm has a large heading adjustment capability, which can realize the rapid prediction of flight capability boundaries.

[0080] Multi-task trajectory planning simulation under nominal conditions For reentry missions under nominal conditions with different ranges, times, and terminal full-state constraints, gliding trajectory planning simulations were performed to verify the mission adaptability of the proposed algorithm. Table 1 shows the initial latitude and longitude, track yaw angle and terminal angle, flight time, and range constraints for each simulation example. The target point latitude and longitude constraint is set as follows: , Terminal range constraint is =50km, correction factor is =1.02.

[0081] Table 1 Simulation Condition Settings The curve obtained from the simulation is as follows Figure 8 The results are shown in Table 2. Table 2 provides the terminal parameters for examples 1-6. It can be seen that, due to energy being used as the simulation cutoff condition, the deviations in terminal height and velocity are relatively small. Specifically, the terminal height deviation is less than 100m, the velocity deviation is less than 2m / s, the local trajectory inclination deviation is less than 0.1°, the trajectory yaw angle deviation is less than 3°, the range deviation is less than 1km, and the flight time deviation is less than 1s. The local velocity inclination angle error is caused by the drag acceleration profile tracking error, while the trajectory yaw angle error is determined by the width of the terminal heading angle error corridor. These results demonstrate that the proposed planning algorithm has high computational accuracy and good applicability to constraints such as different initial firing directions, ranges, flight times, and terminal angles. Furthermore, the number of outer loop iterations for each example is less than 3, and the trajectory generation time is within 3s, reflecting the speed of the proposed planning algorithm.

[0082] Table 2 Terminal results under different simulation conditions Figure 8 Simulation result curves for examples 1-6 are given. Figure 8 As shown in (a) and (b), the designed drag acceleration profile meets the process and terminal constraints, and the profile is smooth, continuous, and easy to track. Examples 1, 2, 4, and 5 verify the applicability of the proposed algorithm to different range constraints. As the target range gradually increases, the drag acceleration profile generally decreases, while the flight altitude gradually increases to improve the aircraft's range capability and achieve the mission requirements. Figure 8 As shown in (c) and (e), to achieve the terminal track yaw angle constraint, the aircraft performs large-scale lateral maneuvers in the early stage to gradually transition the target azimuth angle to near the terminal desired value. In the later stage, multiple tilt reversals are used to gradually converge the ground track and track yaw angle to near the target. Examples 3 and 4 further verify the proposed algorithm's ability to adjust the track yaw angle under the same flight distance conditions. It can be seen that the first tilt reversal points of both tracks are relatively late to achieve a larger heading adjustment range. In addition, from Figure 8 From (b) and (f), it can be seen that since the terminal local ballistic inclination angle of Example 6 is -4°, its flight altitude first increases and then decreases in the terminal phase, thereby reducing the lift effect by reducing atmospheric density, and thus reducing the terminal local ballistic inclination angle. Figure 8 (d) It can be seen that in order to meet the yaw angle constraint requirements of the terminal track, the tilt angle was reversed multiple times when approaching the terminal, with a total number of reversals of about 10-12.

[0083] To address the hypersonic reentry gliding problem considering time and terminal full-state constraints, this invention studies a fast trajectory planning method based on drag acceleration-energy profile. Theoretical analysis and simulation results show that: (1) The proposed method is feasible, adaptable to multiple tasks and fast. Compared with the existing methods, due to the adoption of profile analytical prediction correction design and improved outer loop correction strategy, the proposed method has higher control accuracy in time and terminal full state constraints, as well as higher computational efficiency, and can quickly predict the flight capability boundary.

[0084] (2) The reference drag acceleration profile is obtained based on the two-parameter interpolation of the corridor boundary. Therefore, it can maximize the range of range and flight time adjustment under the condition of satisfying process constraints, and facilitate the rapid quantification of the adjustable range. The fitting of the corridor boundary achieves high accuracy with a small polynomial order, reducing the computational cost and complexity of the method. In addition, the transition section is designed as a cubic polynomial function, which can ensure the continuity, smoothness and easy tracking of the reference profile, and can realize the application of terminal altitude, velocity, local ballistic inclination angle range and flight time constraints. The reference drag acceleration profile is obtained by piecewise function interpolation of the upper and lower boundaries of the corridor. Therefore, this method can achieve full coverage of the trajectory within the corridor constraint range, with a large range of range and flight time adjustment, while ensuring that the thermal flux, dynamic pressure and overload constraints are strictly satisfied.

[0085] (3) The two-stage lateral planning algorithm based on heading adjustment / holding has high control accuracy of terminal position and track yaw angle and a large heading adjustment range. It can also realize the rapid quantification of the adjustable range of terminal track yaw angle, which can provide a reference for collaborative task planning and online allocation.

[0086] (4) The proposed method is feasible, adaptable to multiple tasks and fast. Compared with the existing methods, due to the adoption of profile analytical prediction correction design and improved outer loop correction strategy, the proposed method has higher control accuracy in time and terminal full state constraints, as well as higher computational efficiency, and can quickly predict the flight capability boundary.

[0087] The above-described embodiments are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited thereto. Any simple changes or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the scope of the technology disclosed in the present invention shall fall within the scope of protection of the present invention.

Claims

1. A near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints, characterized in that, Includes the following steps: Considering the constraints of terminal altitude, speed, local ballistic inclination, range and flight time, a two-parameter drag acceleration profile model with corridor boundary interpolation is constructed. Based on the aforementioned two-parameter drag-acceleration profile model, an analytical prediction model for the aircraft's range and flight time is constructed. Based on the predicted range and flight time, the parameters of the two-parameter drag acceleration profile model are corrected to obtain the reference drag acceleration profile. The reference drag acceleration profile is tracked to obtain longitudinal trajectory parameters and tilt angle command amplitude. and flight time deviation; Considering the terminal track yaw angle and position constraints, a two-stage lateral planning method based on heading adjustment / maintenance is designed, specifically: based on the longitudinal trajectory parameters and the roll angle command amplitude... The tilt reversal point is solved iteratively. The lateral trajectory parameters and the tilt angle command symbol are obtained. and terminal location parameters; Considering the case of large lateral maneuvers, the terminal position deviation is calculated based on the terminal position, target point parameters, and track yaw angle constraints. and terminal position deviation symbol ; according to , And update the target range and flight time based on flight time deviation; Based on the updated target range and flight time, the longitudinal and lateral flight trajectories are continuously corrected through outer loop iterations until the terminal accuracy requirements are met, at which point the flight trajectory and roll angle commands are output. ; The construction of the two-parameter drag acceleration profile model with corridor boundary interpolation specifically includes the following steps: Corridor upper and lower boundary fitting: The upper boundary of the corridor is composed of heat flow, dynamic pressure, and overload constraints. Based on the curve shape, the upper boundary of the corridor is fitted into a four-segment quadratic curve: In the formula, To fit the upper boundary of the corridor; , , These are the normalized energies at the inflection points of the upper boundary of the corridor; For energy, For normalized energy, and These are the initial normalized energy for reentry and the terminal normalized energy for reentry, respectively. The lower boundary of the corridor is a balanced gliding constraint. Based on the curve shape, the lower boundary of the corridor is fitted as a two-segment quadratic curve: In the formula, To fit the lower boundary of the corridor, The normalized energy at the lower boundary segment point; , , These are the coefficients of the fitted polynomial, where... ; Parametric design of drag acceleration profile: Reference drag acceleration profile The design is in five-segment form, and the specific expression is as follows: In the formula, , The interpolation coefficients for the undetermined profile are... , Satisfy constraints: also, The normalized energy at the slip point. , , , The normalized energy at the preset segmentation point; where, and For adjustment section, , , This is a transition section; , , , are the polynomial coefficients, where ; Considering that the terminal height and velocity constraints can be transformed into drag acceleration constraints at the terminal normalized energy level, the drag acceleration profile is described below. Apply terminal drag acceleration constraints and local ballistic inclination angle constraints: First, the transition coefficient , , , pass , The conditions for the continuity and differentiability of the function at a given point are determined; among them, The constraints at the location are: In the formula, The terminal drag acceleration change rate constraint is expressed as: , , The function, in its specific form, is derived as follows: Drag acceleration right The expression for the derivative is: in, This is the local trajectory inclination constraint value at the terminal. This is the terminal flight speed constraint value. This is the terminal drag acceleration constraint value. r The dimensionless distance to the geocenter. V The velocity is dimensionless. In the formula, the expressions for the derivatives of each term are: in, It is a high constant; The local ballistic inclination angle; Substituting the expressions for the derivatives into the drag acceleration... right The expression for the derivative is obtained as follows: Then, substitute the terminal constraint values ​​of each state variable into... The expression yields: Therefore, according to The continuous and differentiable conditions of the drag acceleration profile are determined to complete the application of terminal drag acceleration and local velocity tilt angle constraints.

2. The near-analytical gliding trajectory planning method considering full spatiotemporal constraints according to claim 1, characterized in that, The construction of the flight range prediction model includes the following steps: If we define the range as the length of the trajectory projected onto the Earth's surface by a three-dimensional trajectory, then the derivatives of range and energy with respect to time are: In the formula, An additional factor affecting the Earth's rotation. , The dimensionless angular velocity of Earth's rotation; The latitude of the Earth's core. The yaw angle of the track; Considering the Earth's rotation, assume the local ballistic inclination angle , The differential equations for the flight distance and flight time with respect to normalized energy are: In the formula, To increase drag acceleration, , ; For flight range; This represents the average distance from the Earth's center during gliding. Considering Since it is a small amount, it is approximated as a function of the normalized energy. Linear functions: In the formula: In the formula, For the current normalized energy, ; , For the current and terminal states ; , For coefficients, Represented as A linear function; make The differential equations for integral range and time with respect to normalized energy can yield the range and flight time corresponding to the current energy. The specific expressions for range prediction and flight time prediction are as follows: In the formula, ; Will Substituting the specific expressions into the flight range and flight time prediction formulas, the construction of the flight range prediction model includes the following steps: Assuming normalized energy range Inside, and It satisfies the following quadratic function relationship: Through analytical derivation, the flight range prediction function is obtained as follows: In the formula, , , , , are the coefficients of the quadratic function in its general form. Intermediate variables for finding the roots of a quadratic equation ; Assuming normalized energy range Inside, and It satisfies the following cubic function relationship: Through analytical derivation, the flight range prediction function is obtained as follows: In the formula, For the equation The solution is obtained by calculating using the quadratic formula; , , , These are the coefficients of the cubic function in its general form; The construction of a time prediction model includes the following steps: like and Based on the quadratic function relationship described above, the flight time prediction formula can be derived analytically as follows: In the formula: In the formula, , , , , To solve for intermediate quantities; like and Based on the above cubic function relationship, the flight time prediction formula can be obtained through analytical derivation as follows: In the formula: In the formula, , , , , , To solve for intermediate quantities, the equation The solution is obtained by calculating using the quadratic formula.

3. The near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints according to claim 2, characterized in that, The tilt angle command amplitude The acquisition includes the following steps: The tilt angle command amplitude can be obtained by tracking this profile. Taking the second derivative of drag acceleration with respect to energy, we get: In the formula: In the formula, For drag acceleration, For lift acceleration, a b are intermediate variables. Let be the second derivative of drag acceleration with respect to energy. Let velocity be the first derivative with respect to energy. , , These are the drag coefficient, the first derivative of the drag coefficient with respect to energy, and the second derivative of the drag coefficient with respect to energy, respectively. Design the second-order stage Tracking: In the formula, The damping coefficient is... For natural frequency, Substituting into the second-order tracking equation, the tilt angle command amplitude is obtained as follows: In the formula, , Reference drag acceleration energy The first and second derivatives, For drag acceleration energy The first derivative.

4. The near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints according to claim 3, characterized in that, The lateral planning is divided into a heading adjustment segment and a heading maintenance and terminal position correction segment. Based on the longitudinal trajectory parameters, the roll reversal point is iteratively solved. The lateral trajectory parameters and the tilt angle command symbol are obtained. and terminal location parameters, specifically including: During the heading adjustment segment, the heel angle command symbol is represented as... It is determined by the following formula: in, This is the symbol for the initial tilt angle command. Normalized energy for entering the heading angle error corridor; when At this point, the course maintenance and terminal position correction phase begins, with the heel angle symbolized as follows: It is determined by the following formula: In the formula, This is the symbol for the yaw angle command from the previous moment. For heading angle error, This represents the boundary of the heading angle error corridor. The tilt reversal point The iterative solution includes the following steps: (1) Let j = 0, the tilt reversal point is ; (2) Substituting into the reduced-order lateral motion equations and integrating, we obtain the terminal track yaw angle deviation as follows: ,set up To determine the iteration error limit, check if the following condition is true: If true, terminate the calculation and output the result. Otherwise, proceed to (3); in, The initial value is the tilt reversal point. As a constraint on the yaw angle of the terminal track; (3) Let the tilting reversal point be Returning to step (2), the obtained terminal track yaw angle deviation is If the accuracy requirements are met, the calculation terminates and the output is given. Otherwise, proceed to (4); in, This represents the normalized energy increment. (4) Calculate the partial derivatives: Update the tilt reversal point: (5) Order j = j+ 1. Transfer to (2).

5. The near-analytical gliding trajectory planning method considering full spatiotemporal constraints according to claim 4, characterized in that, The lateral planning also includes quantifying the adjustable range of the terminal track yaw angle and determining the initial tilt direction, specifically including the following steps: Let the initial tilt angle direction , Integrating the reduced-order lateral motion equations, we obtain the terminal heading angle. ; Let the initial tilt angle direction , Integrating the reduced-order lateral motion equations, we obtain the terminal heading angle. ; Determine the terminal track yaw angle The adjustment range is ; Further determine the direction of the initial tilt angle .

6. The near-analytical gliding trajectory planning method considering full spatiotemporal state constraints according to claim 5, characterized in that, Determine the sign of the terminal position deviation Specifically, it includes: Let the first The longitudinal path of the trajectory obtained from the second outer loop iteration is ,but: In the formula, , The azimuth angle of the trajectory terminal relative to the reentry point. The azimuth angle of the target point relative to the reentry point; The sign of is determined by the following formula: when hour, ; when hour, ; therefore, The symbol for is represented by the following formula: In the formula, The great circle distance between the reentry point and the target point. For the first The longitudinal path of the trajectory obtained in the next iteration is .

7. The near-analytical gliding trajectory planning method considering full spatiotemporal state constraints according to claim 6, characterized in that, Assuming the mobility coefficient is The steps for gliding trajectory planning are as follows: (1) Let =0, , ,in, and For the first The target range and flight time constraints for each step; (2) Based on the constraints of range and flight time, parameters are simultaneously adjusted according to the drag acceleration profile. , Correction is performed to obtain the reference profile. ; (3) For the reference section Tracking is performed to obtain longitudinal trajectory parameters and tilt angle command amplitude. and flight time ; (4) Based on the terminal position and the yaw angle constraint, iteratively solve for the roll angle reversal point. The lateral trajectory parameters and the tilt angle command symbol are obtained. and terminal location parameters; (5) Calculate the terminal position deviation based on the terminal position parameters. The sign of the terminal position deviation ; (6) Update the target range to Target flight time ; This is the total flight time constraint value; (7) Judgment Check if the condition is met; if it is, the algorithm ends and outputs the flight trajectory; otherwise, Repeat steps (2)-(7); where, This is the convergence error limit.

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