A Predictive Correction Method for Reentry Glide Vehicles Based on Adaptive Lateral Corridor

Abstract

This invention discloses a prediction and correction method for reentry gliders based on an adaptive lateral corridor, relating to the field of navigation, guidance, and control technology for reentry gliders. Addressing the problem of generating prediction and correction trajectories for reentry gliders in the presence of no-fly zones, it proposes an integrated design approach that combines avoidance logic with an adaptive lateral corridor. First, based on the intersection of the reentry glider's lateral trajectory and the no-fly zone, avoidance logic is dynamically introduced to determine whether the reentry glider should take evasive action. Then, utilizing the no-fly zone region that influences the flight trajectory, an effective no-fly zone mapping lateral corridor is proposed to quantify the avoidance logic. Finally, the lateral guidance logic and the avoidance logic are combined to form an adaptive lateral corridor, resulting in a prediction and correction trajectory with corrected corridor boundaries.

Description

Technical Field

[0001] This invention relates to the field of navigation, guidance and control technology for reentry gliders, and in particular to a predictive correction method for reentry gliders based on an adaptive lateral corridor. Background Technology

[0002] With the enhancement of modern computing power, the application of numerical prediction correction methods has become more diverse. Numerical prediction correction methods, by setting lateral and longitudinal control logic, continuously iterate the integral trajectory using the dynamic model of the reentry glider to obtain the predicted range. Control parameters are then corrected by adjusting the predicted and remaining ranges, and guidance is achieved in conjunction with corresponding lateral guidance logic. Procedurally, numerical prediction correction methods are divided into two stages: longitudinal guidance and lateral guidance. The longitudinal guidance stage requires determining the angle of attack profile and the billet angle amplitude. Under normal conditions, to better meet various constraints, the angle of attack profile is pre-set not to be a primary control variable during the prediction correction guidance process. Various constraints are converted to the billet angle corridor, and the billet angle is constrained to achieve process constraints. For the billet angle amplitude, interpolation between two adjacent predicted ranges is typically used, and the secant method is employed for calculation.

[0003] For the lateral guidance phase of reentry gliders, two models are typically employed: the trajectory deviation angle corridor and the lateral range corridor. The lateral range corridor, due to its approximately linear relationship with the remaining range, often achieves higher guidance accuracy and better guidance performance in lateral guidance. LuP et al. defined the lateral range parameter and proposed a lateral guidance law that determines the roll angle reversal position in real time based on the flight state. Li Huifeng et al. used the sum of the lateral range and its differential term as the reversal control quantity, constraining the lateral range variation to always remain within the corridor boundary. Zhang Ke et al., by analyzing the relationship between the lateral range and the remaining range, proposed a dynamically changing lateral range corridor with boundary constraints, improving the lateral guidance accuracy of reentry gliders. Furthermore, during the lateral guidance process, reentry gliders often encounter no-fly zones, necessitating the implementation of appropriate no-fly zone avoidance logic. Among them, Zhu Jianwen et al. used line-of-sight angle to describe the relative positional relationship between the flight path of the reentry glider and the no-fly zone, and proposed a boundary selection method for each no-fly zone, achieving minimum energy avoidance; Liang Z et al. considered the heading restrictions of the no-fly zone in lateral guidance, set up a dynamic heading corridor, and set up waypoints containing flight trajectory position and direction constraints for guidance when the no-fly zones are close to each other; Zhao Jiang et al. set up avoidance logic based on the guidance area of ​​the reentry glider's heading angle to the no-fly zone, and achieved avoidance guidance of the no-fly zone.

[0004] The above methods all have corresponding avoidance logic designed for no-fly zones, but they are somewhat separate from the lateral guidance logic. The logic conversion required by the judgment conditions may lead to guidance failure of the reentry glider or repeated deflection of the reentry glider's tilt angle. Summary of the Invention

[0005] This invention aims to provide a prediction and correction method for reentry gliders based on adaptive transverse corridors, which can achieve effective guidance for flight and avoidance of no-fly zones, and eliminate the redundancy flipping phenomenon of tilt angle caused by the separation of guidance logic and avoidance logic.

[0006] The main idea of ​​the technical solution adopted in this invention is as follows: Addressing the problem of separation between evasion logic and guidance logic in the lateral guidance of numerical prediction correction methods, this invention uses the intersection of the lateral motion trajectory circle formed by the instantaneous turning radius of the reentry glider and the no-fly zone as a criterion for incorporating evasion logic into lateral guidance. Based on the influence of the no-fly zone on the flight trajectory and its relative positional relationship with the reentry glider and the predetermined target point, an effective mapping lateral range for the no-fly zone is proposed. By designing an adaptive lateral range corridor, the evasion logic and lateral guidance logic are integrated, enabling the reentry glider's tilt angle, constrained by the boundary of the adaptive lateral range corridor, to achieve evasion of the no-fly zone and effective lateral guidance through fewer flips.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] The prediction and correction method for reentry gliders based on adaptive transverse corridors is characterized by the following steps:

[0009] S1. Establish a motion model of the reentry glider and determine process constraints, no-fly zone constraints, and terminal constraints;

[0010] S2. Based on the motion model and constraints in step S1, design the longitudinal guidance rate of the reentry glider and determine the values ​​of the control variables angle of attack and roll angle.

[0011] S3. Based on the longitudinal guidance rate in step S2, design a lateral guidance rate that integrates avoidance logic and guidance logic, and determine the sign of the tilt angle.

[0012] Further, step S1 establishes the motion model, process constraints, no-fly zone constraints, and terminal constraints of the reentry glider, including the following steps:

[0013] S101. Establish a motion model for the reentry glider;

[0014] S102. Determine the process constraints, no-fly zone constraints, and terminal constraints that exist during the flight of the reentry glider.

[0015] S103. Establish no-fly zone constraints for reentry gliders.

[0016] Furthermore, the design of the lateral guidance rate in step S3 includes the following steps:

[0017] S301. Determine the lateral corridor of the reentry glider;

[0018] S302. Calculate the instantaneous turning radius of the reentry glider.

[0019] S303. Based on the lateral corridor of the gliding reentry glider determined in step S301 and the instantaneous turning radius obtained in S302, calculate the effective mapping lateral distance of the no-fly zone.

[0020] S304. Design an adaptive cross-flow corridor based on the effective mapping cross-flow calculated in step S303.

[0021] Furthermore, determining the lateral range corridor of the reentry glider in step S301 includes the following steps:

[0022] S3011, Calculate the transverse stroke of the reentry glider.

[0023] The transverse stroke of a reentry glider is represented as the projection of the reentry glider's position and the target's position onto the direction of the reentry glider's velocity, and its expression is as follows:

[0024] χ=arcsin(sin(S togo_f sin(Δψ)) (16);

[0025] In the formula S togo_f Δψ represents the remaining distance between the reentry glider and the target position, and Δψ represents the trajectory deviation angle of the reentry glider from the target position.

[0026] S3012. Calculate the remaining range and line-of-sight angle between the reentry glider and the target position.

[0027] Its expression is as follows:

[0028]

[0029]

[0030] In the formula, Indicates the latitude and longitude of the reentry glider. S represents the latitude and longitude of the target location. togo_f This represents the remaining distance between the reentry glider and the target position.

[0031] S3013. Calculate the trajectory deviation angle of the reentry glider according to step S3012.

[0032] Its expression is as follows:

[0033] Δψ f =ψ-ψ f (19)

[0034] In the formula, ψ is the trajectory deflection angle of the reentry glider. f The deflection angle of the reentry glider to the target position;

[0035] S3014. Determine the lateral corridor of the reentry glider according to steps S3011-S3013.

[0036] Its expression is as follows:

[0037]

[0038]

[0039] In the formula, S togo_f0 For the initial remaining range of the reentry glider to the target position, S togo_f This represents the remaining range between the reentry glider and the target position. During guidance, as S... togo_f Gradually approaching S togo_f0 The transverse corridor is also approaching convergence.

[0040] Furthermore, the calculation of the effective mapping lateral distance of the no-fly zone in step S303 includes the following steps:

[0041] S3031. Calculate the coordinates of the center of the circle representing the lateral motion trajectory of the reentry glider.

[0042] The formula for calculating the coordinates of the center of a circle is as follows:

[0043]

[0044] In the formula, R represents the latitude and longitude of the reentry glider. turn The instantaneous turning radius of the reentry glider is represented by ψ, and the trajectory deflection angle of the reentry glider is represented by ψ.

[0045] S3032. Calculate the coordinates of the position where the lateral motion trajectory circle of the reentry glider intersects with the no-fly zone.

[0046] The coordinate formulas for the intersection points are as follows:

[0047]

[0048] In the formula, It is the latitude and longitude of the center of the no-fly zone, r bη1 is the radius of the no-fly zone, η2 is the angle between the line connecting the two centers and the vertical axis, and η3 is the angle between the first flight intersection point and the line connecting the two centers.

[0049] S3033. Based on the coordinates of the intersection point calculated in S3032, calculate the trajectory deflection angles corresponding to the intersection of the reentry glider's position with the no-fly zone and the two boundaries of the no-fly zone.

[0050] The formula is:

[0051]

[0052] ψ bmax =ψ b +arcsin(r b / S b (35)

[0053] ψ bmin =ψ b -arcsin(r b / S b (36)

[0054] In the formula, Indicates the latitude and longitude of the reentry glider. It is the latitude and longitude of the center of the no-fly zone. It is the latitude and longitude of the intersection point of the reentry glider's lateral motion trajectory circle and the no-fly zone, r b It is the radius of the no-fly zone, S b S is the distance between the reentry glider and the center of the no-fly zone. point ψ is the distance between the reentry glider and the intersection of its lateral motion trajectory circle and the no-fly zone. b The trajectory deflection angle of the reentry glider to the center of the no-fly zone;

[0055] S3034. Based on the intersection of the gliding reentry glider's position with the no-fly zone and the corresponding track deflection angles of the two boundaries of the no-fly zone calculated in S3033, calculate the effective mapping lateral distance of the no-fly zone.

[0056] The calculation formula is as follows:

[0057] χ point =arcsin(sin(S) togo_f sin(ψ) point -ψ f (37)

[0058] χ bmax =arcsin(sin(S) togo_f sin(ψ) bmax -ψ f (38)

[0059]

[0060]

[0061]

[0062] In the formula, χ point χ is the x-axis distance from the intersection of the reentry glider's lateral motion trajectory circle and the no-fly zone to the predetermined target point. bmax χ is the lateral distance from the reentry glider to the right boundary of the no-fly zone and to the predetermined target point. 0max Let ψ be the upper boundary of the basic transverse corridor, and ψ be the trajectory deflection angle of the reentry glider. f ψ is the trajectory deflection of the reentry glider to the target position. b ψ is the trajectory deflection of the reentry glider to the center of the no-fly zone. point ψ is the trajectory deflection of the reentry glider at the intersection of the no-fly zone and the reentry glider. bmax The deflection angle of the reentry glider to the right boundary of the no-fly zone.

[0063] Furthermore, the design of the adaptive cross-span corridor in step S304 includes the following steps:

[0064] S3041, the avoidance logic for no-fly zones is as follows:

[0065] S bi >r bi ,ψ-ψ bi >π / 2 (42)

[0066] In the formula, r b It is the radius of the no-fly zone, S b ψ is the distance between the reentry glider and the center of the no-fly zone, and ψ is the trajectory deflection of the reentry glider. b The trajectory deflection angle of the reentry glider to the center of the no-fly zone is given by the subscript i, which indicates the i-th no-fly zone that affects the flight trajectory.

[0067] S3042, The theoretical value of the adaptive lateral range corridor at time t for the design of the reentry glider is...

[0068]

[0069]

[0070] In the formula, Δχ tb Let Δχ be the effective transverse length of the no-fly zone under the current tilt angle sign at time t. t ′ b Let χ be the effective transverse length of the no-fly zone after the sign of the roll angle changes at time t.0max χ is the upper boundary of the basic transverse corridor in the design. 0min This serves as the lower boundary of the basic transverse corridor design.

[0071] S3043. Calculate the lateral corridor value of the reentry glider at time t as χ. tmax , χ tmin The calculation formula is as follows:

[0072]

[0073]

[0074] in, The theoretical value of the adaptive cross-sectional corridor at time t in the design;

[0075] S3044. The rollover logic for the roll angle is determined using the lateral corridor value of the reentry glider at time t in step S3043, as shown below:

[0076]

[0077] In the formula, χ t Let χ be the transverse stroke of the reentry glider at time t. tmax , χ tmin Let t be the cross-sectional corridor value at time t in the design.

[0078] The beneficial effects of the present invention are as follows: Compared with the prior art, the improvement of the present invention is that, during the guidance process, the instantaneous turning radius of the reentry glider is used to construct an instantaneous lateral motion trajectory circle, and by analyzing the intersection of the reentry glider trajectory with the no-fly zone, avoidance logic is dynamically introduced.

[0079] By projecting the area affected by the no-fly zone onto the predetermined target point and combining the relative relationship between the no-fly zone and the reentry glider's position and the predetermined target point, an effective mapping lateral distance of the no-fly zone is formed. The lateral distance corridor boundary is corrected in real time, and the tilt angle of the reentry glider is controlled to achieve effective guidance for avoiding the no-fly zone and for flight. This eliminates the redundant tilt angle flip phenomenon caused by the separation of guidance logic and avoidance logic. Attached Figure Description

[0080] Figure 1 For HV corridor.

[0081] Figure 2 A schematic diagram of the instantaneous lateral motion trajectory of a reentry glider (I).

[0082] Figure 3 This is a schematic diagram (II) of the instantaneous lateral motion trajectory of the reentry glider of the present invention.

[0083] Figure 4 This is a schematic diagram of the effective mapping of no-fly zones according to the present invention.

[0084] Figure 5 The simulation results for Example 1 are shown in the following figures: (a) Two-dimensional trajectory diagram, (b) Inclination angle variation diagram, and (c) Lateral corridor variation diagram.

[0085] Figure 6 The following are two-dimensional trajectory diagrams for examples, where (a) is the two-dimensional trajectory diagram for example 2 and (b) is the two-dimensional trajectory diagram for example 3.

[0086] Figure 7 The following are examples of tilt angle variation diagrams, where (a) is the tilt angle variation diagram for example 2 and (b) is the tilt angle variation diagram for example 3.

[0087] Figure 8 The following are the cross-sectional changes of the effective mapping of the no-fly zone in the examples: (a) is the cross-sectional change of the effective mapping of the no-fly zone in example 2, and (b) is the cross-sectional change of the effective mapping of the no-fly zone in example 3.

[0088] Figure 9 The following are examples of transverse corridor variation diagrams, where (a) is the transverse corridor variation diagram for example 2 and (b) is the transverse corridor variation diagram for example 3.

[0089] Figure 10 The image shows a 2D landing point diagram of the reentry glider target position, including (a) a 2D trajectory diagram of the reentry glider, (b) a diagram showing the change in the reentry glider's tilt angle, (c) a diagram showing the change in the reentry glider's altitude, and (d) a diagram showing the effect of the reentry glider's lateral guidance.

[0090] Figure 11 Simulation results of adding evasion logic guidance to the transverse corridor are shown in the diagrams, where (a) is a two-dimensional trajectory diagram of the reentry glider and (b) is a diagram showing the change in the tilt angle of the reentry glider.

[0091] Figure 12 Simulation results of adding avoidance logic guidance to the trajectory deviation angle corridor are shown in the figure, where (a) is the two-dimensional trajectory of the reentry glider and (b) is the change of the tilt angle of the reentry glider. Detailed Implementation

[0092] To enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described below with reference to the accompanying drawings and examples.

[0093] The reentry glider prediction and correction method based on adaptive lateral corridor in this application includes the following steps:

[0094] 1. Reentry glider model and constraints

[0095] The dimensionless motion model of the reentry glider is shown in the formula:

[0096]

[0097] In the formula, r represents the dimensionless altitude of the reentry glider. The coordinates of the reentry glider are represented by latitude and longitude, v represents the dimensionless velocity of the reentry glider, θ and ψ represent the trajectory inclination and trajectory deflection of the reentry glider, and L and D represent the dimensionless lift and drag.

[0098]

[0099] In the formula, C L C represents the lift coefficient of a reentry glider. D denoted by , S represents the drag coefficient of the reentry glider, m represents the force-bearing area of ​​the reentry glider, g0 represents the mass of the reentry glider, and g0 represents the zero-altitude gravitational acceleration.

[0100] The energy of a reentry glider is defined as:

[0101] e = 1 / rv 2 / twenty three)

[0102] In the formula, r represents the dimensionless altitude of the reentry glider, and v represents the dimensionless velocity of the reentry glider.

[0103] Reentry gliders are subject to process constraints, no-fly zone constraints, and terminal constraints.

[0104] Where the terminal constraint is expressed as

[0105]

[0106] In the formula, This represents the given terminal altitude, terminal velocity, and latitude and longitude of the reentry glider.

[0107] Process constraints consider the heat flux density constraint, dynamic pressure constraint and overload constraint of the reentry glider.

[0108]

[0109] In the formula, These represent heat flux density, dynamic pressure, and overload, respectively. Let represent the maximum values ​​of heat flux density constraint, dynamic pressure constraint, and overload constraint, respectively, and C represent the aerodynamic thermal coefficient. R is a dimensionless processing parameter. e This represents the Earth's radius.

[0110] This application defines the no-fly zone as an infinitely tall cylinder, through which reentry gliders are prohibited from passing. Its functional expression is:

[0111]

[0112] In the formula φ b , The coordinates (r) of the center of the no-fly zone. b This indicates the latitude and longitude radius of the no-fly zone.

[0113] 2. Longitudinal guidance law design

[0114] 2.1 Angle of Attack Settings

[0115] To meet the thermal protection requirements of reentry gliders, a longitudinal angle-of-attack profile similar to that of the Space Shuttle is used in the references, and the piecewise function is as follows. In this application, V1 = 5000 m / s and V2 = 3000 m / s are given.

[0116]

[0117] In the formula, α max α is the maximum value of the angle of attack profile. K The angle of attack is the maximum lift-to-drag ratio, and V is the reentry velocity of the reentry glider.

[0118] 2.2 Tilting Angle Corridor

[0119] Under process constraints, establish HV corridors, such as Figure 1 As shown. First, the heat flux density constraint, dynamic pressure constraint, and overload constraint are transformed into the HV plane.

[0120]

[0121] r≥(H0ln(ρ0(v·vc) 2 / (2q max ))+R e ) / R e =r qmax (9)

[0122]

[0123] In the formula, H0 is the altitude parameter used for air density calculation, C is the heat flux density coefficient of CAV-H, ρ0 is the atmospheric density parameter, and v represents the dimensionless velocity of the reentry glider. c R is the dimensionless parameter for velocity. e For the Earth's radius, q is the maximum value constrained by heat flux density. max n is the maximum value of the dynamic pressure constraint. maxWhere S is the maximum overload constraint value, S is the force-bearing area of ​​the reentry glider, and C is the maximum value of the overload constraint. L C D The lift and drag coefficients of the reentry glider. The altitude at which the heat flux density of the reentry glider reaches its maximum value is r. qmax r is the altitude at which the dynamic pressure of the reentry glider reaches its maximum value. nmax The altitude at which the overload of the reentry glider reaches its maximum value.

[0124] Then Substitute the quasi-equilibrium gliding conditions In, that is

[0125]

[0126] In the formula, v represents the dimensionless velocity of the reentry glider, and r min The minimum flight altitude required for a reentry glider to satisfy process constraints, L rmin The dimensionless aerodynamic lift at the minimum flight altitude required to satisfy process constraints for a reentry glider, |β| cmax The upper boundary of the inclined corridor.

[0127] Simultaneously, the trajectory roll angle corridor lower boundary |β| is calculated using the equilibrium gliding condition. cmin as follows,

[0128]

[0129] In the formula, v represents the dimensionless velocity of the reentry glider, r represents the dimensionless altitude of the reentry glider, and L represents the dimensionless aerodynamic lift force on the reentry glider.

[0130] Based on formulas (11) and (12), the tilt angle corridor that satisfies the process constraints can be established, |β| cmin ≤|β|≤|β| cmax .

[0131] 2.3 Calculation of the tilt angle

[0132] This application uses a constant tilt angle profile, and the tilt angle amplitude is obtained by the difference f between the predicted range and the remaining range of the reentry glider.

[0133] f = S p (e f )-S togo_f (13)

[0134] In the formula, S p (e f To predict the remaining range, S togo_fThis represents the actual remaining flight distance.

[0135] Under normal conditions, the predictive correction guidance method uses an iterative integration approach to obtain the predicted remaining range, and its calculation formula is as follows:

[0136]

[0137] In the formula, θ is the trajectory inclination angle of the reentry glider, r represents the dimensionless altitude of the reentry glider, D is the dimensionless aerodynamic drag experienced by the reentry glider, and e is the energy of the reentry glider at this moment. f The termination energy for reentry gliders.

[0138] The secant method is used to calculate β0 such that f(β0) = 0. The specific iterative process is as follows:

[0139]

[0140] Among them, a i f represents the adjustment coefficient for the i-th iteration of the secant method. i Let β0(i) represent the difference in range prediction for the i-th iteration, and let β0(i) be the tilt angle value for the i-th iteration.

[0141] 3. Lateral guidance law design

[0142] Lateral guidance primarily involves designing a funnel-shaped deviation corridor, commonly including a lateral range corridor and a track deflection corridor. Compared to a track deflection corridor, the lateral range corridor has fewer roll angle reversals, resulting in better lateral guidance performance. However, in common lateral range corridor designs, the no-fly zone avoidance logic and the lateral range corridor logic are designed separately. This cannot guarantee the lateral range convergence of the reentry glider after avoiding the no-fly zone, meaning lateral guidance may fail, preventing the reentry glider from reaching the intended target point. To address this issue, this application obtains the instantaneous turning radius of the reentry glider based on the horizontal component of its aerodynamic forces. Combining the influence of the no-fly zone on the flight trajectory and the relative positional relationship between the no-fly zone, the reentry glider, and the intended target point, it proposes the concept of an effective no-fly zone mapping lateral range. By changing the lateral range corridor boundary, the roll angle reversal of the reentry glider is controlled, achieving the fusion of the no-fly zone avoidance logic and the lateral guidance logic, ensuring that the lateral range of the reentry glider ultimately converges while avoiding the no-fly zone.

[0143] 3.1 Re-entry glider cross-span corridor

[0144] Under normal conditions, the transverse range of a reentry glider is expressed as the projection of the reentry glider's position and the target's position onto the direction of the reentry glider's velocity. Its expression is as follows:

[0145] χ=arcsin(sin(S togo_f(16)

[0146] In the formula, S togo_f Δψ represents the remaining distance between the reentry glider and the target position, and Δψ is the trajectory deviation angle of the reentry glider from the target position.

[0147] The remaining range and line-of-sight angle of the reentry glider relative to the target position are defined as follows:

[0148]

[0149]

[0150] In the formula, Indicates the latitude and longitude of the reentry glider. S represents the latitude and longitude of the target location. togo_f This represents the remaining distance between the reentry glider and the target position.

[0151] The trajectory deviation angle of the reentry glider is

[0152] Δψ f =ψ-ψ f (19)

[0153] In the formula, ψ is the trajectory deflection angle of the reentry glider. f The deflection angle of the reentry glider to the target position;

[0154] The transverse corridor designed in this application is...

[0155]

[0156]

[0157] In the formula, S togo_f0 For the initial remaining range of the reentry glider to the target position, S togo_f This represents the remaining range between the reentry glider and the target position. During guidance, as S... togo_f Gradually approaching S togo_f0 The transverse corridor is also approaching convergence.

[0158] 3.2 Instantaneous turning radius of reentry glider

[0159] Analysis shows that the horizontal component of the aerodynamic force of the reentry glider provides the centripetal force during the reentry glider's turn, i.e.

[0160]

[0161] The instantaneous turning radius of the reentry glider during its reentry gliding process can be calculated as follows:

[0162]

[0163] To maintain consistency with the dimensionless motion model described above, the dimensionless instantaneous turning radius is:

[0164]

[0165] In the formula, β is the tilt angle of the reentry glider during guidance, m is the mass of the reentry glider, V is the reentry velocity of the reentry glider, L is the aerodynamic lift force on the reentry glider, θ is the trajectory tilt angle of the reentry glider, and R... e The radius is the Earth's radius.

[0166] 3.3 Effective mapping of no-fly zones

[0167] Based on the actual impact of the no-fly zone on the reentry glider's flight area, an effective mapping lateral distance to the predetermined target point is designed. Under the condition that the reentry glider's control parameters remain unchanged, the reentry glider's lateral motion trajectory is based on R... turn Let be a circle with radius ψ, the track deflection angle ψ is tangent to the track circle, and the position of the center of the circle is determined by the sign of the roll angle. Unless otherwise specified, the formulas derived below assume the roll angle is positive. The formula for calculating the coordinates of the center of the circle is as follows:

[0168]

[0169] In the formula, R represents the latitude and longitude of the reentry glider. turn The instantaneous turning radius of the reentry glider is represented by ψ, and the trajectory deflection angle of the reentry glider is represented by ψ.

[0170] If the lateral motion trajectory of the reentry glider intersects with a no-fly zone, the coordinates of the position where it first intersects the no-fly zone can be derived based on the intersection and geometric relationships. The derivation process is as follows:

[0171] When the instantaneous lateral motion trajectory circle intersects with the no-fly zone, as shown in the following situation... Figure 2 As shown, the distance between the centers of the no-fly zone and the instantaneous lateral motion trajectory circles of the reentry glider is...

[0172]

[0173] In the formula, It is the latitude and longitude of the center of the no-fly zone. It is the latitude and longitude of the center of the circle of the lateral motion trajectory of the reentry glider.

[0174] The distance from the center of the no-fly zone to the intersecting chord is

[0175]

[0176] In the formula, r b It is the radius of the no-fly zone, r turn It is the dimensionless instantaneous turning radius of the reentry glider, and S is the distance between the center of the lateral motion trajectory circle of the reentry glider and the center of the no-fly zone.

[0177] The angle between the line connecting the two centers and the vertical axis

[0178]

[0179] The angle between the point of intersection of the flight paths and the line connecting the two centers of the circles

[0180]

[0181] In the formula, φ b It is the longitude of the no-fly zone, φ turn d is the longitude of the center of the lateral motion trajectory circle of the reentry glider, d is the distance from the center of the no-fly zone circle to the intersecting chord, and S is the distance between the center of the lateral motion trajectory circle of the reentry glider and the center of the no-fly zone circle.

[0182] The formula for the coordinates of the intersection point is:

[0183]

[0184] In the formula, It is the latitude and longitude of the center of the no-fly zone, r b η1 is the radius of the no-fly zone, η2 is the angle between the line connecting the two centers and the vertical axis, and η3 is the angle between the first flight intersection point and the line connecting the two centers.

[0185] When the lateral motion trajectory of a reentry glider intersects with a no-fly zone, as follows: Figure 3 As shown, the different formulas used in the derivation of the intersection point coordinates are as follows, while the rest remain unchanged.

[0186]

[0187]

[0188]

[0189] The trajectory deflection angles corresponding to the intersection of the reentry glider's current position with the no-fly zone and the two boundaries of the no-fly zone are:

[0190]

[0191] ψ bmax =ψ b +arcsin(r b / S b (35)

[0192] ψ bmin =ψ b -arcsin(r b / S b (36)

[0193] In the formula, Indicates the latitude and longitude of the reentry glider. It is the latitude and longitude of the center of the no-fly zone. It is the latitude and longitude of the intersection point of the reentry glider's lateral motion trajectory circle and the no-fly zone, r b It is the radius of the no-fly zone, S b S is the distance between the reentry glider and the center of the no-fly zone. point ψ is the distance between the reentry glider and the intersection of its lateral motion trajectory circle and the no-fly zone. b The trajectory deflection angle of the reentry glider to the center of the no-fly zone;

[0194] At this time, the area affected by the no-fly zone on the flight path deviation angle is (ψ). point ,ψ bmax This portion of the no-fly zone is projected onto the lateral stroke of the lateral guidance system, forming the effective lateral stroke of the no-fly zone, such as... Figure 4 As shown, the calculation formula is as follows:

[0195] χ point =arcsin(sin(S) togo_f sin(ψ) point -ψ f (37)

[0196] χ bmax =arcsin(sin(S) togo_f sin(ψ) bmax -ψ f (38)

[0197]

[0198]

[0199]

[0200] In the formula, χ point χ is the x-axis distance from the intersection of the reentry glider's lateral motion trajectory circle and the no-fly zone to the predetermined target point. bmax χ is the lateral distance from the reentry glider to the right boundary of the no-fly zone and to the predetermined target point. 0max Let ψ be the upper boundary of the basic transverse corridor, and ψ be the trajectory deflection angle of the reentry glider. f ψ is the trajectory deflection of the reentry glider to the target position. bψ is the trajectory deflection of the reentry glider to the center of the no-fly zone. point ψ is the trajectory deflection of the reentry glider at the intersection of the no-fly zone and the reentry glider. bmax The deflection angle of the reentry glider to the right boundary of the no-fly zone.

[0201] The effective mapping cross length of the no-fly zone is determined by (ψ) point ,ψ bmax The projected lateral stroke is determined, but not greater than the maximum value of the basic lateral stroke corridor at this time; the sign is determined by the relative position of the reentry glider, the no-fly zone, and the target point, which integrates the logic of avoiding the no-fly zone and the lateral guidance logic of the target point, ensuring that the reentry glider can avoid the no-fly zone while also meeting the accuracy requirements of reentry guidance.

[0202] The no-fly zone affects the flight trajectory not only at the current bank angle but also after the bank angle changes sign. If the no-fly zone intersects with the instantaneous lateral motion trajectory circle after the bank angle changes sign, the effective mapping range Δχ of the no-fly zone can be calculated using the same method, referring to the formulas (25)-(41). b ′.

[0203] 3.4 Adaptive Cross-Section Corridor

[0204] When the instantaneous lateral motion trajectory circle of the reentry glider intersects with a no-fly zone, the no-fly zone in the intersecting portion affects the lateral guidance range. By adaptively changing the lateral guidance range, the no-fly zone can be avoided. The avoidance logic is as follows:

[0205] S bi >r bi ,ψ-ψ bi >π / 2 (42)

[0206] In the formula, r b It is the radius of the no-fly zone, S b ψ is the distance between the reentry glider and the center of the no-fly zone, and ψ is the trajectory deflection of the reentry glider. b The trajectory deflection angle of the reentry glider to the center of the no-fly zone is given by the subscript i, which indicates the i-th no-fly zone that affects the flight trajectory.

[0207] The theoretical value of the adaptive lateral corridor of the reentry glider at time t is...

[0208]

[0209]

[0210] In the formula, Δχ tb Let Δχ′ be the effective transverse length of the no-fly zone under the current tilt angle sign at time t.tb Let χ be the effective transverse length of the no-fly zone after the sign of the roll angle changes at time t. 0max χ is the upper boundary of the basic transverse corridor in the design. 0min This serves as the lower boundary of the basic transverse corridor design.

[0211] When the lateral range of the reentry glider remains within the lateral range corridor, the lateral range converges, and thus the lateral range also converges, meaning the reentry glider can reach the predetermined target point. Therefore, the rate of change of the designed adaptive lateral range corridor must be less than or equal to the rate of change of the reentry glider's lateral range. The lateral range corridor value of the reentry glider at time t is χ. tmax , χ tmin As shown below,

[0212]

[0213]

[0214] in, The theoretical value of the adaptive cross-sectional corridor at time t in the design;

[0215] The logic for flipping the yaw angle is as follows:

[0216]

[0217] In the formula, χ t Let χ be the transverse stroke of the reentry glider at time t. tmax , χ tmin Let t be the cross-sectional corridor value at time t in the design.

[0218] 4.1 Simulation Conditions and Objects

[0219] The simulation calculation uses CAV-H as the object, with a mass of m = 987 kg and S = 0.4897 m. 2 The lift and drag coefficients are provided in the references. The guidance cycle step size is 0.1s, and the operating environment is an i5 CPU, 16GB of memory, and MATLAB 2019 software environment.

[0220] Calculation example 1

[0221] The initial state of Example 1 is φ0 = 0°. h0 = 70km, V0 = 6000m / s, θ0 = -0.1°, ψ0 = 60°, and the terminal state constraint is φ. f =18°, h f =30km, V f ≥1500m / s;

[0222] Example 1 does not set a no-fly zone to verify whether the set lateral corridor can be effectively guided;

[0223] The verification process includes the following steps:

[0224] S1: Establish a motion model for the reentry glider;

[0225] S2: Based on the motion model in step S1, design the longitudinal guidance rate of the reentry glider and determine the values ​​of the control variables angle of attack and roll angle.

[0226] S3: Based on the longitudinal guidance rate in step S2, design a lateral guidance rate that integrates the avoidance logic and guidance logic, and determine the sign of the tilt angle.

[0227] Calculation example 2

[0228] The initial and final states used in this example are the same as in Example 1. The difference is that the latitude and longitude of the no-fly zone are on the same side as the latitude and longitude of the target position in this example. This verifies whether the adaptive lateral corridor designed in this application can effectively guide the reentry glider to avoid the no-fly zone and reach the target position.

[0229] The latitude and longitude coordinates of the center of the no-fly zone and its radius in this example are: b r1 =1°, b r2 =1.1°;

[0230] Calculation example 3

[0231] The steps and procedures used in this example are the same as in Example 2. The only difference is that the latitude and longitude of the no-fly zone are located on the opposite side of the latitude and longitude of the target location in this example. This verifies whether the adaptive lateral corridor designed in this application can effectively guide the reentry glider to avoid the no-fly zone and reach the target location.

[0232] The latitude and longitude coordinates of the center of the no-fly zone and its radius in this example are: b r1 =1°, b r2 =1.1°.

[0233] The guidance results of Example 1 are as follows Figure 4 As shown, when there is no no-fly zone constraint, the lateral range corridor boundary of the reentry glider is symmetrical and changes gently. The lateral range is always in the corridor, and the control tilt angle is flipped at the corresponding moment, which effectively realizes guidance.

[0234] The two-dimensional guidance results for examples 2 and 3 are as follows: Figures 6-9 As shown, from Figure 6As can be seen from the results, in Examples 2 and 3, the reentry glider can effectively avoid no-fly zones using the adaptive lateral corridor of this application. The results of its roll angle variation are as follows: Figure 7 As shown, the effective mapping cross-section and basic cross-section corridor changes of the no-fly zone are as follows: Figure 8 As shown, the changes in the horizontal axis and corridor are as follows: Figure 9 As shown. From Figure 8 As can be seen, at the very beginning of the reentry gliding phase, the instantaneous lateral motion trajectory circle of the reentry glider intersects with the no-fly zone, and the effective mapping lateral range value of the no-fly zone is relatively large, proving that it has a significant impact on the future flight of the reentry glider. Comparing examples 2 and 3, it can be seen that the superposition result of the mapping lateral range differs depending on the location of the no-fly zone. The value of the superposition result depends on two factors: firstly, the intersection area between the no-fly zone and the instantaneous lateral motion trajectory circle of the reentry glider; the larger the intersection area, the larger the value of the effective mapping lateral range of the no-fly zone. Secondly, it depends on the sign of the effective mapping lateral range determined by the relative positional relationship between the no-fly zone, the reentry glider, and the predetermined target point. If the signs of the effective mapping lateral ranges of the no-fly zones are the same, they are added together, and the maximum value is constrained to the maximum value of the basic lateral range corridor of the reentry glider, thus affecting the change of the lateral range corridor boundary value. If the signs are different, the positive or negative sign of the added result indicates the direction of the adaptive lateral range corridor change under the premise of satisfying the reentry glider's avoidance requirements for different no-fly zones and the final guidance accuracy. Observation Figure 7 , Figure 9 As can be seen, despite the presence of a no-fly zone, the roll of the reentry glider did not increase due to the adaptive lateral corridor logic, and it successfully avoided the no-fly zone. The lateral range of the reentry glider remained within the lateral corridor, and the corridor boundary and the lateral range eventually converged, verifying the effectiveness of the method proposed in this application. In summary, through the design of the adaptive lateral corridor in this application, the lateral range of the reentry glider is always located within the corridor, which can effectively guarantee the convergence of the lateral range. The terminal conditions and simulation errors are shown in Table 1.

[0235] In Table 1, the guidance error of the reentry glider is represented by E, and its calculation formula is as follows:

[0236]

[0237] in The numbers represent the guidance latitude, longitude, and altitude errors, respectively. As can be seen from Table 1, the guidance accuracy using the method of this application is within 6km under no-fly zone conditions, and accurate results can also be achieved under adaptive lateral guidance corridor conditions.

[0238] Table 1. Results of the example

[0239]

[0240] (2) Reentry process disturbance simulation

[0241] To further consider the disturbances caused by changes in atmospheric parameters and the vehicle's own parameters during the reentry process of the reentry glider, the robustness of the proposed algorithm to the disturbances during the reentry process is verified. This application conducted 150 Monte Carlo simulations under the condition that the atmospheric constant error (±20%), the mass deviation, force area deviation, and lift-drag coefficient deviation of the reentry glider (±5%) are uniformly distributed.

[0242] Simulation results are as follows Figure 10 As shown, most results show an altitude error of less than 2 km and a horizontal error of around 5 km, with a maximum of no more than 10 km. This indicates that the guidance accuracy of the method described in this application still meets the requirements.

[0243] (3) Comparison of the effectiveness of lateral guidance and evasion methods

[0244] When satisfied At that time, the reentry glider enters the evasion logic via lateral guidance. In the formula, d is the distance from the reentry glider to the center of the no-fly zone, r is the radius of the no-fly zone, and n is determined in advance before guidance.

[0245] The no-fly zone avoidance logic in this example is as follows:

[0246]

[0247] In the formula, β t Let ψ be the tilt angle of the reentry glider at time t. t Let ψ be the trajectory deflection of the reentry glider at time t. b ψ is the trajectory deflection of the reentry glider to the center of the no-fly zone. bmin ,ψ bmax The deflection angle of the reentry glider to the boundary of the no-fly zone.

[0248] When the reentry glider completes its no-fly zone avoidance mission, the lateral guidance switches to corridor guidance mode. The lateral corridor is the basic lateral corridor designed in this invention, and its flip logic is the same as the adaptive lateral corridor flip logic; the track deviation angle corridor is determined by the following formula. Wherein, the track deviation angle corridor boundary (-ψ) max ,ψ max )for:

[0249]

[0250] In the formula, ψ up ,ψ down denoted as the maximum and minimum values ​​of the track deviation angle corridor, e represents the energy of the reentry glider, and e1 and e2 are the two energy boundaries of the track deviation angle corridor.

[0251] Where ψup =15°, ψ down =5°, e1=0.75, e2=0.85;

[0252] The tilt angle flip logic is as follows:

[0253]

[0254] In the formula, β t Let ψ be the tilt angle of the reentry glider at time t. t Let ψ be the trajectory deflection of the reentry glider at time t. f ψ is the trajectory deflection of the reentry glider to the target position. tmax The maximum value of the track deviation angle corridor at time t.

[0255] To demonstrate the superiority of the dynamically introduced avoidance logic and adaptive lateral corridor in this application for no-fly zone avoidance and lateral guidance, drawing on existing no-fly zone avoidance methods, this paper sets up a reentry glider at different distances from the center of the no-fly zone. The ordinary lateral corridor guidance method and the trajectory deviation angle corridor guidance method are combined with the avoidance logic. Guidance is performed under the initial conditions of Example 3, and the guidance results are as follows: Figure 11 , 12 As shown. (Note: d is the distance between the reentry glider and the center of the no-fly zone, and r is the radius of the no-fly zone. The avoidance distance set in existing literature is d = 2.0r.)

[0256] from Figure 11 (a) and Figure 12 As shown in (a), the effectiveness of evasion and guidance varies depending on the distance from the center of the no-fly zone when evasion logic is added. Under transverse corridor guidance, the reentry glider successfully evaded the no-fly zone. However, under trajectory deviation angle corridor guidance, when d=1.6r and d=1.7r, adding evasion logic resulted in the reentry glider crossing the no-fly zone, leading to evasion failure. This demonstrates that transverse corridor guidance is more effective in evading no-fly zones. Figure 11 (b) and Figure 12 As shown in (b), the rollover of the tilt angle varies depending on the distance from the center of the no-fly zone when evasion logic is added. Because the lateral guidance logic and evasion logic of the reentry glider are separate, this evasion logic easily leads to repeated rollovers of the tilt angle when entering the critical state between the no-fly zone and the guidance logic, increasing the number of rollovers. The guidance errors of the two lateral guidance methods combined with different evasion logic settings are shown in Table 2, where F represents the number of rollovers of the reentry glider.

[0257] Table 2 Guidance Errors of Reentry Glider Vehicles under Different Guidance and Evasion Methods

[0258]

[0259] As shown in Table 2, the closer the reentry glider is to the no-fly zone, the higher the final guidance accuracy, but the number of rollovers of the tilt angle also increases, and there is a possibility that the no-fly zone cannot be avoided. The farther the reentry glider is from the no-fly zone, the fewer rollovers of the tilt angle are, and the no-fly zone can be successfully avoided, but the guidance accuracy also drops sharply, which may prevent the reentry glider from reaching the predetermined target point, ultimately leading to guidance failure. Compared with the dynamic introduction of avoidance logic and adaptive lateral corridor guidance proposed in this application, the use of the instantaneous turning radius of the reentry glider to add avoidance logic by judging in real time whether its instantaneous lateral motion trajectory intersects with the no-fly zone solves the contradiction between the selection of the distance for the reentry glider to avoid the no-fly zone and the final guidance accuracy. The results in the table show that the lateral guidance of the reentry glider using the method proposed in this application meets the requirements for final guidance accuracy after avoiding the no-fly zone. Furthermore, the adaptive lateral corridor reduces the number of rollovers of the tilt angle while maintaining a certain corridor width by integrating the avoidance logic and the lateral guidance logic.

[0260] 5. Conclusion

[0261] This application addresses the common problem in reentry glider prediction and correction methods where the lateral guidance logic and no-fly zone avoidance logic are separated in no-fly zone scenarios. By using the instantaneous turning radius of the reentry glider, the instantaneous lateral trajectory circle is calculated. The intersection of this circle with the no-fly zone is then used to dynamically introduce avoidance logic. Furthermore, the influence of the no-fly zone on the flight trajectory is projected onto the flight lateral range, proposing an effective no-fly zone mapping lateral range and establishing an adaptive lateral range corridor for the reentry glider. Finally, simulation results demonstrate that this method not only achieves effective guidance under different no-fly zone conditions and exhibits robustness to reentry disturbances, but also, compared to other guidance logics, achieves the same guidance accuracy while requiring fewer roll angle flips.

[0262] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above examples; the examples and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A receding glide vehicle predictive correction method based on adaptive cross-range corridor, characterized in that: Comprising the following steps: S1, establishing a motion model of the reentry gliding vehicle, and determining process constraints, no-fly zone constraints and terminal constraints; S2, designing a longitudinal guidance rate of the reentry gliding vehicle according to the motion model and the constraints in step S1, and determining values of control variables of an attack angle and a roll angle; S3, designing a lateral guidance rate that fuses avoidance logic and guidance logic together according to the longitudinal guidance rate in step S2, and determining a sign of the roll angle; For the design of the lateral guidance rate in step S3, comprising the following steps: S301, determining a cross-range corridor of the reentry gliding vehicle; S302, calculating an instantaneous turning radius of the reentry gliding vehicle; S303, calculating an effective mapping cross-range of a no-fly zone according to the cross-range corridor of the reentry gliding vehicle determined in step S301 and the instantaneous turning radius obtained in S302; For the calculation of the effective mapping cross-range of the no-fly zone in step S303, comprising the following steps: S3031, calculating a center coordinate of a lateral motion trajectory circle of the reentry gliding vehicle The center coordinate calculation formula is as follows: (25) wherein denotes the longitude and latitude of the reentry glider, denotes the instantaneous turn radius of the reentry glider, is the track angle of the reentry glider; S3032, calculating a coordinate of an intersection position of the lateral motion trajectory circle of the reentry gliding vehicle and the no-fly zone The coordinate formula of the intersection position is as follows: (30) wherein is the latitude of the center of the no-fly zone, is the radius of the no-fly zone, is the angle between the line connecting the two centers and the longitudinal axis, is the angle between the first intersection point and the line connecting the two centers. S3033, calculating a track angle corresponding to a no-fly zone intersection point of the reentry gliding vehicle and a no-fly zone boundary according to the coordinate of the intersection position calculated in S3032 The formula is as follows: (34) (35) (36) wherein , , , denotes the longitude and latitude of the reentry glider, is the longitude and latitude of the center of the flight prohibited zone, is the longitude and latitude of the intersection of the lateral movement trajectory circle of the reentry glider and the flight prohibited zone, is the radius of the flight prohibited zone, is the distance between the reentry glider and the center of the flight prohibited zone, is the distance between the reentry glider and the intersection of its lateral movement trajectory circle and the flight prohibited zone, is the track angle of the reentry glider to the center of the flight prohibited zone; S3034, calculating the effective mapping cross-range of the no-fly zone according to the track angle corresponding to the no-fly zone intersection point of the reentry gliding vehicle and the no-fly zone boundary calculated in S3033 The calculation formula is as follows: (37) (38) (39) (40) (41) wherein is the cross-range from the reentry glider lateral trajectory circle intersection with the restricted area to the predetermined target point, is the cross-range from the reentry glider to the restricted area right boundary to the predetermined target point, is the upper boundary of the base cross-range corridor, is the glide path angle of the reentry glider, is the glide path angle of the reentry glider to the target location, is the glide path angle of the reentry glider to the restricted area circle center, is the glide path angle of the reentry glider to the restricted area intersection, is the glide path angle of the reentry glider to the restricted area right boundary; S304, designing an adaptive cross-range corridor according to the effective mapping cross-range calculated in step S303.

2. The adaptive-cross-range-corridor-based reentry glider predictive-correction method according to claim 1, wherein: Step S1 establishes a motion model of the reentry gliding vehicle, process constraints, no-fly zone constraints and terminal constraints, comprising the following steps: S101, establishing a motion model of the reentry gliding vehicle; S102, determining process constraints, no-fly zone constraints and terminal constraints existing in the flight of the reentry gliding vehicle; S103, establishing no-fly zone constraints of the reentry gliding vehicle.

3. The adaptive-cross-range-corridor-based reentry glider predictive-correction method according to claim 1, wherein: For the determination of the cross-range corridor of the reentry gliding vehicle in step S301, comprising the following steps: S3011, calculating a cross-range of the reentry gliding vehicle The cross-range of the reentry gliding vehicle is represented as a projection of the reentry gliding vehicle and a target position in a speed direction of the reentry gliding vehicle, and its expression is as follows: (16)； wherein is the remaining range of the reentry glider to the target location, is the track angle deviation of the reentry glider to the target location; S3012, calculating a remaining range and a line-of-sight angle of the reentry gliding vehicle and the target position Its expression is as follows: (17) (18) wherein denotes the longitude and latitude of the reentry glider, denotes the longitude and latitude of the target position, denotes the remaining range of the reentry glider to the target position; S3013, calculating a track deviation angle of the reentry gliding vehicle according to step S3012 Its expression is as follows: (19) wherein is the path angle of the reentry glider, is the path angle of the reentry glider to the target location; S3014, determining a cross-range corridor of the reentry gliding vehicle according to steps S3011-S3013 Its expression is as follows: (20) (21) wherein is the initial remaining range of the reentry glider to the target location, is the remaining range of the reentry glider to the target location, which, during the guidance process, is progressively reduced as the reentry glider approaches the target location, the lateral range corridor also tends to converge.

4. The adaptive-cross-range-corridor-based reentry glider predictive-correction method according to claim 1, wherein: For the design of the adaptive cross-range corridor in step S304, comprising the following steps: S3041, the avoidance logic of the no-fly zone is as follows: (42) wherein is the radius of the no-fly zone, is the distance between the reentry glider and the center of the no-fly zone, is the track angle of the reentry glider, is the track angle of the reentry glider to the center of the no-fly zone, the subscript denotes the th no-fly zone affecting the flight trajectory; S3042, design of reentry glider The time-adaptive lateral corridor theoretical value is : (43) (44) wherein is the effective lateral range of the flight restricted zone at time t for the current bank angle, is the effective lateral range of the flight restricted zone at time t for the bank angle after sign change, is the upper boundary of the designed base lateral corridor, is the lower boundary of the designed base lateral corridor. S3043, computing reentry glider The cross-range corridor value at a time instant is , The calculation formula is shown as follows: (45) (46) wherein, , is the designed momentary adaptive lateral corridor theoretical value; S3044, the reentry glider of step S3043 The lateral corridor value at the moment determines the roll angle flip logic, as follows: (47) wherein is the cross-range of the reentry glider at time t, , is the designed cross-range corridor value at time t.

Images