A near analytical hypersonic gliding guidance method for cooperative hunting

Abstract

The application provides a near-analytical hypersonic gliding guidance method for cooperative hunting, belongs to the field of aircraft control, considers terminal height, speed, local trajectory inclination, flight range and flight time constraints, constructs a resistance acceleration profile model; according to the profile model, an analytical prediction model of the flight range and time of the aircraft is constructed, and then a profile updating strategy based on a double / single parameter sequential solving mode is adopted to update the profile parameters online to obtain a reference profile; based on the reference profile, a longitudinal guidance based on standard profile tracking and a two-stage lateral guidance algorithm based on heading adjustment / retention are adopted in combination with a target range correction strategy to complete the rapid generation of three-dimensional guidance instructions considering the space-time full state constraints. Due to the adoption of the profile analytical prediction correction design and the adaptive updating strategy, the application has high time and terminal full state control accuracy, high calculation efficiency and strong online application potential, and can provide technical support for the cooperative hunting task.

Description

Technical Field

[0001] This invention belongs to the field of aircraft control technology, specifically relating to a near-resolution hypersonic glide guidance method for coordinated encirclement. Background Technology

[0002] As a key technology for hypersonic glide vehicles, reentry glide guidance is an important means to improve their flight autonomy, mission adaptability, intelligence level, and anti-jamming capabilities. 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 the hypersonic reentry glide phase faces a variety of complex constraints, mission conditions, and uncertainties, which pose significant challenges to the mission adaptability, anti-jamming capabilities, and robustness of reentry glide guidance.

[0003] 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 cooperative encirclement operations based on all-round, multi-angle saturation attacks necessitates that aircraft, in addition to meeting the conditions of simultaneous / sequential arrival, also satisfy different incident azimuth and landing angle constraints to achieve spatiotemporal coordination. At this point, the reentry gliding guidance problem evolves into a strongly coupled, rapidly time-varying, multi-constraint nonlinear programming problem with constraints on typical processes, time, and terminal states, further increasing the difficulty of solving the gliding guidance problem. However, existing literature rarely includes gliding guidance methods that simultaneously consider the above constraints. Related research hotspots mainly include two aspects: reentry gliding guidance methods under traditional constraints and guidance methods considering time and angle constraints.

[0004] Existing methods considering time and angle constraints mainly focus on the terminal guidance phase. However, these methods are generally based on the assumption of constant velocity and do not consider process constraints such as heat flux, dynamic pressure, and overload, making them difficult to apply to reentry gliding guidance problems. While existing gliding guidance methods have addressed gliding guidance problems with flight time and angle constraints to some extent, they generally employ numerical integration for range and time prediction or generate commands based on numerical optimization algorithms, resulting in long computation times and hindering online applications. Furthermore, most methods require segmented design of the gliding guidance law, and the selection of segment points significantly limits the maneuverability and adjustability of gliding flight, thus narrowing the adjustment range for time and angle. It is noteworthy that while standard profile tracking guidance methods are widely used in reentry gliding guidance problems, existing research rarely mentions algorithms and strategies for online profile updates. In fact, profile update methods are crucial for improving the accuracy and robustness of guidance algorithms. Summary of the Invention

[0005] To improve the multi-task applicability, real-time performance, and robustness of gliding guidance algorithms, this invention provides a near-analytical hypersonic gliding guidance method for cooperative encirclement.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A near-resolution hypersonic glide guidance method for cooperative encirclement includes the following steps: Considering the constraints of terminal altitude, speed, local ballistic inclination, range and flight time, a drag acceleration profile model based on two-parameter interpolation of the corridor boundary is constructed. Based on the drag acceleration profile model, construct the analytical prediction model of the aircraft's waiting flight range and time, and perform analytical prediction of the waiting flight range and time. Based on the prediction results of the analytical prediction model for the flight path and the analytical prediction model for the time, a drag acceleration profile update strategy based on a dual / single parameter sequential solution mode is adopted to update the parameters of the drag acceleration profile model online, thereby obtaining the updated reference profile. ; Longitudinal guidance: for reference profile Tracking is performed to obtain longitudinal trajectory parameters and tilt angle command amplitude. ; Lateral guidance: Based on longitudinal trajectory parameters and a two-stage lateral guidance method for heading adjustment / holding, the roll reversal point is determined. Iterative solution and determination of the sign of the tilt angle ; 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. ; Based on tilt angle command amplitude and the sign of the tilt angle Generate yaw angle command To achieve guided flight and detect terminal position deviations The target flight range of the aircraft is corrected in real time.

[0007] The near-resolution hypersonic glide guidance method for cooperative encirclement provided by this invention has the following beneficial effects: (1) The present invention considers the terminal altitude, speed, local ballistic inclination angle, range and flight time constraints, and constructs a drag acceleration profile model based on the corridor boundary dual parameter interpolation. Compared with the existing method based on standard profile, the multi-segment smooth drag acceleration profile designed by the present invention based on the corridor boundary dual parameter interpolation can achieve full coverage of the trajectory within the corridor constraint range, and can also achieve the application of the terminal local ballistic inclination angle constraint.

[0008] (2) The profile update strategy based on the dual / single parameter sequential solution mode can effectively solve the problem that the dual parameter profile cannot find a feasible solution in the glide end due to insufficient planarable space, thus improving the terminal accuracy and convergence of the profile update.

[0009] (3) The dual-stage lateral guidance algorithm based on heading adjustment / holding has high control accuracy of terminal position and track yaw angle and large heading adjustment capability, and can also realize the fast adjustment range of terminal track yaw angle.

[0010] (4) The proposed guidance method is feasible, adaptable to multiple tasks and robust; it has high control accuracy in time and terminal full state, as well as high computational efficiency and strong online application potential, which can provide technical support for multi-vehicle collaborative capture missions. Attached Figure Description

[0011] 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.

[0012] 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 a lateral guidance method; Figure 4 This is a schematic diagram of a large lateral maneuver trajectory; Figure 5 A flowchart of the near-analytical hypersonic glide guidance method for cooperative encirclement provided by the present invention; Figure 6 Simulation results of the guidance algorithm hitting the target under the condition of deflection; Figure 7 The curves represent the simulation results of the guidance algorithm under nominal conditions. Detailed Implementation

[0013] 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.

[0014] To address the operational requirements of coordinated encirclement, this invention proposes a near-analytical hypersonic glide guidance method, specifically a near-analytical guidance method based on analytical prediction and correction design of drag acceleration-energy profiles, online adaptive updates, and robust tracking. First, a multi-segment smooth drag acceleration standard profile based on dual-parameter interpolation of the corridor boundary is designed, and analytical prediction expressions for waiting time and range considering the influence of Earth's rotation are derived. Then, the standard profile design is realized by correcting the profile parameters. Subsequently, an online adaptive update strategy for the drag acceleration profile based on a dual / single-parameter sequential solution mode is presented, enabling online updates of the standard profile. Based on this, a longitudinal guidance algorithm based on standard profile tracking and a two-stage lateral guidance algorithm based on heading adjustment / holding are designed, thereby achieving rapid online generation of three-dimensional guidance commands. Finally, simulations using CAV-H reentry gliding as an example are conducted to verify the effectiveness, robustness, real-time performance, and multi-mission applicability of the proposed method.

[0015] First, the reentry guidance 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 is the track angle. 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 constraints for terminal drag acceleration and the flight range before takeoff.

[0024] Therefore, the reentry guidance problem can be described as follows: under the influence of uncertainties such as initial state, model, and environmental parameters, by designing angle of attack and roll control commands, the aircraft can glide without power until it meets the terminal full-state and flight time constraints under the constraints of initial conditions, dynamic equations, process, and control. Since the angle of attack command can be determined in advance based on range capability and heat protection requirements, the above problem is reduced to roll command. The problem to be solved.

[0025] Based on different trajectory characteristics, the reentry gliding trajectory can be divided into the initial descent phase and the gliding phase. Because the initial descent phase involves a relatively high altitude and limited available aerodynamic forces, making effective control of the aircraft difficult, a constant roll angle is used in this phase. Perform open-loop control when the drag acceleration Then, the aircraft transitions to the gliding phase. The sign (positive or negative) of the constant roll angle is determined based on the initial and terminal heading constraints.

[0026] Based on this, this invention proposes a near-analytical hypersonic glide guidance method for cooperative encirclement. This method mainly comprises three parts: standard profile design, online adaptive updating, and profile tracking guidance. The standard profile design includes parameterized design of the drag acceleration profile, analytical prediction and correction of the pre-flight range and flight time, etc. The online profile updating is achieved through an adaptive updating strategy based on a dual / single parameter sequential solution mode to meet the constraints of terminal energy, range, flight time, and local ballistic inclination angle. Secondly, a longitudinal guidance algorithm based on standard profile tracking and a two-stage lateral guidance algorithm based on heading adjustment / holding are designed, thereby enabling the rapid online generation of three-dimensional guidance commands.

[0027] Step 1: Standard Section Design The purpose of standard profile design is to determine a reference drag acceleration profile that satisfies process constraints, terminal altitude, drag acceleration, range, flight time, and local trajectory inclination constraints. To this end, a two-parameter drag acceleration profile with corridor boundary interpolation was first designed. Specifically, this is a drag acceleration profile model based on corridor boundary two-parameter interpolation. The analytical prediction expressions for the waiting range and time, considering the effects of Earth's rotation, were derived in detail. Finally, standard profile design was achieved through profile parameter correction.

[0028] Step 1.1: Corridor boundary 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, composed of heat flux, dynamic pressure, and overload constraints, can be fitted as a four-segment quadratic curve based on its shape: (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.

[0029] 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... .

[0030] 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.

[0031] Step 1.2, Parametric Design of Drag Acceleration Profile As mentioned earlier, the purpose of standard profile design is to design a reference drag-acceleration profile within the reentry corridor. This is to meet the requirements of terminal drag acceleration, local ballistic inclination angle, range, and time constraints. Considering these constraints, the standard drag acceleration profile can be designed as a piecewise polynomial with dual interpolation parameters, allowing the solution for the profile parameters to be obtained based on the satisfaction of range and time constraints.

[0032] 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.

[0033] 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 must be met: (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.

[0034] The following example, using terminal drag acceleration and local trajectory tilt angle constraints, illustrates an algorithm for applying endpoint constraints to solve for polynomial coefficients. The method for applying constraints is as follows: 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 is derived in the following form.

[0035] Drag acceleration right The derivative can be expressed as: (18) In the formula, the expressions for the derivatives of each term are: (19) In the formula, It is a high constant; 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 drag acceleration and local velocity tilt angle constraints.

[0036] 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 satisfy the constraints of process, terminal drag acceleration, 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 at 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.

[0037] Step 1.3, Flight Range and Time Analysis and Prediction When designing a standard drag-acceleration profile, it is necessary to predict the remaining flight path and time corresponding to the profile. Define the flight path. Let be the length of the trajectory projected onto the Earth's surface by the remaining three-dimensional trajectory. Then, the derivatives of the flight path 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 refers to the local track yaw angle.

[0038] Considering the Earth's rotation, assume , Then the flight path ,time The differential equation for normalized energy is: (twenty three) In the formula, To increase drag acceleration, , .

[0039] 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 current normalized energy, in terms of full standard profile design, ; , For the current and terminal states When the flight path is near a great circle, In It can be determined from the current line of sight. Approximate representation. Therefore, the coefficients... , All parameters are known. It can be represented as A linear function.

[0040] make By integrating equation (23), we can obtain the flight range and flight time corresponding to the current energy. The specific expression is as follows: (26) In the formula, .

[0041] 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 waiting time and flight range. The specific algorithm is given below.

[0042] (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 .

[0043] Assuming normalized energy range Inside, and It satisfies 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 using the quadratic formula, without the need for numerical methods. , , , These are the coefficients of the cubic function in its general form.

[0044] (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, , , , , As an intermediate variable; 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.

[0045] 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 for each segment can be predicted using the above analytical formula. By summing the calculation results for each segment, the predicted results for the waiting time and flight distance can be obtained.

[0046] The above method avoids using numerical integration to predict the flight range and time, thus having high computational efficiency. Secondly, compared with the traditional piecewise linear profile, the above analytical prediction formula is derived for quadratic and cubic polynomial profiles, expanding the form of the profile function. At the same time, it can compensate for the flight range and time prediction errors caused by the Earth's rotation, thus having high prediction accuracy.

[0047] Step 1.4, Correction Algorithm From equation (26), we can see that the flight path is... With time Parameters only , The function, that is: (35) In the formula, and These are the pre-flight range and flight time parameters relative to the profile. , Analytical functions.

[0048] Since the above-mentioned predicted flight range is the projected length of the remaining three-dimensional trajectory on the ground, if the remaining great circle range is used directly in the early stages of flight... Updating the profile using the target range as the baseline will result in significant terminal deviation. Therefore, a maneuvering coefficient method can be used to correct the target range. Assuming the maneuvering coefficient is... The waiting flight range and time constraints are as follows: (36) In the formula, , , This represents the remaining great circle flight distance, target flight distance, and flight time corresponding to the current state.

[0049] Therefore, equation (36) can be expressed as about , A system of two nonlinear equations: (37) In the formula: , .

[0050] The aforementioned system of two linear equations can be solved using Newton's iteration method, thereby enabling the design of the standard profile. Due to the waiting flight range... and waiting 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.

[0051] Step 2: Online adaptive updating of standard profiles Due to the continuous impact of various uncertainties and interferences during flight, the actual flight will inevitably deviate from the nominal trajectory, resulting in a decrease in terminal handover accuracy and time control accuracy. Simultaneously, the derivation of analytical prediction functions for waiting flight range and time also introduces… , The assumptions made in this regard lead to a discrepancy between the predicted and actual values. Therefore, to improve the terminal accuracy of the guidance algorithm under the influence of random disturbances, it is necessary to design a method for online updating of the standard profile.

[0052] Depending on the scope of the updated profile, profile updating methods can be divided into global updating and local updating methods. Global updating updates the entire profile in each guidance cycle, offering a larger adjustable space and better convergence of feasible solutions. However, each update requires tracking and transitioning to the new profile, which can easily cause oscillations in the flight control system. In contrast, local updating methods update only the remaining profile based on the current state, resulting in better profile continuity. However, in the final stages of flight, the limited planarable space may lead to the inability to find a feasible solution. Therefore, to ensure the continuity and smoothness of the updated profile while meeting the dual constraints of pre-flight range and flight time, this invention designs an online adaptive updating strategy for drag acceleration profiles based on a dual / single parameter sequential solution mode, based on the idea of ​​local profile updating. The specific profile updating algorithm and strategy are given below.

[0053] (1) Standard profile update algorithm based on two-parameter correction Let the normalized energy and drag acceleration corresponding to the current flight state in the k-th guidance cycle be: The remaining energy is Then, the updated drag acceleration profile can be obtained from the improved equation (15): (38) In the formula: (39) In the formula, , , , These are the segmented feature points of the remaining profile in the k-th guidance cycle. , , , The profile scaling factor can be pre-loaded into the onboard computer and allocated online to each profile segment based on the current energy. As mentioned earlier, the polynomial coefficients can be obtained through the continuity and differentiability conditions of the function at the left and right endpoints of the segment. Therefore, in the k-th guidance cycle, the standard profile... Only with parameters , Therefore, the flight range is relevant. With time All are parameters , The function can be adjusted by the correction algorithm described in step 1.4. , Perform the solution and complete the online update of the profile.

[0054] (2) Standard profile update algorithm based on parameter weighting Because the programmable space for drag acceleration in the terminal phase of gliding is narrow, the aforementioned two-parameter-based profile update algorithm may fail to find a feasible solution. Therefore, to further improve the reliability and convergence of the profile update algorithm, this invention designs a standard profile update algorithm based on parameter weighting, as follows: Let the normalized energy and drag acceleration corresponding to the current flight state in the k-th guidance update cycle be: The remaining energy is The drag acceleration profile can be obtained by modifying equation (38) as follows: (40) In the formula: (41) In the formula, For single-section parameters, , These are the segmented feature points of the remaining profile in the k-th guidance cycle. , The profile scaling factor can be pre-loaded into the onboard computer and allocated to each profile segment based on the current energy level. The aforementioned updated profile is divided into three segments, among which... The adjustment segment is obtained by interpolating the upper and lower boundaries of the corridor; , For the transition section, cubic polynomial curves are used, and the calculation of their polynomial coefficients is consistent with the standard profile update algorithm based on two-parameter correction. Update: x For the parameters of the section to be designed, such as size or curvature; Therefore, in the kth guidance cycle, the standard profile Only with parameters Therefore, both the flight path and time can be expressed as parameters. The function. Considering the relatively short waiting range at the end of the gliding phase, the remaining great circle range can be directly used. If the target flight range is used for profile updates, then the flight range constraint equations and time constraint equations are as follows: (42) In the formula, The target flight range, The time required for the target to be ready for flight.

[0055] The above equation can be expressed as about The underdetermined nonlinear equations: (43) In the formula: , .

[0056] To simultaneously satisfy the flight range and time constraints, Newton's iterative method is used to solve the subproblems separately. and The obtained profile parameters are as follows: , The final profile parameters can then be expressed in the following weighted form: (44) In the formula, constant The specific time can be determined based on the required range and time accuracy.

[0057] The above method solves for single-section parameters. This method satisfies both the flight range and time constraints, and compared to the two-parameter update method, it avoids the situation where no feasible solution can be found in the terminal phase of flight due to the narrow planarable space. This improves the convergence and reliability of the update algorithm. Although it sacrifices some profile design accuracy, the flight range and flight time can gradually converge to the terminal expected value through multiple profile updates.

[0058] As mentioned earlier, the profile update algorithm based on dual-parameter correction exhibits high accuracy in the early and mid-glide stages, simultaneously satisfying the pre-flight range and time constraints. Conversely, the parameter-weighted profile update algorithm demonstrates better convergence and reliability in the late-glide stage. Therefore, this invention combines these two profile update algorithms to design a standard profile update strategy, the specific process of which is as follows: In the k-th guidance cycle, assume the energy and drag acceleration corresponding to the current flight state are as follows: The remaining energy is The guidance law switching energy point is .

[0059] (1) When When the aircraft is far from the target point, the range and flight time can be adjusted more effectively, and the remaining drag acceleration profile can be updated using a standard profile update algorithm based on dual-parameter correction.

[0060] (2) When When the aircraft is close to the target, the standard profile update algorithm based on parameter weighting is switched to update the profile until the terminal constraint conditions are met.

[0061] The profile update strategy proposed in this invention provides special handling for situations where feasible solutions cannot be found due to insufficient planarable space in the terminal phase of gliding. It takes into account both the terminal accuracy and convergence of profile update. At the same time, the proposed method uses an analytical approach to predict the flight distance and time throughout the process, which significantly improves the computational efficiency of profile update and has the potential for online real-time update.

[0062] Step 3: Standard Profile Tracking Guidance After completing the standard profile design and update using the above methods, a corresponding profile tracking guidance algorithm needs to be designed to generate guidance commands. As mentioned earlier, the angle of attack command can be determined by a preset profile, thus transforming the gliding guidance problem into solving the bill of lading command problem. Profile tracking guidance is divided into longitudinal guidance and lateral guidance. Longitudinal guidance is achieved by tracking the drag acceleration profile to obtain the bill of lading amplitude command, while lateral guidance is achieved through a combination of heading adjustment, heading maintenance, and terminal position correction algorithms to determine the bill of lading sign. Furthermore, by designing a three-dimensional guidance algorithm considering longitudinal and lateral coupled motion, online rapid generation of guidance commands was achieved.

[0063] Step 3.1, Longitudinal Guidance 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: (45) In the formula: (46) Design the second-order stage Tracking: (47) In the formula, The damping coefficient is... For natural frequency, 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. Substituting equation (47) into (45), we obtain the tilt angle command amplitude as: (48) 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.

[0064] Step 3.2, Lateral Guidance The purpose of lateral guidance 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, this invention designs a two-stage lateral guidance method based on heading adjustment / holding, which 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, 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 working mechanism of this guidance 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.

[0065] (1) Lateral reduced-order motion model Considering the Earth's rotation, assume Then, the lateral reduced-order motion equation can be obtained by deriving equation (1): (49) In the formula, .

[0066] definition: (50) Then we have: (51) 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 is then used for iterative calculations in subsequent lateral guidance.

[0067] (2) Lateral guidance 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 2As 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 guidance 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 guidance 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.

[0068] To achieve the above objectives, Figure 3 A schematic diagram of the lateral guidance method is provided. The heading-maintaining phase employs a heading angle error corridor control method, while the heading-adjusting phase is achieved by adjusting the roll reversal point. [Settings...] 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 guidance method is given below.

[0069] First, the sign of the heel angle during the heading adjustment segment can be determined by the following formula: (52) 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: (53) 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.

[0070] Based on this, the tilt reversal point can be solved iteratively within each guidance cycle. To satisfy the terminal track yaw angle constraint, the specific steps are as follows: ①Let j= 0, the tilt reversal point is ; ② Substituting the reduced-order lateral motion equation into equation (49) 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: (54) If true, terminate the calculation and output the result. Otherwise, proceed to step ③; in, The initial value is the tilt reversal point. For the first j The tilt reversal point corresponding to each iteration. The yaw angle constraint is used for the terminal track.

[0071] ③ Set the tilt reversal point 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 step ④; in, This represents the increment of normalized energy.

[0072] ④ Calculate the partial derivatives: (55) Update the tilt reversal point: (56) ⑤ Order j = j+ 1. Proceed to ②.

[0073] 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]. .

[0074] (3) The terminal track yaw angle adjustable range quantification and initial tilt direction determination algorithm are implemented through lateral guidance, which is an extended application of the method.

[0075] 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 2As 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.

[0076] Based on the above analysis, the drag acceleration profile can be further given. Under certain conditions, the terminal track yaw angle Adjustable range and initial tilt angle direction The specific algorithm is as follows: ① Let the initial tilt angle direction be , The lateral reduced-order equation of motion of the integral (49) yields the maximum terminal track yaw angle. ; ②Let the initial tilt angle direction , The lateral reduced-order equation of motion of integral (49) yields the minimum terminal track yaw angle. ; ③ Determine the terminal track yaw angle The adjustment range is ; ④ Further determine the direction of the initial tilt angle .

[0077] 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.

[0078] The segmentation points of the lateral guidance method of this invention can be adjusted according to the flight process and lateral maneuverability, thus enhancing autonomy and mission adaptability.

[0079] The guidance method proposed in this invention will be further described below.

[0080] 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's ready-to-fly range would introduce some deviation. Therefore, it is necessary to correct the target's ready-to-fly range in real time based on the terminal position error obtained from lateral guidance. However, unlike EAGLE, for situations involving large lateral maneuvers, simply using the difference in the great circle length is insufficient for accurate range correction. For example... 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 Distance between the trajectory terminal and the target point .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. Using this as a correction factor would cause the target's waiting flight range to continuously increase, 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.

[0081] Let the first The longitudinal path of the trajectory obtained in the next iteration is ,but: (57) In the formula, This refers to the terminal azimuth deviation. , The azimuth angle between the trajectory terminal and the reentry point. The azimuth angle between the target point and the reentry point.

[0082] Combination Figure 4 From (a) and (b), we can see that The symbols and terminal points and target track yaw angles Related: (1) When hour, ; (2) When hour, ; therefore, The symbol can be represented by the following formula. (58) 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 .

[0083] The guidance algorithm process is as follows Figure 5 As shown. Since the standard profile update uses analytical prediction and correction, it has good real-time performance, while the lateral guidance algorithm requires a small amount of integration on the reduced-order lateral motion equations, which is more time-consuming. Compared to the drag acceleration profile, the guidance algorithm has lower real-time requirements for updating the roll reversal point. Therefore, the lateral guidance command update cycle can be designed to be n times the standard profile update cycle. In the k-th guidance cycle, assume the energy and drag acceleration corresponding to the current flight state are... The remaining energy is The guidance law switching energy point is The specific process is as follows: (1) The algorithm begins, k=0; (2) If If true, the residual drag acceleration profile is updated using the standard profile update algorithm based on two-parameter correction, thus obtaining the reference profile. Otherwise, the standard profile update algorithm based on parameter weighting is used for profile update; (3) For the reference section Tracking is performed to obtain longitudinal trajectory parameters and tilt angle command amplitude. Longitudinal trajectory parameters include altitude, velocity, and local ballistic inclination. (4) Determine if k is an integer multiple of n. If it is true, update the lateral guidance command and obtain the tilt reversal point. Slope angle command symbol and terminal position deviation Otherwise, skip the lateral instruction update step; (5) Generate tilt angle command And conduct guided flight; (6) Judgment conditions If the condition is met, then k = k + 1, and update the target flight path to be determined. Repeat steps (2) to (6); otherwise, guidance ends.

[0084] It is worth noting that the aforementioned three-dimensional guidance algorithm obtains longitudinal trajectory parameters through profile tracking and uses them as input to the lateral reduced-order motion equation, improving the prediction accuracy of terminal position and track yaw angle. Furthermore, the obtained terminal position deviation is used to correct the target's waiting flight range in real time, continuously improving the accuracy of profile updates. In addition, considering that standard profile updates use analytical prediction and correction methods, while lateral guidance command updates require a small amount of integration into the lateral reduced-order motion equation, a variable step-size integration strategy can be adopted to improve the real-time performance of guidance command generation.

[0085] Example 1 The guidance method provided by the present invention will be simulated and analyzed below through specific embodiments.

[0086] Simulation conditions Simulations were conducted using the American general-purpose aircraft CAV-H as the model. Initial and terminal state constraints were set as follows: =80km, =6500m / s, =0°; =25km, =2000m / s, , , =0km; Process constraints are set as follows: , , The control constraints are: =80°, =5°, =5°; the preset angle of attack profile is shown in equation (9), and the relevant parameters are set as follows: , , , The preset parameters for the drag acceleration profile are: =2m / s 2 , , , , , , Mobility coefficient =1.02. All simulations were performed on a desktop computer equipped with an Intel Core i7-8700 3.20GHz Intel processor, using the Visual Studio 2017 platform.

[0087] Algorithm robustness verification To verify the accuracy and robustness of the proposed guidance algorithm under disturbed conditions, 500 Monte Carlo target simulations were conducted. The reentry point longitude was set. ,latitude track yaw angle The terminal local trajectory inclination angle constraint is The yaw angle constraint is: , Flight time constraints The parameter bias settings are shown in Table 1, and the other simulation conditions are the same as those in the simulation conditions above.

[0088] The simulation results are shown in Table 2 and Figure 6 As shown. Figure 6(a) is the drag acceleration-energy profile. Figure 6 (b) is the height-velocity curve. Figure 6 (c) represents the ground track. Figure 6 (d) is the dip angle curve. Figure 6 (e) is the local velocity-time curve. Figure 6 (f) shows the track yaw angle-time curve. Statistical analysis shows that a single profile update takes about 50ms, and a lateral guidance command update takes about 0.8s.

[0089] Table 1 Parameter Pull Settings Table 2. Simulation results of target shooting with terminal parameters Table 2 presents the terminal parameter results corresponding to the target firing simulation. It can be seen that, since energy is used as the simulation cutoff condition, the deviations in terminal altitude and velocity are relatively small. Specifically, the mean and standard deviation of terminal altitude are less than 500m, the mean and standard deviation of velocity are less than 2m / s, the mean and standard deviation of terminal position are both less than 2km, the local velocity tilt angle error is less than 0.2°, the track yaw angle deviation is less than 3°, and the mean and standard deviation of flight time deviation are less than 1.2s. This indicates that the proposed guidance algorithm has high terminal accuracy and strong robustness. Figure 6 (a) It can be seen that the drag acceleration profile under disturbance conditions is continuous and smooth, and all of it is within the re-entry corridor, satisfying all process constraints; in addition, Combination Figure 6 From (b) and (e), we can see that in At this time, the drag acceleration increases and the altitude curve decreases to accelerate the energy decay rate, reduce flight time, and compensate for guidance errors caused by random disturbances. Figure 6 From (d) and (f), it can be seen that the roll angle amplitude meets the control constraint requirements, the number of roll reversals is approximately 8-10, and the track yaw angle converges to near the desired value after multiple roll reversals. Figure 6 As shown in (b), (c), and (e), the terminal height, velocity, local ballistic inclination angle, and position all converge to near the expected values, indicating that the proposed guidance algorithm has good terminal accuracy and convergence.

[0090] Multi-task simulation under nominal conditions For reentry missions under nominal conditions with different ranges, times, and terminal full-state constraints, reentry glide guidance simulations were conducted to verify the mission adaptability of the proposed algorithm. Table 3 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: , The correction factor is =1.02, and other simulation conditions are consistent with those in the simulation conditions above.

[0091] Table 3 Simulation Condition Settings The curve obtained from the simulation is as follows Figure 7 As shown in Table 4. Figure 7 (a) is the drag acceleration-energy curve. Figure 7 (b) is the height-velocity curve. Figure 7 (c) represents the ground track. Figure 7 (d) is the tilt angle-time curve. Figure 7 (e) is the track yaw angle curve. Figure 7 (f) is the local velocity inclination curve.

[0092] Table 4 Terminal results under different simulation conditions Table 4 presents the terminal parameters for examples 1-6. It is evident that, due to the use of energy as the simulation cutoff condition, the deviations in terminal altitude and velocity are relatively small. Specifically, the terminal altitude deviation is less than 100m, the velocity deviation is less than 2m / s, the local trajectory inclination deviation is less than 0.1°, the track yaw angle deviation is less than 3°, the range deviation is less than 1km, and the flight time deviation is less than 1s. These results demonstrate that the proposed guidance algorithm exhibits high computational accuracy and good applicability to various constraints such as initial firing direction, range, flight time, and terminal angle.

[0093] Figure 7 Simulation result curves for examples 1-6 are given. Figure 7 As shown in (a) and (b), the drag acceleration profile satisfies 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 7 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 7From (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 7 (d) It can be seen that in order to meet the accuracy requirements of the terminal track yaw angle, the tilt angle was reversed multiple times when it approached the terminal, with a total number of reversals of about 10-12.

[0094] In summary, this invention studies a near-analytical guidance method based on drag acceleration-energy profile for hypersonic glide guidance under full spatiotemporal constraints. Simulation results show that: (1) The proposed guidance method is feasible, adaptable to multiple tasks and robust. Compared with the existing methods, the proposed method can take into account the control accuracy of time and terminal full state due to the adoption of profile analysis prediction correction design, adaptive update strategy and two-stage lateral guidance logic. It also has high computational efficiency and strong online application potential.

[0095] (2) Compared with the existing standard profile-based method, the designed multi-segment smooth drag acceleration profile based on corridor boundary dual-parameter interpolation can achieve full coverage of the trajectory within the corridor constraint range, and can also achieve the application of terminal local ballistic tilt angle constraint.

[0096] (3) The profile update strategy based on the dual / single parameter sequential solution mode can effectively solve the problem that the dual parameter profile cannot find a feasible solution in the glide end due to insufficient planarable space, thus improving the terminal accuracy and convergence of the profile update.

[0097] (4) The dual-stage lateral guidance algorithm based on heading adjustment / holding has high control accuracy of terminal position and track yaw angle and large heading adjustment capability. It can also realize the rapid quantification of the adjustable range of terminal track yaw angle, which can provide a reference for collaborative mission planning and online allocation.

[0098] 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-resolution hypersonic glide guidance method for cooperative encirclement, characterized in that, Includes the following steps: Considering the constraints of terminal altitude, speed, local ballistic inclination, range and flight time, a drag acceleration profile model based on two-parameter interpolation of the corridor boundary is constructed. Based on the drag acceleration profile model, construct the analytical prediction model of the aircraft's waiting flight range and the analytical prediction model of its time, and perform analytical prediction of the waiting flight range and time. Based on the prediction results of the flight range analysis prediction model and the time analysis prediction model, the drag acceleration profile model parameters are updated online using a drag acceleration profile update strategy based on a dual / single parameter sequential solution mode to obtain the updated reference profile. Longitudinal guidance: Tracking the reference profile to obtain longitudinal trajectory parameters and tilt angle command amplitude. ; Considering the terminal track yaw angle and position constraints, a two-stage lateral guidance method based on heading adjustment / maintenance is designed. Specifically, based on the longitudinal trajectory parameters, the roll reversal point is iteratively solved. And determine the sign of the tilt angle. and terminal location parameters; Considering large lateral maneuvers, the terminal position deviation is calculated based on the terminal position parameters, target point, and track yaw angle constraints. and symbols ; Based on the tilt angle command amplitude and the sign of the tilt angle Generate current yaw angle command To achieve guided flight and detect terminal position deviations and symbols It can make real-time corrections to the target flight range of the aircraft. The construction of the drag acceleration profile model based on two-parameter interpolation of the corridor boundary 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 the terminal height and velocity constraints, it is possible to obtain the drag acceleration profile. Apply terminal constraints to satisfy them, therefore for the drag acceleration profile Apply terminal drag acceleration constraints and local trajectory tilt 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 the formula, 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 the formula, 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-resolution hypersonic glide guidance method for cooperative encirclement as described in claim 1, characterized in that, The construction of the analytical prediction model for the flight path includes the following steps: Define the flight path Let be the length of the trajectory projected onto the Earth's surface by the remaining three-dimensional trajectory. Then, the derivatives of the flight path 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. This refers to the local track yaw angle; Considering the Earth's rotation, assume , Then the flight path ,time The differential equation for normalized energy is: In the formula, To increase drag acceleration, , ; 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 Points waiting flight range ,time The differential equation for normalized energy can be used to obtain the flight range and flight time corresponding to the current energy. The specific expression is as follows: In the formula, , This represents the average distance from the Earth's center during gliding. Will Substituting the specific flight range and flight time into the expressions, and assuming the 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 the time-analysis prediction model includes the following steps: like and Satisfying the quadratic function relationship Through analytical derivation, the flight time prediction formula can be obtained as follows: In the formula: In the formula, , , , , As an intermediate variable; like and Satisfying a cubic function relationship Through analytical derivation, the flight time prediction formula can be obtained as follows: In the formula: In the formula, , , , The coefficients of the transformed equation are... The solution is obtained by calculating using the quadratic formula.

3. The near-resolution hypersonic glide guidance method for cooperative encirclement as described in claim 2, characterized in that, The drag acceleration profile update strategy based on the dual / single parameter sequential solution mode is as follows: In the k-th guidance cycle, assume that the energy and drag acceleration corresponding to the current flight state are... The remaining energy is The guidance law switching energy point is : when At this time, the aircraft moves away from the target point, and the remaining drag acceleration profile is updated using the standard profile update algorithm based on two-parameter correction. when When the aircraft approaches the target point, the standard profile update algorithm based on parameter weighting is used to update the profile until the terminal constraint conditions are met.

4. The near-resolution hypersonic glide guidance method for cooperative encirclement as described in claim 3, characterized in that, The method of updating the residual drag acceleration profile using a standard profile update algorithm based on two-parameter correction specifically includes the following steps: Let the energy and drag acceleration corresponding to the current flight state in the k-th guidance cycle be: The remaining energy is The following drag-acceleration profile is designed for profile updating: In the formula: In the formula, , , , These are the segmented feature points of the remaining profile in the k-th guidance cycle. , , , The segmentation ratio is used to allocate each segment of the profile online based on the current energy; in the k-th guidance cycle, the standard profile... Only with parameters , Therefore, the flight range is relevant. With time All are parameters , The function, obtained by using Newton's iteration method to evaluate the parameters. , Perform the solution and complete the online update of the profile.

5. The near-resolution hypersonic glide guidance method for cooperative encirclement as described in claim 4, characterized in that, The standard profile update algorithm based on parameter weighting is used to update the profile, specifically including the following steps: Let the energy and drag acceleration corresponding to the current flight state in the k-th guidance update cycle be... The remaining energy is The following drag-acceleration profile is designed for profile updating: In the formula: In the formula, For the undetermined profile parameters, , These are the segmented feature points of the remaining profile in the k-th guidance cycle. , The profile scaling factor is pre-loaded into the onboard computer and allocated to each profile segment based on the current energy level; the updated profile is divided into three segments, among which... The adjustment segment is obtained by interpolating the upper and lower boundaries of the corridor; , For the transition section, cubic polynomial curves are used, and the calculation of their polynomial coefficients is consistent with the standard profile update algorithm based on two-parameter correction. Standard profile during the kth guidance cycle Only with parameters Therefore, the flight path and time are both expressed as parameters. The function; considering the relatively short waiting range at the end of the gliding phase, the remaining great circle range is directly used. If the target flight range is used for profile updates, then the flight range constraint equations and time constraint equations are as follows: In the formula, The target flight range, Waiting time for the target flight; The flight range constraint equations and time constraint equations are expressed as follows: The underdetermined nonlinear equations: In the formula: , ; To simultaneously satisfy the flight range and time constraints, Newton's iterative method is used to solve the subproblems separately. and The obtained profile parameters are as follows: , The final profile parameters are expressed in the following weighted form: In the formula, constant The allocation is determined based on the requirements for flight distance and time accuracy.

6. The near-resolution hypersonic glide guidance method for cooperative encirclement as described in claim 5, characterized in that, The two-stage lateral guidance based on heading adjustment / holding is divided into a heading adjustment phase and a heading hold and terminal position correction phase, completing the roll reversal point. Iterative solution and sign of the tilt angle The determination specifically includes: During the heading adjustment segment, the heel angle symbol Determined by the following formula: in, The initial tilt angle sign, Normalized energy for entering the heading angle error corridor; when At this point, the course maintenance and terminal position correction segment begins, and the heel angle sign for this segment is... Determined by the following formula: In the formula, The sign of the tilt angle at 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. For the first j The tilt reversal point corresponding to each iteration. 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, The increment of normalized energy; (4) Calculate the partial derivatives: Update the tilt reversal point: (5) Order j = j+ 1. Transfer to (2).

7. The near-resolution hypersonic glide guidance method for cooperative encirclement as described in claim 6, characterized in that, The lateral guidance also includes quantifying the terminal track yaw angle adjustment range and determining the initial tilt direction, specifically including the following steps: Let the initial tilt angle direction , Integrating the reduced-order lateral motion equations yields the maximum terminal track yaw angle. ; Let the initial tilt angle direction , Integrating the reduced-order lateral motion equations yields the minimum terminal track yaw angle. ; Determine the terminal track yaw angle The adjustment range is ; Determine the direction of the initial tilt angle .

8. The near-resolution hypersonic glide guidance method for cooperative encirclement as described in claim 7, characterized in that, The terminal position deviation is calculated based on the terminal position parameters, target point, and track yaw angle. The symbols specifically include: Let the first The longitudinal path of the trajectory obtained in the next iteration is ,but: In the formula, This refers to the terminal azimuth deviation. , This is 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.

9. The near-resolution hypersonic glide guidance method for cooperative encirclement as described in claim 8, characterized in that, The lateral guidance command update cycle is designed to be n times the standard profile update cycle. In the k-th guidance cycle, assume the energy and drag acceleration corresponding to the current flight state are... The remaining energy is The guidance law switching energy point is The profile update and guidance specifically include the following steps: (1) Let k=0; (2) If If true, the residual drag acceleration profile is updated using the standard profile update algorithm based on two-parameter correction to obtain the standard profile. Otherwise, the standard profile update algorithm based on parameter weighting is used for profile update; (3) Standard profile Tracking is performed to obtain longitudinal trajectory parameters and tilt angle command amplitude. ; (4) Determine if k is an integer multiple of n. If it is true, update the lateral guidance command and obtain the tilt reversal point. Slope angle command symbol and terminal position deviation Otherwise, skip the lateral instruction update step; (5) Based on the tilt angle command amplitude and the sign of the tilt angle Generate yaw angle command And conduct guided flight; (6) Judgment conditions If the condition is met, then k = k + 1, and update the target flight path to be determined. , return (2); otherwise, end.

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