Method for Generating Multi-Aircraft Cooperative Maneuver Instruction Sets under Multiple Constraints

Abstract

This disclosure provides a method for generating a multi-aircraft cooperative maneuver command set under multiple constraints. First, based on process constraints, the upper and lower limits of the tilt angle of a single aircraft are determined. Then, based on restricted area constraints, and considering both control and process constraints, the lower limit of the tilt angle for each flight segment i on the single aircraft's trajectory around the restricted area, and the turning time between flight segments, are determined. Based on the upper and lower limits of the tilt angle, and considering the constraints of aircraft structural performance on the tilt angle value, the range of tilt angle values ​​for each flight segment i is determined. According to the cooperative flight mode of the aircraft, the lateral maneuver mode is further divided into a same-direction cooperative mode and an opposite-direction cooperative mode. Based on the determined tilt angle range and turning time for the restricted area, command sets for the same-direction and opposite-direction cooperative modes are generated. Using this invention, multi-aircraft cooperative maneuver command set generation is achieved under the premise of considering overload, heat flux, dynamic pressure process constraints, and control constraints.

Description

Technical Field

[0001] This invention belongs to the field of aircraft cooperative guidance and control technology, specifically relating to a method for generating a multi-aircraft cooperative maneuver command set under multiple constraints. Background Technology

[0002] High-speed aircraft possess advantages such as high speed, long range, and strong maneuverability, making them of significant strategic importance. As mission environments and requirements become increasingly complex, the mission capabilities and survivability of a single high-speed aircraft are insufficient to meet mission demands. Multi-aircraft cooperative missions are becoming an inevitable trend in the future development of high-speed aircraft. To accomplish cooperative missions (such as cooperative avoidance of no-fly zones and cooperative maneuvers), multiple aircraft typically fly in certain cooperative maneuver modes. However, during flight, aircraft are constrained by dynamic pressure, overload, and heat flux to ensure safety. Furthermore, due to limited maneuverability, they are also subject to control constraints. Therefore, how to generate a cooperative maneuver command set that meets mission requirements under multiple constraints is an important problem that needs to be studied.

[0003] Currently, there is a lot of research on the technology of generating maneuver commands for single high-speed aircraft. For example, Xie Yu et al. proposed a design method for a lateral oscillating maneuver trajectory (see Design of Oscillating Maneuver Penetration Trajectory for Hypersonic Glide Vehicles [J]. Acta Aeronautica Sinica, 2011, (12): 2174-2181.), and established a tilt angle model for high-speed aircraft based on the idea of ​​dynamic inverse; Zhang Bolun et al. established a nonlinear maneuver model for high-speed aircraft based on state variables related to aerodynamic parameters (see Maneuver Model and Trajectory Prediction for Near-Space Hypersonic Vehicles [J]. Systems Engineering and Electronics, 2019, Vol. 41 (9): 2072-2079.); Liu Zhengzhuo et al. derived analytical solutions for elevation and lateral range based on the altitude-velocity profile of the aircraft, and designed maneuver trajectories based on the analytical solution (see Design of Maneuver Trajectory for Hypersonic Glide Vehicles Based on Analytical Solution [J]. Aerospace Defense, 2024, Vol. 7 (3): 102-110.). Luo et al. derived an extended MPSP guidance method with multiple waypoint constraints. Based on the minimum dynamic pressure constraint, they proposed a high-speed vehicle large-space maneuvering strategy (see Maneuvering Penetration Guidance Strategy for Hypersonic Vehicles Based on Dynamic Pressure Constraints [J]. Journal of Chinese Inertial Technology, 2021, Vol. 29 (1): 112-118.). Wang et al. first established typical longitudinal and lateral maneuvering behavior patterns of the vehicle and constructed a maneuvering behavior trajectory library under multiple constraints (see Intelligent Trajectory Recognition and Prediction Method for Hypersonic Gliding Vehicles [J]. Flight Mechanics, 2024, Vol. 42 (4): 64-71, 87.). C. Zimmerman et al. proposed an automatic calculation method for orbital re-entry trajectory under thermal constraints (see An automated method to compute orbital re-entry trajectories with heating constraints, Journal of Guidance, Control, and Dynamics 26 (2003) 523–529.).

[0004] Research on the generation of cooperative maneuver commands for multiple high-speed aircraft is relatively limited. Yan Honglei et al. studied a cooperative formation algorithm for multiple high-speed aircraft, but did not consider process constraints (see Cooperative Formation Control Method for Underactuated Hypersonic Glide Vehicle Clusters [J]. Aerospace Defense, 2024, Vol. 7 (1): 56-62.); Song Rui et al., under the premise of considering process constraints, generated guidance commands for each aircraft based on a sequential convex optimization method that satisfies flight time constraints, and multiple aircraft could simultaneously reach the specified terminal position (see Cooperative Reentry Trajectory Planning for Hypersonic Vehicles Based on Sequential Convex Optimization [J]. Tactical Missile Technology, 2020, (6): 7-16.), but this method is based on a complex optimization algorithm and cannot generate commands online in real time.

[0005] Existing methods for generating maneuver commands for high-speed aircraft are primarily designed for single-aircraft maneuvers. Since multi-aircraft cooperative maneuvers require meeting requirements for coordinated flight (e.g., unidirectional or anisotropic flight) and collision avoidance, single-aircraft maneuver command generation methods cannot be directly applied to multi-aircraft cooperative maneuver command generation. Furthermore, among the few existing command generation methods for multi-aircraft cooperative maneuvers, some fail to consider process constraints (i.e., their constraints are not fully addressed), while others employ complex algorithms leading to poor online feasibility. Summary of the Invention

[0006] In view of this, this invention proposes a method for generating multi-aircraft cooperative maneuver command sets suitable for online real-time generation, taking into account process constraints such as overload, heat flux, and dynamic pressure, as well as control constraints such as angle of attack and roll angle, to meet the requirements of multi-aircraft cooperative missions.

[0007] To solve the above-mentioned technical problems, the present invention is implemented as follows.

[0008] A method for generating a multi-vehicle cooperative maneuver command set under multiple constraints includes:

[0009] Step 1: Based on process constraints, determine the positive and negative upper limits [σ] of the single aircraft's roll angle for the longitudinal maneuvering mode. min ,σ max ];

[0010] Step 2: Based on the restricted area constraints, and considering both control and process constraints, determine the lower limit of the roll angle for each flight segment i on the single aircraft's lateral maneuvering trajectory around the restricted area, for the aircraft's lateral maneuvering mode. Turning time between flight segments;

[0011] Step 3: Based on the upper limit of the tilt angle [σ] min ,σ max ] and lower limit Considering the constraints of aircraft structural performance on the roll angle value, the range of roll angle values ​​for each flight segment i is determined. As the range of roll angles selected in the instruction set;

[0012] Step 4: Based on the aircraft's cooperative flight mode, the aircraft's lateral maneuvering mode is further divided into same-direction cooperative mode and opposite-direction cooperative mode, according to the tilt angle range for the no-fly zone determined in Step 3. Based on the turning time determined in step 2, generate instruction sets for both unidirectional and anisodirectional cooperative modes.

[0013] Preferably, in steps 1 and 2, the process constraints include overload constraints, thermal flow constraints, and dynamic pressure constraints.

[0014] Preferably, in step 1, the determination of the positive and negative upper limits [σ] of the tilt angle of a single aircraft min ,σ max ]for:

[0015] Distinguishing based on the aircraft's longitudinal maneuvering pattern:

[0016] For the longitudinal maneuver mode being a jump-glide maneuver, the angle of attack command is already determined. Under process constraints, the roll angle amplitude |σ| corresponding to different velocities is calculated to obtain a two-dimensional roll angle-velocity curve that satisfies the process constraints; the maximum amplitude |σ| in the two-dimensional curve is then taken. max The upper limit of the positive and negative values ​​of the single aircraft's roll angle is obtained based on the maximum amplitude value as [σ]. min ,σ max ]=[-σ max ,σ max ];

[0017] For the longitudinal maneuver mode being a quasi-balanced gliding maneuver, the angle of attack command is unknown. The angle of attack is allowed to vary continuously within its range. For different angles of attack, the roll angle amplitude |σ| corresponding to different velocities is calculated under process constraints. A three-dimensional plane satisfying the process constraints—roll angle-velocity-angle of attack—is obtained through fitting, and the maximum amplitude |σ| in this three-dimensional plane is taken. max The upper limit of the positive and negative values ​​of the single aircraft's roll angle is obtained based on the maximum amplitude value as [σ]. min ,σ max ]=[-|σ| max ,|σ| max ].

[0018] Preferably, in step 2, the trajectory of the aircraft flying around the restricted area is distinguished according to the lateral maneuvering mode:

[0019] In the case of a no-fly zone, the lateral maneuver mode employs a semi-circular maneuver, with the trajectory around the no-fly zone consisting of two turning segments. Each segment is divided into a transition segment and a constant roll angle turning segment, with the curvature directions of the two turning segments being opposite. The roll angle command corresponding to the semi-circular maneuver is expressed as:

[0020]

[0021] In the formula, σ1 and σ2 are constant values ​​of the tilt angle with opposite signs; t1 is the time of change of the tilt angle command, that is, the duration of the command σ1. and These represent the transition time for the change in tilt angle; t f Total flight time;

[0022] For situations involving two no-fly zones, the lateral maneuver mode employs an S-shaped maneuver, with the flight path around the no-fly zone consisting of three turning segments. Each segment is divided into a transition segment and a constant roll angle turning segment, with the curvature directions of adjacent turning segments being opposite. The roll angle command corresponding to the S-shaped maneuver is expressed as:

[0023]

[0024] In the formula, σ1, σ2 and σ3 are the tilt angles of the constant tilt angle turning segment in the three-segment turning process, and σ1 and σ2 have opposite signs, and σ2 and σ3 have opposite signs; t1 and t2 are the tilt angle command change times in the three-segment turning process; and t represents the transition time for the change in tilt angle; f This represents the total flight time.

[0025] Preferably, in step 2, the lower limit of the tilt angle for each flight segment i on the trajectory of a single aircraft flying around a restricted area is determined. The turning time between the flight segment and the flight segment is:

[0026] Taking the minimum distance from the central axis of the cylindrical no-fly zone as the optimization objective J, and considering process constraints, control constraints, and no-fly zone constraints, the optimization model is as follows:

[0027]

[0028] stα′ min ≤α≤α′ max ,σ′ min ≤σ≤σ′ max

[0029]

[0030] n≤n

[0031] max

[0032] q≤q max

[0033] |λ k -λ N | 2 +|φ k -φ N | 2 ≥R N 2

[0034] In the formula, λ T φ T The longitude and latitude of the central axis of the no-fly zone; λ k φ kR represents the longitude and latitude of the high-speed aircraft at time k; N |λ is the radius of the no-fly zone; k -λ N | 2 +|φ k -φ N | 2 ≥R N 2 Restricted by the restricted area; n and q represent the heat flux, overload, and dynamic pressure of the aircraft involved in the process constraints, respectively; α and σ represent the angle of attack and roll angle of the aircraft involved in the control constraints, respectively, with the subscripts "min" and "max" indicating the minimum and maximum values ​​of each variable; σ′ min σ′ max These represent the minimum and maximum values ​​of the tilt angle σ, taken considering the feasibility of the aircraft; α′ min ,α′ max These represent the minimum and maximum angles of attack α for the feasibility of the aircraft, respectively; f represents f time points;

[0035] For the optimization model, the sequential quadratic programming (SQP) method is used to calculate the roll angle σ of each flight segment i on the aircraft's trajectory around the restricted area. i The turning time between the flight segments is calculated, where the roll angle σ i That is, the lower limit of the bank angle of flight segment i.

[0036] Preferably, step 3 is: Let the range of values ​​for the tilt angle σ, considering the feasibility of the aircraft, be [σ′]. min ,σ′ max ];

[0037] [σ] min ,σ max ] and [σ′ min ,σ′ max Find the intersection to obtain the range [σ]. min * ,σ max * ];

[0038] For flight segment i, if The range of values ​​for the tilt angle of flight segment i is: if The range of values ​​for the tilt angle of flight segment i is:

[0039] Preferably, the method further includes: for aircraft not in restricted areas, the lateral maneuvering mode employs a serpentine maneuver; the maneuvering command for the serpentine maneuvering aircraft is a maneuvering amplitude of l. z and maneuver frequency ω z;

[0040] Based on process constraints, determine the positive and negative upper limits [σ] of the aircraft's tilt angle. min ,σ max ];

[0041] Based on the feasibility of the aircraft, the range of values ​​for the aircraft's tilt angle σ is determined to be [σ′]. min ,σ′ max ];

[0042] [σ min ,σ max ] and [σ′ min ,σ′ max By taking the intersection, the range of tilt angles [σ] that satisfy both process constraints and control constraints can be obtained. min * ,σ max * ];

[0043] The maneuver amplitude is given according to the mission requirements. z The range and the tilt angle range [σ] min * ,σ max * Computer dynamic frequency ω z Range of values;

[0044] When multiple aircraft perform coordinated maneuvers, they adopt synchronized maneuvers with the same frequency ω. z same.

[0045] Preferably, the step of giving a maneuver amplitude l according to mission requirements z Range and tilt angle range [σ] min * ,σ max * Computer dynamic frequency ω z The range of values ​​is:

[0046] Given a given maneuver amplitude l z and tilt angle range [σ min * ,σ max * Under the condition of ],

[0047] When the longitudinal maneuver is a jump maneuver, the dynamic frequency ω is calculated using relation (I). z :

[0048]

[0049] When the longitudinal maneuver is a quasi-equilibrium gliding maneuver, the angle of attack varies with the roll angle. The relationship (II) is used to calculate the dynamic frequency ω. z :

[0050]

[0051] Where D is drag, L is lift, x is the coordinate projection of the spacecraft in the launch coordinate system Ox, m is the mass of the spacecraft, V is the velocity of the spacecraft, r is the distance from the center of the Earth to the spacecraft, and g is the acceleration due to gravity.

[0052] Beneficial effects:

[0053] (1) When multiple high-speed aircraft fly together, in order to ensure safety, overload, thermal flux and dynamic pressure constraints must be met. In this invention, a roll angle-velocity corridor that satisfies these process constraints is designed, thereby obtaining the roll angle range that satisfies the constraints. For the no-fly zone constraint, an optimization model for flying around the no-fly zone at the shortest distance is established, and the minimum roll angle command that satisfies the no-fly zone constraint is obtained through SQP optimization. By combining the roll angle command range that satisfies the process constraints, the roll angle command range that satisfies the no-fly zone constraints, and the roll angle command range that satisfies the control constraints, a command set that satisfies multiple constraints during multi-aircraft cooperative maneuvering is obtained.

[0054] (2) Once the mission is determined, the no-fly zone in the flight environment is determined, and the process constraints are given, the guidance command range that satisfies multiple constraints when multiple aircraft perform different cooperative maneuvers can be calculated using this invention. The aircraft can directly take values ​​within this range during flight without performing complex calculations. Therefore, it can be realized online in real time. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of a semi-circular maneuver trajectory.

[0056] Figure 2 This is a schematic diagram of an S-shaped maneuver trajectory.

[0057] Figure 3 This is a schematic diagram of a serpentine maneuver trajectory.

[0058] Figure 4 This is a tilt angle-velocity profile.

[0059] Figure 5 This is a cross-sectional view showing the tilt angle, velocity, and angle of attack.

[0060] Figure 6 The optimized trajectory diagram for semi-circular maneuvers.

[0061] Figure 7 Optimize the trajectory for S-shaped maneuvers.

[0062] Figure 8The set of trajectories for the cooperative maneuver behavior model is as follows: (a) is the trajectory set for cooperative maneuver behavior mode 1; (b) is the trajectory set for cooperative maneuver behavior mode 2; (c) is the trajectory set for cooperative maneuver behavior mode 3; (d) is the trajectory set for cooperative maneuver behavior mode 4; (e) is the trajectory set for cooperative maneuver behavior mode 5; (f) is the trajectory set for cooperative maneuver behavior mode 6; (g) is the trajectory set for cooperative maneuver behavior mode 7; (h) is the trajectory set for cooperative maneuver behavior mode 8; (i) is the trajectory set for cooperative maneuver behavior mode 9; and (j) is the trajectory set for cooperative maneuver behavior mode 10.

[0063] Figure 9 This is a flowchart of the present invention. Detailed Implementation

[0064] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0065] This invention provides a method for generating a multi-vehicle cooperative maneuver command set under multiple constraints. This method can satisfy process constraints such as overload, thermal flux, and dynamic pressure, as well as control quantity constraints such as angle of attack and roll angle, and no-fly zone constraints, and can be applied online in real time.

[0066] The method for generating a multi-vehicle cooperative maneuver command set under multiple constraints according to the present invention includes the following steps, see below. Figure 9 :

[0067] Step 1: Establishing the motion model of the aircraft.

[0068] Ignoring Earth's rotation, the point mass model of a high-speed spacecraft is as follows:

[0069]

[0070] In the formula, r is the geocentric distance of the high-speed aircraft, λ is the longitude, φ is the latitude, V is the velocity, θ is the trajectory inclination angle, and ψ is the velocity. V Let α be the heading angle, L be the lift force on the aircraft, D be the drag force on the aircraft, m be the mass of the aircraft, g be the acceleration due to gravity, and σ be the roll angle. For a high-speed aircraft, given the angle of attack α and the roll angle σ, its motion can be determined.

[0071] Step 2: Setting up the aircraft's cooperative maneuvering mode.

[0072] Aircraft maneuvering modes are divided into longitudinal maneuvering modes and lateral maneuvering modes. Longitudinal maneuvering modes are further divided into quasi-balanced gliding and jump gliding modes; lateral maneuvering modes are divided into semi-circular maneuvering, S-shaped maneuvering, and serpentine maneuvering. Different aircraft in a multi-aircraft configuration can choose to maneuver in the same direction or in opposite directions. Various cooperative maneuvering modes can be obtained through combinations of these maneuvering modes. The following sections provide a detailed description of single-aircraft maneuvering modules and cooperative maneuvering modes.

[0073] (1) Longitudinal maneuvering mode

[0074] Longitudinal maneuvering modes are mainly divided into quasi-balanced gliding and jump gliding.

[0075] 1.1 Quasi-balanced gliding mode

[0076] Quasi-equilibrium gliding refers to a state in which the dynamic characteristics of a high-speed aircraft reach a relatively stable state during gliding flight within the atmosphere. This means that the lift, gravity, centrifugal force, and other forces acting on the aircraft are dynamically balanced in the longitudinal plane, resulting in a relatively smooth and predictable flight trajectory. When the target aircraft is quasi-equilibrium gliding longitudinally, the trajectory inclination angle and angular velocity in equation (1) are... If the value is 0, the quasi-equilibrium gliding condition can be obtained as follows:

[0077]

[0078] Furthermore, since the trajectory angle θ is a relatively small value for quasi-equilibrium gliding motion, the quasi-equilibrium gliding condition can be approximated as follows:

[0079]

[0080] In this formula, r is the distance from the Earth's center to the altitude, which differs from the altitude H by one Earth radius R0. After determining the constraints on the altitude H in the subsequent steps, substituting these constraints into equation (3) yields the relationship between σ and V. In the above equation, σ is the tilt angle, which is generally set to 0 initially. L is the lift angle, which is related to the angle of attack. Under quasi-equilibrium gliding conditions, the angle of attack should satisfy:

[0081]

[0082] Where α is the angle of attack, q is the dynamic pressure of the aircraft, S is the reference area of ​​the aircraft, and C L This is the lift coefficient.

[0083] 1.2 Jumping and gliding

[0084] The skip-glide maneuver is a longitudinal maneuver where the target's flight in the longitudinal plane does not meet the quasi-equilibrium gliding conditions; that is, it is a maneuver behavior pattern when the net force acting on it is not zero. Therefore, its altitude, speed, etc., exhibit periodic changes. Let the angle of attack α be determined using a segmented flight scheme:

[0085]

[0086] In the formula, K is the lift-to-drag ratio; α max and α max(K) V1 and V2 are the angles of attack corresponding to the maximum flight angle of attack and the maximum lift-to-drag ratio, respectively; V1 and V2 are the segmented speed parameters of the design.

[0087] (2) Lateral maneuvering mode

[0088] In actual flight scenarios, there are often different mission requirements such as avoiding no-fly zones, maneuvering to escape, and reaching a designated target location. Different lateral maneuvering behavior modes should be adopted based on the different mission intentions that the target may have in the horizontal plane.

[0089] 2.1 Semicircular Maneuver

[0090] When a no-fly zone, such as an area vulnerable to detection or electromagnetic interference, exists between the target aircraft and its target, the aircraft originally flying towards the target cannot fly directly towards it. It must perform a near-semi-circular maneuver to avoid the no-fly zone before attacking the target. A trajectory diagram is shown below. Figure 1 As shown.

[0091] At this point, the aircraft's motion can be viewed as two specific turning processes. Both turns are completed under the condition of satisfying the reentry corridor and each uses a constant roll angle, but the directions of curvature are opposite. Therefore, the change in roll angle can be divided into two stages, with opposite signs for the roll angles in these two stages. The roll angle command corresponding to this maneuver mode is represented as follows:

[0092]

[0093] In the formula, σ1 and σ2 are constant values ​​of the tilt angle with opposite signs; t1 is the time of change of the tilt angle command, that is, the duration of the command σ1. and These represent the transition time for the change in tilt angle; t f This represents the total flight time.

[0094] 2.2 S-shaped maneuver

[0095] When there are two no-fly zones that are far apart between the aircraft and the target, the aircraft can fly around the middle of the two no-fly zones while meeting the process constraints, forming an S-shaped trajectory and hitting the target.

[0096] At this point, under the premise of satisfying the re-entry corridor, the tilt angle is set as a three-segment constant function with opposite signs for two adjacent segments, and the tilt angle change time and change transition time are set.

[0097]

[0098] In the formula, σ1, σ2 and σ3 are constant values ​​of the tilt angle, and σ1 and σ2 have opposite signs, and σ2 and σ3 have opposite signs; t1 and t2 are the tilt angle command change times; and t represents the transition time for the change in tilt angle; f This represents the total flight time.

[0099] 2.3 Serpentine Maneuver

[0100] When an aircraft enters a maneuvering avoidance zone and there is no no-fly zone ahead, it can use a serpentine maneuvering mode to effectively avoid the maneuvering avoidance zone ahead.

[0101] When the target employs a serpentine lateral maneuver, based on the dynamic inverse method, assuming the starting position of the high-speed aircraft's maneuver is the launch point and the ending position is the endpoint, the required tilt angle can be derived in the launch coordinate system. The lateral trajectory is described by a sine function, and the lateral maneuver distance is expressed as...

[0102] z(t) = z0 + l z sin[ω z x(t)+ω z0 (8)

[0103] In the formula, x and z are the coordinate projections of the aircraft onto the Ox and Oz axes of the launch coordinate system, respectively; z0 is the value of z at the start of the maneuver; l z ω is the maneuver amplitude. z ω is the maneuver frequency; z0 Let l be the phase angle at the start of the maneuver, set to 0 for calculation convenience. Considering energy consumption, we assume that a larger maneuver amplitude corresponds to a smaller maneuver frequency, i.e., l z When large, ω z Smaller.

[0104] Taking the second derivative of both sides of equation (8) with respect to time t, we get

[0105]

[0106] Considering that the target's serpentine maneuvering amplitude is usually small, its trajectory inclination angle and trajectory deviation angle can be regarded as small quantities, that is,

[0107]

[0108] Substituting equation (10) into equation (9) yields

[0109] Lsinσ=-l z ω z [Dcos(ω z x)+ω z mV 2 sin(ω z x)] (11)

[0110] When the longitudinal maneuver is a jump maneuver, the roll angle σ1 can be directly derived from equation (11).

[0111]

[0112] When the longitudinal maneuver is quasi-equilibrium gliding, the angle of attack varies with the roll angle. Substituting equation (11) into equation (2), we can obtain the roll angle σ2 as follows:

[0113]

[0114] (3) Cooperative maneuver mode

[0115] Taking the coordinated maneuver of two high-speed gliders as an example, the two targets longitudinally employ quasi-balanced gliding or jump gliding motion patterns. Laterally, they employ same-direction and opposite-direction semi-circular maneuvers, same-direction and opposite-direction S-shaped maneuvers, or serpentine maneuvers. In the same-direction maneuver, the two aircraft fly around the no-fly zone from the same side, with the same change in the sign of their tilt angles. In the opposite-direction maneuver, the two aircraft fly around the no-fly zone from opposite sides, with opposite changes in their tilt angles. The intersection of longitudinal and lateral maneuvering patterns results in 10 types of three-dimensional maneuvers, as shown in Table 1.

[0116] Table 1 Cooperative Maneuver Modes and Command List

[0117]

[0118]

[0119] Step 3: Design of cooperative maneuver commands that satisfy multiple constraints.

[0120] (1) Instruction design that satisfies process constraints: Based on process constraints, determine the positive and negative upper limits [σ] of the single aircraft's roll angle. min ,σ max ].

[0121] Due to the structural limitations of high-speed aircraft, constraints such as thermal flow constraints, overload constraints, and dynamic pressure constraints must be met during aircraft maneuvers.

[0122] The thermal flux constraint of an aircraft can be expressed as

[0123]

[0124] In the formula, For heat flow, k represents the maximum heat flux density. s =9,8704e-8, n=0.5, m=3.15, ρ is the atmospheric density at the current altitude, and V is the speed of the aircraft.

[0125] The overload constraint of an aircraft can be expressed as

[0126]

[0127] In the formula, n represents the aircraft overload, n max ρ represents the maximum overload the aircraft can withstand; L represents lift, which is related to ρ; D represents drag, which is related to ρ.

[0128] The dynamic pressure constraint of an aircraft can be expressed as

[0129]

[0130] In the formula, q is the dynamic pressure of the aircraft, q max This is to ensure that the aircraft can withstand the maximum dynamic pressure.

[0131] When establishing a model set of cooperative maneuvering behaviors for high-speed aircraft, it is necessary to consider the aircraft's thermal flux constraints, dynamic pressure constraints, and overload constraints. These constraints can be transformed into the altitude-velocity (HV) plane, and the roll angle command amplitude can be obtained through quasi-equilibrium gliding conditions.

[0132] 1. Design of tilt angle commands during jump-gliding maneuvers

[0133] When the cooperative maneuver behavior mode of the high-speed gliding aircraft is mode 6-10 in Table 1, that is, when the longitudinal maneuver mode of the high-speed aircraft is a jump gliding maneuver, the angle of attack command has been determined. Based on this, a two-dimensional tilt angle-velocity corridor is established to obtain the feasible range of the tilt angle command.

[0134] First, the thermal flux constraints, overload constraints, and dynamic pressure constraints need to be transformed into the altitude-velocity (HV) plane. The empirical formula describing the change of atmospheric density ρ with altitude H is as follows:

[0135] ρ(H)=ρ0e -βH (17)

[0136] In the formula, ρ0 is the atmospheric density at sea level, and the atmospheric density coefficient β = 1 / 7110.

[0137] Substituting equation (17) into the heat flow constraint equation (14), the heat flow constraint can be transformed into a height-velocity (HV) re-entry into the corridor boundary, and the boundary conditions can be expressed as follows:

[0138]

[0139] Similarly, substituting equation (17) into equations (15) to (16), the overload and dynamic pressure constraints can be transformed into height-velocity (HV) re-entry corridor boundaries, and the boundary conditions can be expressed as follows:

[0140]

[0141]

[0142] Equations (18) to (20) represent the altitude boundaries corresponding to heat flux, overload, and dynamic pressure constraints, respectively, which together determine the lower boundary of the altitude-velocity profile of the high-speed aircraft. The amplitude of the maneuver command roll angle depends on the lower boundary of the HV profile, and therefore the roll angle amplitude is...

[0143]

[0144] In the formula, R0 is the Earth's radius.

[0145] The lift and drag coefficients in the above formulas can be found in lift and drag coefficient tables. Alternatively, the coefficient expressions can be obtained by fitting data from the lift and drag coefficient tables. For example, for a certain aircraft, its lift coefficient C... L Drag coefficient C D for

[0146]

[0147] Where Ma is the Mach number.

[0148] Under the process constraints of formulas (18)-(20), adding R0 to H as r and substituting it into formula (3) yields the relationship between σ and V. Based on different velocities, the corresponding tilt angle amplitude |σ| can be obtained, forming a tilt angle-velocity (σ-V) corridor. This (σ-V) corridor is a two-dimensional curve of tilt angle-velocity. The maximum amplitude |σ| in the two-dimensional curve is taken. max The upper limit of the positive and negative values ​​of the single aircraft's roll angle is obtained based on the maximum amplitude value as [σ]. min ,σ max ]=[-|σ| max ,|σ| max ].

[0149] If the maximum heat flux density of the aircraft 5000kW / m 2 Maximum overload n max The maximum dynamic pressure is q = 5. max For a pressure of 100 kPa, the tilt angle-velocity (σ-V) corridor satisfying the process constraints in mode 6-10 is obtained, as follows: Figure 4 As shown.

[0150] The minimum roll angle σ that satisfies the process constraints when the aircraft performs a longitudinal jump-glide maneuver. min for Figure 4 The maximum value of the lower bound of the mid-tilt angle (red curve), and the maximum tilt angle σ that satisfies the process constraints. max for Figure 4 The minimum value of the upper bound of the mid-roll angle (black curve) yields the range of roll angles [σ] that satisfy the process constraints when the aircraft performs a jump-glide maneuver in the longitudinal direction. min ,σ max ].

[0151] 2. Range of tilt angles during quasi-balanced gliding maneuvers

[0152] When the cooperative maneuvering behavior mode of the high-speed gliding aircraft is mode 1-5 in Table 1, that is, when the longitudinal maneuvering mode of the high-speed aircraft is quasi-balanced gliding maneuver, since the angle of attack in the quasi-balanced gliding mode will change with the tilt angle, it is necessary to establish a three-dimensional tilt angle-velocity-angle of attack corridor to find the tilt angle range that satisfies the process constraints.

[0153] Given that the angle of attack of the aircraft in this paper ranges from 0° to 20°, a small step size is used to ensure continuous variation of the angle of attack within this range. The σ-V profiles at different angles of attack are then calculated, and these profiles are fitted into a three-dimensional surface to obtain the σ-V-α profiles that satisfy the process constraints for modes 1-5. Under the aforementioned simulation conditions, the calculated σ-V-α relationship is as follows: Figure 5 As shown. Take the maximum amplitude |σ| in the three-dimensional plane. max The upper limit of the positive and negative values ​​of the single aircraft's roll angle is obtained based on the maximum amplitude, which is [σ]. min ,σ max ]=[-|σ| max ,|σ| max ].

[0154] When the aircraft performs a longitudinal quasi-balanced gliding maneuver, the minimum roll angle σ that satisfies the process constraints is... min for Figure 5 The maximum value of the lower bound of the mid-tilt angle (blue surface), and the maximum tilt angle σ that satisfies the process constraints. max for Figure 5 The minimum value of the upper bound of the mid-roll angle (yellow surface) is used to obtain the range of roll angles [σ] that satisfy the process constraints when the aircraft performs a quasi-balanced gliding maneuver in the longitudinal direction. min ,σ max ].

[0155] (2) Design of instructions that satisfy no-fly zone constraints based on SQP (Sequence Quadratic Programming) algorithm.

[0156] For semi-circular and S-shaped maneuvers, in addition to meeting process constraints such as thermal flow, dynamic pressure, and overload, it is also necessary to meet the constraints of no-fly zones in the high-speed aircraft's mission.

[0157] Assuming there is a no-fly zone between the high-speed aircraft and the target (this invention considers the no-fly zone as a cylinder with no altitude), the aircraft adopts different maneuvering behavior patterns to fly around the no-fly zone according to the number and location of the no-fly zone.

[0158] To obtain the minimum roll angle command under different maneuvering behavior modes, the optimization objective J is to minimize the distance from the centerline of the cylindrical no-fly zone. Considering both process and control constraints, the optimization model is as follows:

[0159]

[0160] stα′ min ≤α≤α′ max ,σ′ min ≤σ≤σ′ max

[0161]

[0162] n≤n max

[0163] q≤q max

[0164] |λ k -λ N | 2 +|φ k -φ N | 2 ≥R N 2 (twenty three)

[0165] Where J = |λ k -λ N | 2 +|φ k -φ N | 2 To optimize the objective, α′ min ≤α≤α′ max ,σ′ min ≤σ≤σ′ max To control quantity constraints; n≤n max , q≤q max For process constraints; |λ k -λ N | 2 +|φ k -φ N | 2 ≥R N 2 Restricted by the restricted area.

[0166] In the formula, λ T φ T The longitude and latitude of the central axis of the no-fly zone. n, q, α, and σ represent the heat flux, overload, dynamic pressure, angle of attack, and roll angle of the high-speed aircraft. The subscripts "min" and "max" indicate the minimum and maximum values ​​of each variable, respectively. σ′ min σ′ max These represent the minimum and maximum values ​​of the tilt angle σ, taken considering the feasibility of the aircraft. α′ min ,α′ max λ represents the minimum and maximum values ​​of the angle of attack α, respectively, for the feasibility of the aircraft.i φ i Let R be the longitude and latitude of the high-speed aircraft at time i. N This is the radius of the no-fly zone.

[0167] For the optimization model shown in equation (23), the sequential quadratic programming method (SQP method) is used to calculate the tilt angle σ of each flight segment i on the trajectory of the aircraft around the restricted area. i The turning time between the flight segments is calculated, where the roll angle σ i That is, the lower limit of the bank angle of flight segment i.

[0168] The Sequential Quadratic Programming (SQP) algorithm is an iterative algorithm widely used for nonlinear optimization problems. Its algorithm first uses Taylor expansion to simplify the objective function of the nonlinear constraint problem into a quadratic function at the iteration point, and simplifies the constraints into linear functions. Then, by solving this simplified quadratic programming subproblem, the search direction at the current iteration point is obtained, and the iteration point is updated accordingly. This process is iterated until the stopping criterion is met, thus gradually approaching the optimal solution of the original nonlinear optimization problem. Designing a roll angle command based on the SQP algorithm to satisfy no-fly zone constraints can effectively handle nonlinear constraints and has high accuracy.

[0169] When there is a no-fly zone between the aircraft and the target, or two no-fly zones that are close to each other, a semi-circular maneuver can be used. In this case, the transition time of the change in the side angle in equation (6) is... And total flight time t f Given, we select u = [σ1, σ2, t1] as the optimization variables of the system. Assume the high-speed aircraft has an initial longitude and latitude of 0°, an initial altitude of 60000m, an initial speed of 7000m / s, and a longitudinal maneuvering mode of quasi-equilibrium gliding. The target longitude is unspecified and located on the equatorial plane. The longitude and latitude of the central axis of the no-fly zone are (40°, 0°), and the radius is 100km. Based on the SQP algorithm, we perform optimization, and the optimized result is u = [12.4°, -11.4°, -750s]. The optimized trajectory is as follows: Figure 6 .

[0170] When the aircraft and the target are in two no-fly zones that are far apart, and the aircraft uses an S-shaped maneuver to fly around the middle of the two no-fly zones, the transition time of the change in the side angle in equation (7) is as follows. And total flight time t fGiven, we select u = [σ1, σ2, σ3, t1, t2] as the optimization variables for the system. Assume the initial longitude, latitude, initial altitude, and initial velocity of the high-speed aircraft are the same as before, and the longitudinal maneuvering behavior remains a quasi-equilibrium gliding maneuver. The latitude and longitude of the central axis of No-Fly Zone 1 are (40°, 0°), with a radius of 100km, and the latitude and longitude of the central axis of No-Fly Zone 2 are (60°, 0°), with a radius of 50km. Based on the SQP algorithm, the optimization result is u = [30.60°, -30.2°, 19.7°, 350s, 900s], and the optimized trajectory is as follows. Figure 7 .

[0171] (3) Design of aircraft cooperative maneuver commands that satisfy multiple constraints

[0172] For an aircraft performing a semi-circular maneuver laterally, assuming the control quantity, i.e. the maneuver command, obtained from equation (23) is... Based on the obtained range of tilt angles satisfying the process constraints during longitudinal jump gliding or quasi-equilibrium gliding, [σ] min ,σ max Because process constraints were considered during optimization, therefore and It must be in [σ] min ,σ max Within [σ′]. Due to the requirements of aircraft structure and performance, there are control constraints, and the roll angle range is within [σ′]. min ,σ′ max [Inside]. When an aircraft performs a maneuver, it needs to simultaneously satisfy process constraints and control constraints, for [σ] min ,σ max ] and [σ′ min ,σ′ max Find the intersection, and the final range of the tilt angle is [σ]. min * ,σ max * Since equation (23) considers both control constraints and process constraints during optimization, therefore It must be in [σ] min * ,σ max * Within the range.

[0173] This invention aims to generate a set of models, i.e., a cluster of motion trajectories for the aircraft. Therefore, when the aircraft performs a semi-circular maneuver to the left (σ1 < 0), the value range of σ1 is... The range of σ² is [σ² * ,σ max * ], t1 is Let this be instruction set a; when the aircraft performs a semi-circular maneuver to the right (σ1 > 0), the range of σ1 is... The range of σ² is [σ min * ,σ2 * ], t1 is Let this be denoted as instruction set b. When two high-speed aircraft maneuver together, a unidirectional semi-circular maneuver in which both aircraft move to the left is denoted as maneuver behavior mode ALL; a unidirectional semi-circular maneuver in which both aircraft move to the right is denoted as maneuver behavior mode ARR; a unidirectional semi-circular maneuver in which aircraft 1 moves to the left and aircraft 2 moves to the right is denoted as ALR; and a unidirectional semi-circular maneuver in which aircraft 1 moves to the right and aircraft 2 moves to the left is denoted as ARL. When the cooperative maneuver behavior mode is ALL, the cooperative instruction set [a1, a2] is used, meaning that both aircraft 1 and aircraft 2 use instruction set a. Similarly, the cooperative maneuver behavior mode ARR uses the cooperative instruction set [b1, b2], the cooperative maneuver behavior mode ALR uses the cooperative instruction set [a1, b2], and the cooperative maneuver behavior mode ARL uses the cooperative instruction set [b1, a2].

[0174] For an aircraft performing a lateral S-shaped maneuver, assuming the control quantity, i.e. the maneuver command, obtained from equation (23) is... The range of the tilt angle is [σ]. min * ,σ max * To generate a model set, i.e., to generate a cluster of motion trajectories for the aircraft, when the aircraft performs an S-shaped maneuver to the right (σ1 < 0), the value of σ1 ranges from... The range of σ² is [σ² * ,σ max * The range of values ​​for σ3 is [σ min * ,σ3 * ], t1 is t2 take Let this be instruction set c; when the aircraft performs an S-shaped maneuver to the right (σ1 > 0), the range of σ1 is... σ2 in [σ min * ,σ2 * The range of σ3 is [σ3] * ,σ max * ], t1 is t2 is Let this be denoted as instruction set d. When two high-speed aircraft maneuver together, a unidirectional S-shaped maneuver in which both aircraft maneuver to the left is denoted as cooperative maneuver behavior mode BLL; a unidirectional S-shaped maneuver in which both aircraft maneuver to the right is denoted as cooperative maneuver behavior mode BRR; a unidirectional S-shaped maneuver in which aircraft 1 maneuvers to the left and aircraft 2 maneuvers to the right is denoted as cooperative maneuver behavior mode BLR; and a unidirectional S-shaped maneuver in which aircraft 1 maneuvers to the right and aircraft 2 maneuvers to the left is denoted as cooperative maneuver behavior mode BRL. In cooperative maneuver behavior mode BLL, the cooperative instruction set [c1, c2] is used, meaning that both aircraft 1 and aircraft 2 use instruction set a. Similarly, cooperative maneuver behavior mode BRR uses cooperative instruction set [d1, d2], cooperative maneuver behavior mode BLR uses cooperative instruction set [c1, d2], and cooperative maneuver behavior mode BRL uses cooperative instruction set [d1, c2].

[0175] When no no-fly zone exists, high-speed aircraft can employ a serpentine maneuver pattern laterally to effectively navigate maneuvering avoidance zones. Therefore, for aircraft performing serpentine maneuvers laterally, no-fly zone constraints are not required; only the roll angle range [σ] of process constraints and control constraints needs to be satisfied. min * ,σ max * From equations (12) to (13), it can be seen that the swerve tilt angle is determined by the maneuver amplitude l. z and maneuver frequency ω z It is determined that designing the maneuver commands for a serpentine aircraft involves designing the maneuver amplitude and frequency. When establishing a serpentine maneuver model set, the selection of the maneuver amplitude must consider mission requirements and the aircraft's own energy, with a range of [l]... zmin ,l zmax Based on the pan angle range and the maneuver amplitude range, the range of maneuver frequency values ​​[ω] is calculated. zmin ,ω zmax When two high-speed aircraft maneuver together, they generally adopt the same frequency coordinated maneuver, with aircraft 1 and aircraft 2 having the same maneuver frequency.

[0176] For aircraft employing serpentine maneuvers in lateral maneuvering mode, the command set is generated as follows:

[0177] ① Based on process constraints, determine the positive and negative upper limits [σ] of the aircraft's roll angle for the longitudinal maneuver mode. min ,σ max The longitudinal maneuver mode can select either a jump-glide maneuver or a quasi-balanced glide maneuver.

[0178] ②Based on the feasibility of the aircraft, the range of values ​​for the aircraft's tilt angle σ is determined to be [σ′]. min ,σ′ max ].

[0179] ③[σmin ,σ max ] and [σ′ min ,σ′ max By taking the intersection, the range of tilt angles [σ] that satisfy both process constraints and control constraints can be obtained. min * ,σ max * ].

[0180] ④ Specify the maneuver amplitude l according to mission requirements. z The range and the tilt angle range [σ] min * ,σ max * Computer dynamic frequency ω z The range of values. The specific calculation method is as follows: given a given maneuver amplitude l... z and tilt angle range

[0181] [σ min * ,σ max * Under the condition that the longitudinal maneuver is a jump maneuver, the dynamic frequency ω is calculated using the relation (11). z When the longitudinal maneuver is a quasi-equilibrium gliding, the angle of attack changes with the roll angle. The dynamic frequency ω is calculated using the relationship (12). z .

[0182] The following section verifies the method for generating cooperative maneuver command sets for multiple high-speed aircraft under multiple constraints.

[0183] 1. Simulation Condition Settings

[0184] Taking two high-speed aircraft as an example, their initial longitude is 0°, their latitude is 0.5° and -0.5° respectively, their initial altitude is 60,000m, and their initial speed is 7,000m / s. The control constraint's roll angle range is [-80°, 80°]. Assume the target's longitude is unspecified and it is located on the equatorial plane. Suppose there are 0, 1, or 2 no-fly zones between the high-speed aircraft and the target. No-fly zone 1 has a central axis with latitude and longitude of (40°, 0°) and a radius of 100km. No-fly zone 2 has a central axis with latitude and longitude of (60°, 0°) and a radius of 50km. The control constraint's roll angle range is...

[0185] [-80°, 80°], the angle of attack range is [0°, 20°], the process constraints are set as before, and the lift and drag coefficients are as shown in equation (22).

[0186] 2. Simulation Result Analysis

[0187] Different lateral maneuvering behavior modes are adopted for different no-fly zone situations. Based on the optimization model of equation (23), the SQP algorithm is used to optimize and obtain the optimal maneuvering commands for each lateral maneuvering behavior mode, as shown in Table 2. Since aircraft 1 and aircraft 2 are identical and symmetrical about the equatorial plane where the axis of the no-fly zone is located, the optimization result of aircraft 1 maneuvering to the left is equal in magnitude and opposite in direction to the optimization result of aircraft 2 maneuvering to the right, and the optimization result of aircraft 1 maneuvering to the right is equal in magnitude and opposite in direction to the optimization result of aircraft 2 maneuvering to the left. Therefore, Tables 2 to 3 only show the lateral cooperative maneuvering modes ALL, ALR, BLL, and BLR in Section 3.3.

[0188] Table 2 Optimal Maneuver Commands for Lateral Maneuvering Mode

[0189]

[0190] Based on the optimized commands in Table 2, a trajectory set for the cooperative maneuvering behavior mode of high-speed aircraft is constructed. The selection of the command set is described in Section 3.3. The roll angle range satisfying the process constraints and control constraints when the longitudinal maneuvering mode is jump-glide is [-80°, 80°]. Considering the energy consumption of the aircraft, the maximum absolute value of the roll angle is 60° when the high-speed aircraft performs a quasi-balanced gliding maneuver. The roll angle range satisfying the process constraints and control constraints when the longitudinal maneuvering mode is quasi-balanced gliding is [-54.8°, 54.8°]. Combined with the optimal maneuvering commands obtained from the optimization in Table 2, the range of maneuvering commands for the cooperative maneuvering behavior mode is shown in Table 3. In the table, Q represents a longitudinal quasi-balanced gliding maneuver, and S represents a longitudinal jump-glide maneuver.

[0191] Table 3. Range of Maneuver Commands for Cooperative Maneuver Behavior Patterns

[0192]

[0193]

[0194] When the lateral maneuver mode is a serpentine maneuver, based on the mission and the energy of the aircraft, the range of the lateral sway amplitude of the two high-speed aircraft is assumed to be l. z ∈[50,300]km, from equations (12)~(13), the range of values ​​for the maneuver frequency under the process constraints can be obtained as follows:

[0195]

[0196] Based on the range of maneuver commands under the above constraints, and combining the two longitudinal maneuver modes, the roll angle commands corresponding to the cooperative maneuver behavior modes in Table 3 are uniformly assigned 1000 values. Let the range of roll angle commands be [σ...]. i " min ,σ i "max ], then the tilt angle command for the trajectory set is

[0197]

[0198] In the formula, i = 1, 2, 3; n = 1, 2... Substituting these values ​​into the motion model of the high-speed aircraft, we can obtain the trajectory set for all cooperative maneuvering modes.

[0199] The maneuver command range for Cooperative Maneuver Behavior Mode 1 is the same as that for Cooperative Maneuver Behavior Mode ALL(Q) in Table 3, and the range for Cooperative Maneuver Behavior Mode 2 is the same as that for Cooperative Maneuver Behavior Mode ALR(Q) in Table 3. Similarly, Cooperative Maneuver Behavior Mode 3 is the same as BLL(Q), Cooperative Maneuver Behavior Mode 4 is the same as BLR(Q), Cooperative Maneuver Behavior Mode 6 is the same as ALL(S), Cooperative Maneuver Behavior Mode 7 is the same as ALR(S), Cooperative Maneuver Behavior Mode 8 is the same as BLL(S), Cooperative Maneuver Behavior Mode 9 is the same as BLR(Q), and the range for lateral maneuver amplitude is the same for Cooperative Maneuver Behavior Mode 5 and Behavior Mode 10. The maneuver frequency is shown in equation (24). The trajectory set of the cooperative maneuver behavior pattern obtained by simulation based on the above conditions is as follows: Figure 8 .

[0200] Depend on Figure 8 As can be seen from (a) to (e), the longitudinal trajectories of the two aircraft are relatively straight, achieving quasi-balanced gliding flight quite well. Figure 8 In (f) to (j), the trajectories of the two aircraft exhibit an oscillating shape, with the aircraft performing a jump-gliding motion. Regarding lateral maneuvers, Figure 8 of (a), Figure 8 In (f), since the initial tilt angles σ1 of both aircraft are negative, both successfully bypassed the no-fly zone by performing a leftward semi-circular maneuver in the same direction. Figure 8 (b) Figure 8 In (g), the initial tilt angle σ1 of aircraft 1 is negative, and the initial tilt angle σ1 of aircraft 2 is positive. Therefore, the two bypassed the no-fly zone from different directions with opposite semi-circular maneuvering behavior patterns. Figure 8 (c) Figure 8 In (h), the initial tilt angles σ1 of both aircraft are positive. Therefore, both aircraft successfully bypassed the two no-fly zones by performing a rightward S-shaped maneuver in the same direction. Figure 8 (d) Figure 8 In (i), the initial tilt angle σ1 of aircraft 1 is negative and the initial tilt angle σ1 of aircraft 2 is positive. Therefore, the two aircraft bypassed the two no-fly zones from different directions with opposite S-shaped maneuvering behavior patterns. Figure 8 of (e) Figure 8In scenario (j), there is no no-fly zone, and the two aircraft perform coordinated maneuvers with the same frequency. They also maneuver laterally using a serpentine maneuver to escape. Simulation data shows that both high-speed aircraft satisfy overload, dynamic pressure, and thermal flux constraints during these coordinated maneuvers. The command generation time is on the order of milliseconds, meeting the requirement for real-time online generation of coordinated maneuver commands. Therefore, this invention has broad application prospects in multi-aircraft coordination.

[0201] The specific embodiments described above only illustrate the design principles of the present invention. The shapes and names of the components in this description may differ and are not limited. Therefore, those skilled in the art can modify or make equivalent substitutions to the technical solutions described in the foregoing embodiments; and these modifications and substitutions do not depart from the inventive spirit and technical solutions of the present invention, and should all fall within the protection scope of the present invention.

Claims

1. A method for generating a multi-aircraft cooperative maneuver command set under multiple constraints, characterized in that, include: Step 1: Based on process constraints, determine the positive and negative upper limits [σ] of the single aircraft's roll angle for the longitudinal maneuvering mode. min ,σ max ]; Step 2: Based on the restricted area constraints, and considering both control and process constraints, determine the lower limit of the roll angle for each flight segment i on the single aircraft's lateral maneuvering trajectory around the restricted area, for the aircraft's lateral maneuvering mode. Turning time between flight segments; Step 3: Based on the upper limit of the tilt angle [σ] min ,σ max ] and lower limit Considering the constraints of aircraft structural performance on the roll angle value, the range of roll angle values ​​for each flight segment i is determined. As the range of roll angles selected in the instruction set; Step 4: Based on the aircraft's cooperative flight mode, the aircraft's lateral maneuvering mode is further divided into same-direction cooperative mode and opposite-direction cooperative mode, according to the tilt angle range for the no-fly zone determined in Step 3. Based on the turning time determined in step 2, generate instruction sets for both unidirectional and heterodirectional cooperative modes.

2. The method as described in claim 1, characterized in that, In steps 1 and 2, the process constraints include overload constraints, thermal flow constraints, and dynamic pressure constraints.

3. The method as described in claim 1, characterized in that, In step 1, the upper and lower limits of the tilt angle of a single aircraft [σ] are determined. min ,σ max ]for: Distinguishing based on the aircraft's longitudinal maneuvering pattern: For the longitudinal maneuver mode being a jump-glide maneuver, the angle of attack command is already determined. Under process constraints, the roll angle amplitude |σ| corresponding to different velocities is calculated to obtain a two-dimensional roll angle-velocity curve that satisfies the process constraints; the maximum amplitude |σ| in the two-dimensional curve is then taken. max The upper limit of the positive and negative values ​​of the single aircraft's roll angle is obtained based on the maximum amplitude value as [σ]. min ,σ max ]=[-σ max ,σ max ]; For the longitudinal maneuver mode being a quasi-balanced gliding maneuver, the angle of attack command is unknown. The angle of attack is allowed to vary continuously within its range. For different angles of attack, the roll angle amplitude |σ| corresponding to different velocities is calculated under process constraints. A three-dimensional plane satisfying the process constraints—roll angle-velocity-angle of attack—is obtained through fitting, and the maximum amplitude |σ| in this three-dimensional plane is taken. max The upper limit of the positive and negative values ​​of the single aircraft's roll angle is obtained based on the maximum amplitude value as [σ]. min ,σ max ]=[-|σ| max ,|σ| max ].

4. The method as described in claim 1, characterized in that, In step 2, the trajectory of the aircraft flying around the restricted area is distinguished according to the lateral maneuvering mode: In the case of a no-fly zone, the lateral maneuver mode employs a semi-circular maneuver, with the trajectory around the no-fly zone consisting of two turning segments. Each segment is divided into a transition segment and a constant roll angle turning segment, with the curvature directions of the two turning segments being opposite. The roll angle command corresponding to the semi-circular maneuver is expressed as: In the formula, σ1 and σ2 are constant values ​​of the tilt angle with opposite signs; t1 is the time of change of the tilt angle command, that is, the duration of the command σ1. and These represent the transition time for the change in tilt angle; t f Total flight time; For situations involving two no-fly zones, the lateral maneuver mode employs an S-shaped maneuver, with the flight path around the no-fly zone consisting of three turning segments. Each segment is divided into a transition segment and a constant roll angle turning segment, with the curvature directions of adjacent turning segments being opposite. The roll angle command corresponding to the S-shaped maneuver is expressed as: In the formula, σ1, σ2 and σ3 are the tilt angles of the constant tilt angle turning segment in the three-segment turning process, and σ1 and σ2 have opposite signs, and σ2 and σ3 have opposite signs; t1 and t2 are the tilt angle command change times in the three-segment turning process; and t represents the transition time for the change in tilt angle; f This represents the total flight time.

5. The method as described in claim 1, characterized in that, In step 2, the lower limit of the tilt angle for each flight segment i on the single aircraft's trajectory around the restricted area is determined. The turning time between the flight segment and the flight segment is: Taking the minimum distance from the central axis of the cylindrical no-fly zone as the optimization objective J, and considering process constraints, control constraints, and no-fly zone constraints, the optimization model is as follows: In the formula, λ T φ T The longitude and latitude of the central axis of the no-fly zone; λ k φ k R represents the longitude and latitude of the high-speed aircraft at time k; N |λ is the radius of the no-fly zone; k -λ N 2 +φ k -φ N 2 ≥R N 2 Restricted by the restricted area; n and q represent the heat flux, overload, and dynamic pressure of the aircraft involved in the process constraints, respectively; α and σ represent the angle of attack and roll angle of the aircraft involved in the control constraints, respectively, with the subscripts "min" and "max" indicating the minimum and maximum values ​​of each variable; σ′ min σ′ max These represent the minimum and maximum values ​​of the tilt angle σ, taken considering the feasibility of the aircraft; α′ min ,α′ max These represent the minimum and maximum angles of attack α for the feasibility of the aircraft, respectively; f represents f time points; For the optimization model, the sequential quadratic programming (SQP) method is used to calculate the roll angle σ of each flight segment i on the aircraft's trajectory around the restricted area. i The turning time between the flight segments is calculated, where the roll angle σ i This refers to the lower limit of the bank angle for flight segment i.

6. The method as described in claim 1, characterized in that, Step 3 is as follows: Let the range of values ​​for the tilt angle σ, considering the feasibility of the aircraft, be [σ′]. min ,σ′ max ]; [σ] min ,σ max ] and [σ′ min ,σ′ max Find the intersection to obtain the range [σ]. min * ,σ max * ]; For flight segment i, if The range of values ​​for the tilt angle of flight segment i is: if The range of values ​​for the tilt angle of flight segment i is:

7. The method as described in claim 1, characterized in that, The method further includes: for aircraft not in restricted areas, the lateral maneuvering mode employs a serpentine maneuver; the maneuvering command for the serpentine maneuvering aircraft is a maneuvering amplitude of l. z and maneuver frequency ω z ; Based on process constraints, for the longitudinal maneuver mode, the positive and negative upper limits [σ] of the aircraft's roll angle are determined. min ,σ max ]; Based on the feasibility of the aircraft, the range of values ​​for the aircraft's tilt angle σ is determined to be [σ′]. min ,σ′ max ]; [σ min ,σ max ] and [σ′ min ,σ′ max By taking the intersection, the range of tilt angles [σ] that satisfy both process constraints and control constraints can be obtained. min * ,σ max * ]; The maneuver amplitude is given according to the mission requirements. z The range of the tilt angle and the range of the slant angle [σ] min * ,σ max * Computer dynamic frequency ω z Range of values; When multiple aircraft perform coordinated maneuvers, they adopt synchronized maneuvers with the same frequency ω. z same.

8. The method as described in claim 7, characterized in that, The maneuver amplitude is given according to the task requirements. z Range and tilt angle range [σ] min * ,σ max * Computer dynamic frequency ω z The range of values ​​is: Given a given maneuver amplitude l z and tilt angle range [σ min * ,σ max * Under the condition of ], When the longitudinal maneuver is a jump maneuver, the dynamic frequency ω is calculated using relation (I). z : When the longitudinal maneuver is a quasi-equilibrium gliding maneuver, the angle of attack varies with the roll angle. The relationship (II) is used to calculate the dynamic frequency ω. z : Where D is drag, L is lift, x is the coordinate projection of the spacecraft in the launch coordinate system Ox, m is the mass of the spacecraft, V is the velocity of the spacecraft, r is the distance from the center of the Earth to the spacecraft, and g is the acceleration due to gravity.

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