Multi-hypersonic vehicle cooperative formation reentry trajectory rapid planning method

Abstract

The application particularly relates to a multi-gliding vehicle cooperative formation reentry trajectory rapid planning method, which comprises the following steps: predicting the arrival time, heading angle and position adjustable range of each vehicle virtual rendezvous point based on a time-space capability boundary prediction method; determining each vehicle real rendezvous point constraint according to the arrival time, heading angle, position and formation configuration of each vehicle virtual rendezvous point; adaptively solving each vehicle real rendezvous point constraint value based on coordination information; taking each vehicle real rendezvous point constraint value as a terminal constraint, and planning each vehicle rendezvous section trajectory based on a semi-analytical algorithm considering obstacle avoidance constraints; planning a trajectory for a leader based on a semi-analytical algorithm considering obstacle avoidance constraints; and generating formation instructions for each follower based on the height and heading angle of adjacent communicable vehicles through a gradual consistency control algorithm, and realizing formation keeping section trajectory planning based on the formation instructions. The multi-gliding vehicle rendezvous section and formation keeping section trajectory planning can be rapidly realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aircraft control technology, in particular to a multi-gliding aircraft cooperative formation reentry trajectory rapid planning method. BACKGROUND

[0002] Multi-gliding aircraft cooperative formation can overcome the single gliding aircraft task execution type single, weak penetration ability and other shortcomings, significantly improve the aircraft cluster multi-task execution ability, penetration ability and anti-interference ability, and is a necessary means to realize cooperative detection, cooperative penetration, cooperative positioning and other cooperative tasks. However, compared with cruise aircraft, unmanned aerial vehicles and other full-drive aircraft, the control ability of gliding aircraft is weak, and there is no effective control means for the speed, and the speed underactuated characteristics make it difficult to realize strict formation flight, and only relying on traditional cooperative reentry trajectory planning method can not meet the strict formation constraint requirements.

[0003] At present, the reentry trajectory can be generally divided into rendezvous and assembly segment and formation keeping segment. In the rendezvous and assembly flight process, each aircraft uses aerodynamic force to realize active regulation of flight time and state, so that it tends to be consistent at the assembly place, thereby forming a favorable formation situation. In the formation keeping flight process, each aircraft generates formation instructions combined with its own state and formation reference information, so as to maintain the formation configuration until the task is handed over. However, the introduction of complex constraint conditions such as assembly area and formation configuration makes the feasible region of the underactuated gliding aircraft cooperative formation reentry trajectory planning problem extremely small, and the rapid solution difficulty is significantly improved. Therefore, it is necessary to carry out research on the cooperative reentry trajectory rapid planning problem facing the rendezvous and assembly flight.

[0004] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present application, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] The present application provides a multi-gliding aircraft cooperative formation reentry trajectory rapid planning method, which can quickly and efficiently realize multi-gliding aircraft rendezvous and assembly segment and formation keeping segment trajectory planning.

[0006] Other characteristics and advantages of the present application will become apparent from the following detailed description, or will be learned by practice of the present application.

[0007] According to a first aspect of the present application, a multi-gliding aircraft cooperative formation reentry trajectory rapid planning method is provided, the method comprising:

[0008] The rendezvous and assembly segment trajectory planning comprises:

[0009] The arrival time, the heading angle and the position adjustable range of each aircraft virtual rendezvous point are predicted based on the space-time capability boundary prediction method; the real rendezvous point constraints of each aircraft are determined according to the arrival time, the heading angle, the position and the formation configuration of each aircraft virtual rendezvous point; the real rendezvous point constraint values of each aircraft are adaptively solved based on the coordination information and the arrival time, the heading angle and the position adjustable range of each aircraft virtual rendezvous point; the real rendezvous point constraint values of each aircraft are taken as terminal constraints, and the semi-analytical algorithm considering the obstacle avoidance constraint is used to plan the rendezvous and docking segment trajectory of each aircraft.

[0010] The formation keeping segment trajectory planning includes:

[0011] The leader is trajectory planned based on the semi-analytical algorithm considering the obstacle avoidance constraint; the formation instructions are generated by each follower based on the height and the heading angle of the adjacent communicable aircraft through the asymptotic consensus control algorithm; and the formation keeping segment trajectory planning is realized based on the formation instructions.

[0012] In some example embodiments, the arrival time adjustable range of each aircraft virtual rendezvous point includes:

[0013] The aircraft range and the time adjustable range are approximately a rhombus, in the case of the virtual rendezvous point position being determined, the rendezvous and docking segment target range is also determined, at this time, the flight time adjustable range is simplified as a straight line parallel to the time axis, and the intersection point of the straight line and the upper and lower boundaries of the rhombus is the arrival time adjustable range of each aircraft rendezvous point in the case of the virtual rendezvous point position being determined.

[0014] In some example embodiments, the heading angle adjustable range of each aircraft virtual rendezvous point includes:

[0015] The line-of-sight angle change of the segment point compared to the reentry point depends on the size of the maximum roll reversal opportunity, and the heading angle adjustable range is obtained by planning the reentry trajectory corresponding to the maximum roll reversal opportunity in the case of different initial roll angle signs sgn(σ0).

[0016] In some example embodiments, the position adjustable range of each aircraft virtual rendezvous point includes:

[0017] The position adjustable range of each aircraft virtual rendezvous point is determined based on the adjustable formation azimuth angle, and the following formula is used:

[0018]

[0019] Where (λ VRP ,φ VRP ) is the virtual rendezvous point position, A VRP is the formation azimuth angle, S FMS is the formation range, R e is the earth radius, and φf is the latitude of the terminal. f is the longitude of the terminal.

[0020] In some example embodiments, the each real rendezvous point constraint includes altitude, speed, longitude, latitude, local ballistic inclination, heading angle, heading angle error, and time constraint, and is specifically as follows:

[0021]

[0022] wherein the subscript VRP represents virtual rendezvous point related information, the subscript RRP represents real rendezvous point related information, and are respectively the altitude, speed, longitude, latitude, local ballistic inclination, heading angle, and time constraint values corresponding to the virtual rendezvous state, is the normalized energy at the real rendezvous point, f h,i (Γ), f λ,i (Γ), f φ,i (Γ) are respectively the altitude, longitude, and latitude correction amounts caused by the formation configuration Γ, ψ RRPLOS,i and are respectively the line-of-sight angle and line-of-sight angle error constraint values at the real rendezvous point.

[0023] In some example embodiments, the semi-analytical algorithm based on consideration of obstacle avoidance constraints is specifically as follows: the lateral planning part of the near-analytical gliding trajectory planning method considering the spatiotemporal full state constraints is improved by selecting one of the trajectories as the to-be-adjusted trajectory and avoiding collision by adjusting the time of the previous roll reversal before the collision point, and includes:

[0024] defining the flight trajectory between the collision point and the previous roll reversal position as a collision avoidance adjustment segment;

[0025] by analyzing the characteristics of the aircraft collision process and the collision avoidance adjustment segment, selecting the flight range S c , the average altitude , the average speed , the average roll angle amplitude , the minimum safety distance p safe , and the reversal timing adjustment amount as key parameters;

[0026] iterating S c , and as simulation conditions, and obtaining the position change amount Δp of the adjusted trajectory at the original collision point energy by the trajectory simulation method;

[0027] constructing the input as S c , p safeand Output is the interpolation table; finally, when trajectory adjustment is required, input S c 、 p safe and Find and output the Δp≥p safe required That is, the reverse opportunity adjustment quantity that meets the collision avoidance constraint can be obtained.

[0028] In some exemplary embodiments, the leader is trajectory planned based on a semi-analytical algorithm considering obstacle avoidance constraints, without considering terminal time and heading angle constraints.

[0029] According to the second aspect of the application, a multi-slip aircraft cooperative formation reentry trajectory rapid planning system is provided, comprising a rendezvous assembly segment planning module and a formation keeping segment trajectory planning module;

[0030] The rendezvous assembly segment trajectory planning module adopts a coordination-execution two-layer architecture for trajectory planning;

[0031] The coordination layer includes a space-time capability boundary prediction submodule and a coordination information adaptive solver submodule; the space-time capability boundary prediction submodule is used to predict the arrival time, heading angle and position adjustable range of each aircraft virtual assembly point based on a space-time capability boundary prediction method; the coordination information adaptive solver submodule is used to determine the real assembly point constraints of each aircraft according to the virtual assembly point arrival time, heading angle, position and formation configuration of each aircraft; the real assembly point constraint values of each aircraft are adaptively solved based on the coordination information and the virtual assembly point arrival time, heading angle and position adjustable range of each aircraft; the execution layer includes an assembly trajectory planning submodule, which is used to take the real assembly point constraint values of each aircraft as terminal constraints and plan the rendezvous assembly segment trajectory of each aircraft based on a semi-analytical algorithm considering obstacle avoidance constraints;

[0032] The formation keeping segment trajectory planning module adopts a leader-follower cooperative architecture for trajectory planning;

[0033] The leader includes a leader trajectory planning submodule, which is used to plan the trajectory of the leader based on a semi-analytical algorithm considering obstacle avoidance constraints; the follower layer includes a follower trajectory planning submodule, which is used to generate formation instructions based on the height and heading angle of adjacent communicable aircraft through a gradual consistency control algorithm, and realize formation keeping segment trajectory planning based on the formation instructions.

[0034] The multi-slip aircraft cooperative formation reentry trajectory rapid planning method provided by the embodiments of the application is a two-stage cooperative reentry trajectory planning based on the "rendezvous assembly-formation keeping" strategy. Theoretical analysis and simulation results show that:

[0035] (1) Compared with the existing method of solving the problem of formation in the case of small initial deviation, the proposed method is oriented to the task planning level, and proposes an IAFM flight scheme and a formation algorithm framework, which can quickly and efficiently realize trajectory planning of the rendezvous and formation keeping phase of multiple gliding vehicles.

[0036] (2) Compared with the existing method of using uncontrollable rendezvous points or manually divided points, the proposed method embeds the time and space capability boundary of multiple vehicles into the adaptive calculation of coordination information, which greatly improves the adjustment capability of the vehicle and the success rate of cooperative formation flight.

[0037] (3) Compared with the existing method of cooperative formation flight in the same height plane, the proposed method uses virtual height and heading angle as coordination information and realizes formation keeping flight based on the consistency principle, which eliminates the restriction on the longitudinal motion of each vehicle and enables it to maintain the formation configuration at different height planes.

[0038] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF DRAWINGS

[0039] The drawings incorporated into the specification and forming part of the specification, show embodiments consistent with the present application, and together with the specification, serve to explain the principles of the present application. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained from these drawings without creative labor for those skilled in the art.

[0040] Figure 1 Flight scheme diagram schematically showing an exemplary embodiment of the present application;

[0041] Figure 2 Range-time adjustable range diagram schematically showing an exemplary embodiment of the present application;

[0042] Figure 3 Under-actuated vehicle formation rendezvous trajectory planning method flowchart schematically showing an exemplary embodiment of the present application;

[0043] Figure 4 Gliding vehicle communication topology diagram schematically showing an exemplary embodiment of the present application;

[0044] Figure 5 Simulation result curve diagram schematically showing an exemplary embodiment of the present application: (a) ground trajectory; (b) three-dimensional trajectory of the formation keeping phase; (c) height-time curve; (d) heading angle-time curve.

[0045] Figure 6 FIG. 1 is a schematic diagram of an underactuated aerial vehicle formation rendezvous trajectory planning system according to an example embodiment of the present application. DETAILED DESCRIPTION

[0046] Example embodiments now will be described more fully hereinafter with reference to the accompanying drawings. Example embodiments, however, can be implemented in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the example embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in one or more embodiments.

[0047] In addition, the drawings are to be considered in all respects as illustrative and not restrictive; identical reference numerals have been used, where possible, to denote identical or similar features, and thus repetition of the description thereof will be omitted. Some of the block diagrams shown in the drawings are functional entities that do not necessarily have to correspond to physically or logically independent entities. These functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0048] The existing research results focus on the intersection and rendezvous segment trajectory planning method or the formation keeping segment trajectory planning method, and few of them comprehensively consider the integrated planning method of the rendezvous and formation flight cooperative reentry trajectory. The existing research results have the following shortcomings: (1) The essence of the intersection and rendezvous segment trajectory planning method is a reentry trajectory planning method considering the space-time full state constraint. The method mainly includes a trajectory optimization-based method and a prediction-correction-based method. The former has high terminal accuracy, but the problem constraint condition is relatively harsh, the initial value dependence is strong, and it is difficult to efficiently and reliably converge. The latter is generally designed based on the assumption of balanced gliding, which leads to small flight time and small adjustable range of terminal angle, and it is difficult to fully exert the reentry capability of the aircraft and to realize the terminal time and space full state constraint of the formation shift requirement. (2) The existing reentry gliding aircraft formation keeping segment trajectory planning method mainly includes a control theory-based method, a multi-constraint trajectory optimization-based method and a reinforcement learning-based method. The control theory-based method has fast formation instruction calculation speed, but it is usually difficult to meet the relative position constraint of the formation direction, and only the height direction and the lateral direction can meet the formation configuration constraint. The multi-constraint trajectory optimization-based method has the disadvantages of long trajectory calculation time and difficulty in online application. The reinforcement learning-based method is difficult to adapt to complex and variable task scenarios, that is, the multi-task applicability is weak. (3) The existing gliding cooperative formation trajectory planning and control research is mainly based on good initial conditions of the formation control method design, that is, the initial formation state deviation is small, which cannot meet the rendezvous and formation requirements under the condition of large-scale dispersion. Or because the performance of the formation rendezvous trajectory planning algorithm is poor, the formation forming segment needs to be introduced to further adjust the flight state to ensure smooth entry into the formation control stage.

[0049] The present application is based on the previous research results of a near-analytical gliding trajectory planning method considering space-time full state constraints, and aims at the cooperative formation task requirements of underactuated gliding aircraft.

[0050] Aiming at the cooperative formation problem of multiple reentry gliding vehicles, the present application proposes a two-stage reentry trajectory planning method based on the "rendezvous-formation keeping" strategy. Firstly, according to the cooperative formation task requirements and flight characteristics, the reentry trajectory is divided into a rendezvous segment and a formation keeping segment. In the rendezvous segment, a trajectory planning method based on a coordination-execution double-layer architecture is proposed, wherein the coordination layer includes a time-space capability boundary prediction and a coordination information adaptive solving link, which can realize high-precision design and distribution of the real rendezvous point constraint before launch; the execution layer designs a reentry trajectory planning algorithm based on resistance acceleration profile analysis prediction correction and double-stage tilt reversal adaptive planning to meet the real rendezvous point space-time full state constraint and collision avoidance constraint. In the formation keeping segment, a consistency cooperation strategy based on the leader-follower architecture is adopted, the leader obtains the reentry trajectory meeting the terminal constraint by the proposed reentry trajectory planning algorithm, and the follower plans the trajectory by referring to the height and heading angle of the adjacent communicable vehicles, so as to realize long-range formation keeping.

[0051] Without loss of generality, the present application makes the following remote rendezvous and formation scene settings: 1) the target formation area is a circle with the task handover point as the center and the formation range as the radius; 2) the initial position of each vehicle in the formation keeping segment is the real rendezvous point, and the area surrounded by the real rendezvous points of each vehicle is the formation rendezvous area, and the geometric center of the area is the virtual rendezvous point; 3) each vehicle has completed the initial reentry state, the task handover point state, and the formation range and formation azimuth angle information before reentry; 4) the cooperative formation task requires multiple reentry gliding vehicles to form a formation configuration and formation speed condition in the specified formation rendezvous area from their respective reentry points, and to maintain the configuration flying to the task handover area.

[0052] Under the above task scene settings, to solve the cooperative formation problem of gliding vehicles, the present application designs a rendezvous and formation keeping flight scheme. As shown in Figure 1 the scheme divides the reentry formation flight of each gliding vehicle into an initial descent segment, a rendezvous segment and a formation keeping segment, and defines the segment points between the initial descent segment and the rendezvous segment, and between the rendezvous segment and the formation keeping segment as the transition point and the real rendezvous point respectively. The initial descent segment is a transition flight phase between the reentry point and the transition point, in which the aerodynamic force is weak and the control ability is poor, so it is not suitable for large-scale maneuvering adjustment. During the rendezvous flight process, each vehicle actively adjusts the flight time and state by using aerodynamic force, so as to meet the real rendezvous point constraint condition and form an initial formation situation. During the formation keeping flight process, each vehicle generates formation instructions by combining its own state and formation reference information, so as to maintain the formation configuration until the task handover is completed.

[0053] Based on the flight scheme established above, the application designs a cooperative formation trajectory planning method framework, which is divided into three parts of initial descent segment, rendezvous segment and formation keeping segment trajectory planning, as follows:

[0054] In the initial descent segment trajectory planning part, a constant bank angle strategy is adopted for open-loop control of the aircraft, and when the drag acceleration is greater than a given threshold D TP , it is considered that the aircraft enters the rendezvous flight phase.

[0055] In the rendezvous segment trajectory planning part, a rendezvous trajectory planning method based on the coordination-execution double-layer architecture is designed. The coordination layer includes two modules of space-time capability boundary prediction and coordination information adaptive solution. Firstly, the space-time capability boundary prediction method is used to quickly predict the adjustable range of the arrival time, heading angle and position of the virtual rendezvous point of each aircraft. On this basis, the space-time adjustment capability of each aircraft and the formation task demand are considered, and the real rendezvous point constraint of the formation is determined through the coordination information adaptive solution link. The execution layer designs a rendezvous trajectory planning algorithm based on resistance acceleration profile analysis prediction correction and two-stage bank reversal adaptive adjustment, to receive the real rendezvous point constraint information of each aircraft and realize high-precision rendezvous of multiple aircraft, providing favorable initial conditions for formation keeping.

[0056] In the trajectory planning part of the formation keeping segment, a trajectory planning method based on the leader-follower cooperative architecture and the theory of gradual consistency is designed. The leader uses the proposed reentry trajectory planning algorithm to generate a formation keeping segment trajectory that satisfies the accurate arrival of the task handover point. Each follower takes the altitude and heading angle of the adjacent communicable aircraft as reference information, and generates formation instructions through the gradual consistency control algorithm to maintain the formation configuration for a long time, thereby realizing formation trajectory planning.

[0057] The motion model of the aircraft is described as follows:

[0058] Assuming that the earth is a rotating sphere and each aircraft is of the same model, a dimensionless three-degree-of-freedom center of mass dynamics model with energy as the independent variable is established as follows:

[0059]

[0060] In the formula, subscript i=1,2,...,N is the number of formation aircraft, and the dimensionless state quantity in formula (1) is x=[r,θ,φ,V,γ,ψ] T , wherein r is the dimensionless geocentric distance, θ is the geocentric longitude, φ is the geocentric latitude, V is the dimensionless speed, γ is the local ballistic inclination angle, ψ is the track yaw angle, and υ is the bank angle. L and D are the dimensionless lift acceleration and drag acceleration, which are the lift coefficient C L and the drag coefficient C Das functions of the altitude h and the Mach number Ma, where the Mach number Ma can be calculated from the current altitude and velocity, C γ,i 、C ψ,i 、 and is an additional term caused by the earth rotation.

[0061] The constraint model of the aircraft is described as follows:

[0062] Considering the cooperative formation task mode and the characteristics of the gliding aircraft, the trajectory planning method needs to meet the single aircraft constraints and the formation constraints when designing.

[0063] Among them, the single aircraft constraints include process constraints, control constraints and terminal constraints, which are specifically:

[0064] (1) Process constraints

[0065] The process constraints mainly include the stagnation point heat flux density dynamic pressure q i , overload n i and balanced glide condition, which are specifically:

[0066]

[0067] In the formula, k Q is the heat flux density coefficient, g0 is the sea level gravity acceleration, q max and n max are the corresponding constraint peak values, σ QEGC is the balanced glide tilt angle, which is uniformly taken as 0°. Among them, the first three constraints are hard constraints, and the balanced glide condition is a soft constraint that does not need to be strictly met.

[0068] In order to facilitate subsequent profile design, the initial and terminal energies of the i-th aircraft in the reentry section are respectively E 0,i and E f,i , the dimensionless energy E i is normalized, that is The initial and terminal normalized energies of the reentry section are respectively and On this basis, formula (2) is converted into the resistance acceleration D i The function relationship of the normalized energy , respectively corresponding to and , then the D-E profile reentry corridor boundary can be determined by the following formula:

[0069]

[0070] In the formula, upper and lower bounds of the reentry corridor, respectively. Thus, equation (3) can be transformed into a drag acceleration constraint:

[0071]

[0072] (2) Control constraints

[0073] The control constraints are designed to limit the attack angle i and the bank angle i magnitudes, i.e.:

[0074] α min ≤ α i ≤ α max , σ min ≤ |σ i | ≤ σ max (5)

[0075] where min , max , min and max are the upper and lower bounds of the attack angle and bank angle magnitudes, respectively.

[0076] Considering the thermal protection and the range requirements of the gliding vehicle, a three-segment linear attack angle profile is designed as follows:

[0077]

[0078] where max , L / Dmax are the maximum flight attack angle and the maximum lift-to-drag attack angle, respectively; and a , b are the attack angle profile segment parameters.

[0079] (3) Terminal constraints

[0080] The leader terminal constraints include the task handover point altitude, speed, longitude, latitude, local ballistic angle and heading angle error constraints, which are specified as follows:

[0081]

[0082] where fLOS is the terminal line-of-sight angle, and are the corresponding terminal constraint values. It is worth noting that the follower is mainly responsible for maintaining the formation configuration, so it is not set with strict terminal constraints.

[0083] where the rendezvous formation constraints are specified as:

[0084] In addition to the basic monomer aircraft constraints, each aircraft also needs to meet the formation constraints during formation flight, mainly including the rendezvous point constraints, rendezvous process constraints and formation process constraints, as follows.

[0085] (1) Rendezvous point constraints

[0086] In order to improve the solving efficiency of the real rendezvous point constraints of each aircraft, the present application constructs the relationship between the cooperative formation task and the real rendezvous point constraints of each aircraft with the virtual rendezvous point constraints as the link. The virtual rendezvous point constraint value can be determined according to the formation segment range requirement and the comprehensive meeting segment flight capability; the real rendezvous point constraint value of each aircraft is determined according to the virtual rendezvous point constraint value and the formation configuration.

[0087] The virtual rendezvous point constraints include virtual rendezvous point height, speed, longitude, latitude, local ballistic inclination, heading angle and time constraints, and the specific forms are as follows:

[0088]

[0089] In the formula, the subscript VRP represents the virtual rendezvous point related information, and are the constraint values corresponding to the virtual rendezvous state respectively.

[0090] It is worth noting that, due to the influence of the formation configuration, the real rendezvous point position constraints of each aircraft are not completely the same as the virtual rendezvous point position constraints, and need to be corrected according to the geometric relationship of the formation configuration, and then the accurate constraint values are obtained. Here, the formation configuration function is defined as Γ, and the real rendezvous point constraints of each aircraft include height, speed, longitude, latitude, local ballistic inclination, heading angle, heading angle error and time constraints, and the specific forms are as follows:

[0091]

[0092] In the formula, the subscript RRP represents the real rendezvous point related information, is the normalized energy at the real rendezvous point, f h,i (Γ), f λ,i (Γ), f φ,i (Γ) are the height, longitude and latitude correction amounts caused by the formation configuration Γ, ψ RRPLOS,i and are the line of sight angle and line of sight angle error constraint values at the real rendezvous point respectively.

[0093] (2) Rendezvous process constraints

[0094] Considering the flight safety in the dynamic rendezvous process, each aircraft needs to meet the following collision avoidance constraints in the meeting rendezvous segment:

[0095]

[0096] where subscript IAS represents the information related to the rendezvous and formation phase, is the arbitrary normalized energy during the formation phase; Δp i is the relative position vector between any two vehicles; p safe is the minimum safe position to avoid collision, which can be given according to the vehicle structure size and task requirements.

[0097] (3) Formation process constraints

[0098] During the formation keeping phase, the distance between the formation is usually much larger than the size of the vehicle itself, so under the condition that the formation configuration keeping algorithm works normally, the vehicles will hardly collide. Therefore, during the formation keeping phase, the present application mainly considers the following formation process constraints:

[0099]

[0100] where subscript FMS represents the information related to the rendezvous and formation phase, is the arbitrary normalized energy during the formation phase; ΔV i and Δp i are the velocity vector and position vector between any two vehicles, respectively, represents the expected value of Δp i , which can be determined according to the desired formation configuration; ε p , ε V are the relative position and velocity vector error limits, respectively.

[0101] On the basis of the previous related research result “A near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints”, the present application proposes a reentry trajectory planning method that simultaneously satisfies the spatiotemporal full-state constraints and the collision avoidance constraints, which can be used as the basic algorithm for subsequent rendezvous and formation phase trajectory planning and leader trajectory planning during the formation keeping phase. Only the improved content based on “A near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints” is introduced below.

[0102] To deal with the collision problem that may occur during the formation process, the present application proposes a semi-analytical reentry trajectory rapid planning algorithm considering collision avoidance constraints, which makes the following improvements to the lateral planning part of the previous research result “A near-analytical gliding trajectory planning method considering spatiotemporal full-state constraints”:

[0103] After the trajectory planning is completed, if it is detected that there is a collision risk between the trajectories of the two aircrafts, one of the trajectories can be selected as a trajectory to be adjusted, and a method of fine-tuning the time of the previous roll reversal before the collision point is used to avoid the collision. The specific method is as follows. First, the flight trajectory between the collision point and the position of the previous roll reversal is defined as an anti-collision adjustment section. Second, by analyzing the characteristics of the collision process of the aircraft and the anti-collision adjustment section, the key parameters of the range S c , the average height , the average speed , the average roll angle amplitude , the minimum safety distance p safe , and the reversal time adjustment amount are selected. Then, S c , and are iterated as simulation conditions, and the position change amount Δp of the adjusted trajectory at the original collision point energy is obtained through a large number of trajectory simulations. On this basis, an interpolation table is constructed with S c , p safe and as inputs and as output. Finally, when trajectory adjustment is required, S c , p safe and are input to find and output that meets the requirement of Δp≥p safe , so as to obtain the reversal time adjustment amount that meets the anti-collision constraint.

[0104] The improved trajectory planning method obtains a reference profile that meets the terminal height, speed, local ballistic angle, range and time constraints through longitudinal analytical planning. The lateral planning generates a lateral trajectory that meets the terminal position and heading constraints, and then generates a three-degree-of-freedom trajectory that meets the terminal constraint form such as equation (9) through trajectory iteration correction. For the reentry trajectory planning problem that does not need to meet the terminal time and heading angle constraints, i.e., the terminal constraint form is equation (7), the improved longitudinal planning can be simplified to a single-parameter profile form, the lateral planning can be simplified to a heading angle error corridor method, and the trajectory iteration correction strategy can be simplified to only correcting the range error without considering anti-collision processing.

[0105] A multi-slip aircraft cooperative formation reentry trajectory rapid planning method, as shown in Figure 3 , includes rendezvous and assembly segment trajectory planning and formation keeping segment trajectory planning.

[0106] The rendezvous and assembly segment trajectory planning includes:

[0107] The time and space capability boundary prediction method is used to predict the arrival time, heading angle and position adjustable range of each aircraft virtual rendezvous point; the arrival time, heading angle, position and formation configuration of each aircraft virtual rendezvous point are used to determine the real rendezvous point constraint of each aircraft; the real rendezvous point constraint value of each aircraft is adaptively solved based on the coordination information and the arrival time, heading angle and position adjustable range of each aircraft virtual rendezvous point; the real rendezvous point constraint value of each aircraft is taken as a terminal constraint, and a semi-analytical algorithm considering obstacle avoidance constraints is used to plan a rendezvous and docking segment trajectory of each aircraft;

[0108] The formation keeping segment trajectory planning includes:

[0109] The leader is planned a trajectory based on the semi-analytical algorithm considering obstacle avoidance constraints; each follower generates a formation instruction based on the height and heading angle of the adjacent communicable aircraft through a gradual consistency control algorithm, and realizes the formation keeping segment trajectory planning based on the formation instruction.

[0110] In the following, each step of the phased array radar design method in the example embodiment will be described in more detail with reference to the accompanying drawings and examples.

[0111] In the rendezvous and docking segment trajectory planning, the time and space capability boundary prediction method is used to predict the arrival time, heading angle and position adjustable range of each aircraft virtual rendezvous point.

[0112] For example, the flight capability boundary of each aircraft at the virtual rendezvous point is the basis for solving subsequent coordination information, and is also the key to providing a good initial state of the formation and improving the success rate of the formation. Considering the cooperative formation task demand, calculation cost and parameter importance, the arrival time t VRP,i , the heading angle ψ VRP,i and the position (λ VRP,i , φ VRP,i ) adjustable range of each aircraft at the virtual rendezvous point are selected to represent the flight capability. Through the fast prediction method of t VRP,i , ψ VRP,i and (λ VRP,i , φ VRP,i ), a selection range is provided for subsequent coordination information solving, and the specific method is as follows.

[0113] (1) Fast prediction of time adjustable range

[0114] From the above semi-analytical reentry trajectory fast planning algorithm considering collision avoidance constraints, it can be seen that for a gliding aircraft with determined task conditions, the range and time are only functions of k1 and k2, that is, for any set of k1 and k2, there is a set of S and t corresponding thereto. When the aircraft flies along the upper boundary of the corridor, the trajectory corresponds to the shortest range and flight time, that is, Conversely, when flying along the lower boundary of the corridor, its trajectory corresponds to the longest possible flight distance and time, at which point there is...

[0115] Therefore, by iterating through k1 and k2, the adjustable range of each aircraft's range and flight time can be quickly obtained, as shown in the following figure. Figure 2 As shown. By Figure 2 It can be seen that the adjustable range of the aircraft's range and time is approximately a rhombus. With the virtual rendezvous point location determined, the target range of the rendezvous segment is also determined. At this point, the adjustable range of flight time simplifies to a straight line parallel to the time axis, as shown by the black solid line in the figure. The intersections of this line with the upper and lower boundaries of the rhombus can be approximated as the adjustable range of the rendezvous time for each aircraft under the condition of a determined virtual rendezvous point location [t]. VRPmin,i ,t VRPmax,i ].

[0116] (2) Adjustable heading angle range for rapid prediction

[0117] As can be seen from the above-mentioned fast planning algorithm for semi-analytical reentry trajectories considering collision avoidance constraints, during the rendezvous and assembly segment of flight, the segmentation points... Compared to reentry point Change in line of sight Depends on the timing of the tilt reversal Size. The larger the value, the longer the lateral maneuver time of the aircraft in a certain direction, corresponding to a larger lateral distance and a greater change in the line-of-sight angle, hence Δψ LOS,0S For about It is a monotonic function. Therefore, the adjustable range of the heading angle [ψ] can be obtained by planning the reentry trajectory corresponding to the maximum roll reversal timing under different initial roll angle signs sgn(σ0). VRPmin,i ,ψ VRPmax,i At this point, the adjustable range of heading angles for each aircraft under the condition that the virtual assembly point location is determined can be obtained.

[0118] (3) Adjustable range of virtual rally point location for rapid prediction

[0119] As the above analysis shows, given a defined mission condition and virtual assembly point location, the adjustable range of flight time and heading angle at the virtual assembly point can be quickly predicted. However, determining the location of the virtual assembly point is often a complex and sensitive issue. Therefore, based on the aforementioned method for predicting the adjustable range of angles, this invention proposes a method for predicting the adjustable range of virtual assembly point locations, providing a theoretical basis and selection range for setting mission conditions.

[0120] Define the assembly azimuth as the task handover point. Relative to the spherical azimuth of the virtual rendezvous point, the position of the given mission handover point and the formation range SFMS In this case, the adjustable range of the virtual rendezvous point position is an arc segment on the boundary of the target detection area, and the virtual rendezvous point position is only related to the formation azimuth angle A. VRP This is relevant, therefore it can be found by searching for A. VRP The adjustable range is then used to obtain the adjustable range of the virtual cluster point position, and the specific method is as follows.

[0121] In A VRP Under certain conditions, the virtual assembly point position can be calculated using spherical geometry formulas, and the aforementioned adjustable heading angle prediction algorithm can be used to quickly obtain [ψ]. VRPmin,i ,ψ VRPmax,i To ensure that the intersection of the adjustable heading angle ranges of all aircraft at the corresponding virtual assembly point is a non-empty set, and that they can successfully enter the heading angle error corridor of the formation holding segment, we have:

[0122]

[0123] In the formula, [ψ min ,ψ max ] is A VRP Adjustable range of virtual rally point heading angle under given conditions, Δψ bF1 To maintain the initial width of the formation's heading angle error corridor. Therefore, equation (12) can be used as a feasibility criterion for the formation azimuth or virtual rendezvous point location, and used to screen feasible formation azimuth and virtual rendezvous point locations. Based on this, the adjustable range of the formation azimuth can be found using the following process [A VRPmin A VRPmax ]:

[0124] Step 1: Set the spherical azimuth angle of the mission handover point relative to the reentry points of each aircraft as follows: The average reentry azimuth angle is calculated as follows: And set the initial formation azimuth angle as

[0125] Step 2: Change A at equal intervals in a clockwise direction VRP And sequentially determine the current A VRP Whether equation (12) is satisfied, until the first infeasible formation azimuth is encountered, and the previous feasible formation azimuth is recorded as A. VRPmax ;

[0126] Step 3: Change A at equal intervals in a counterclockwise direction VRP And sequentially determine the current A VRP Whether equation (12) is satisfied, until the first infeasible formation azimuth is encountered, and the previous feasible formation azimuth is recorded as A. VRPmin .

[0127] So far, the adjustable range of the formation azimuth angle has been completed, and after the following geometric operation, the adjustable range of the corresponding virtual rendezvous point position (λ VRP ,φ VRP ) can be obtained:

[0128]

[0129] In the rendezvous trajectory planning, based on the coordination information and the adjustable range of the virtual rendezvous point arrival time, heading angle and position of each aircraft, the real rendezvous point constraint value of each aircraft is adaptively calculated;

[0130] For example, the rendezvous point constraint design is a key point for connecting the rendezvous section and the formation keeping section, and directly determines the feasibility of the rendezvous trajectory planning and the effect of the formation configuration keeping. Therefore, the present application selects the virtual rendezvous point flight time t VRP and the full state vector x VRP =[h VRP ,λ VRP ,φ VRP ,V VRP ,γ VRP ,ψ VRP ] as the first coordination information; the real rendezvous point flight time and the full state vector as the second coordination information, and the first and second coordination information are quickly calculated by an adaptive method, as follows.

[0131] (1) First coordination information calculation method

[0132] a.λ VRP ,φ VRP calculation method

[0133] Before the cooperative formation task is executed, the adjustable range of the formation heading angle and the virtual rendezvous point position can be quickly predicted by using the space-time capability boundary, and the formation azimuth angle A VRP and the virtual rendezvous point position (λ VRP ,φ VRP ) can be selected according to the actual task requirements.

[0134] b.V VRP calculation method

[0135] Considering that each aircraft has almost the same rendezvous state, and the flight trajectory of the formation keeping section is relatively stable, it can be considered that the change range of the aerodynamic parameters of each aircraft in the formation keeping section is small, and thus the lift-drag ratio of each aircraft can be approximated as a constant (L / D) VRP . According to the formation range requirement and the range estimation formula, the formation range can be expressed as:

[0136]

[0137] The derivation yields V VRP for:

[0138]

[0139] In the formula, K = 2S FMS / R e (L / D) VRP .

[0140] ch VRP Solution method

[0141] V is obtained using equation (15) VRP Based on the approximate solution, to further ensure that each aircraft has sufficient energy at the virtual assembly point to support its formation-keeping flight mission, the following method is designed to determine the energy E at the virtual assembly point. VRP With height h VRP .

[0142] First, considering both computational efficiency and trajectory approximation, taking the leader aircraft as the planning object and Equation (7) as the terminal constraint, an approximate trajectory is constructed using a simplified version of a near-analytical gliding trajectory planning method that considers spatiotemporal full-state constraints; second, in the range-energy profile of the approximate trajectory, the flight range S to be flown is extracted. togo =S FMS The corresponding energy under the condition, and regard it as E VRP Finally, V VRP Substituting into the dimensionless energy expression E=V 2 h can be calculated from / 2-1 / r. VRP .

[0143] d.γ VRP Solution method

[0144] In addition, to enhance the formation's range capability, γ can be... VRP Equal to the equilibrium gliding track angle γ QEGC Then we have:

[0145]

[0146] In the formula, D VRP Let V be the dimensionless drag acceleration at the virtual junction. VRP h VRP Determined; a1 and a2 are physical quantities related to the virtual cluster state, with specific expressions as follows:

[0147]

[0148] et VRP Solution method

[0149] After determining the virtual rendezvous point position, the time adjustable range of each vehicle reaching the virtual rendezvous point can be quickly predicted by using the space-time capability boundary, i.e., [t VRPmin,i ,t VRPmax,i ], so as to determine the adjustable range of t VRP by the following formula:

[0150]

[0151] In actual tasks, the success rate of formation rendezvous is often the primary consideration. Therefore, the middle value of the adjustable range is selected as the coordinated flight time, i.e., t VRP =(t min +t max ) / 2. If the time adjustable range of each vehicle has no intersection, i.e., t VRP does not exist, then formula (18) can be established by adjusting the reentry time of each vehicle.

[0152] f.ψ VRP Solving method

[0153] After determining the virtual rendezvous point position, the adjustable range of ψ VRP is determined by comprehensively considering the adjustment capability of each vehicle and the flight capability of the formation keeping segment, according to formula (18), i.e.,

[0154] [ψ min ,ψ max ]=[ψ VRPmin ,ψ VRPmax ]∩[A VRP -Δψ bF1 ,A VRP +Δψ bF1 ] (19)

[0155] In order to improve the convergence of the rendezvous and docking segment lifting trajectory planning algorithm, ψ VRP may be further taken as the middle value of [ψ min ,ψ max ], i.e., ψ VRP =(ψ min +ψ max ) / 2.

[0156] (2) Two-level coordination information solving method

[0157] After obtaining the above-mentioned one-level coordination information, the formation configuration function Γ is substituted into formula (9), so as to quickly solve the two-level coordination information of each vehicle, i.e., the real rendezvous point constraint. Thus, the high-precision and adaptive solving and distribution of the real rendezvous point constraint of each vehicle have been completed.

[0158] Exemplarily, each aircraft real rendezvous point constraint value is taken as a terminal constraint, and a semi-analytical algorithm considering obstacle avoidance constraints is used to plan a rendezvous trajectory for each aircraft.

[0159] Rendezvous trajectory planning is the basis for achieving high-precision rendezvous of multiple aircrafts and is an important link for providing a good initial state for the formation keeping stage. As an execution layer, the rendezvous trajectory planning link can quickly achieve trajectory planning for each aircraft rendezvous stage by using a semi-analytical algorithm considering obstacle avoidance constraints after receiving the real rendezvous point constraint of each aircraft.

[0160] In the rendezvous trajectory planning, the semi-analytical algorithm considering obstacle avoidance constraints is used to plan a trajectory for the leader.

[0161] Exemplarily, the leader can plan a trajectory by using the semi-analytical algorithm considering obstacle avoidance constraints. However, unlike the rendezvous stage, the leader of the formation keeping stage does not need to consider the terminal time and heading angle constraints, so a simplified version of the semi-analytical algorithm considering obstacle avoidance constraints can be used for trajectory planning.

[0162] In the rendezvous trajectory planning, each follower generates formation instructions based on the height and heading angle of the adjacent communicable aircraft by using an asymptotic consensus control algorithm, and plans a trajectory for the formation keeping stage based on the formation instructions.

[0163] Exemplarily, the follower uses the trajectory of the adjacent communicable aircraft as reference information, generates a formation trajectory by using the asymptotic consensus theory, and realizes long-distance formation keeping. The specific method is as follows.

[0164] After completing the rendezvous, each follower can realize formation keeping and trajectory planning by using the asymptotic consensus theory based on the state information of the adjacent communicable aircraft, while meeting various process constraints. Considering the difficulty of state measurement and physical meaning in actual flight process, this embodiment selects a virtual height and a heading angle ψ i as the longitudinal and lateral coordination variables, respectively, where Δh i is the expected relative height determined by the formation configuration. When the virtual height is consistent, it has and h i -h j = Δh i - Δh j , that is, the distance between aircraft i and aircraft j in the height direction is Δh i - Δh j .

[0165] First, for the longitudinal plane, consider the first and second derivatives of the virtual height with respect to time as follows:

[0166]

[0167] Based on this, and applying second-order consistency theory, the virtual control input is designed as follows:

[0168]

[0169] In the formula, To control gain. Under the action of the control law, each aircraft and A gradual consensus can be achieved, thus forming a longitudinal formation. Furthermore, the actual control input angle of attack α for each aircraft can be obtained. i With tilt angle σ i The equation should be satisfied Solving the above equations yields the required longitudinal component of lift (L). i cosσ i ) c for:

[0170]

[0171] Secondly, for the lateral plane, consider the first derivative of the heading angle with respect to time as follows:

[0172]

[0173] Based on this, and applying first-order consistency theory, the virtual control input is designed as follows:

[0174]

[0175] In the formula, K ψ1 >0 represents the control gain. Similarly, under the control law, the ψ of each aircraft... i A gradual consensus can be achieved, thus forming a lateral formation. Furthermore, the actual control input angle of attack α for each aircraft can be obtained. i With tilt angle σ i It should also satisfy the equation Solving the above equations yields the required lateral lift component (L). i sinσ i ) c for:

[0176] (L i sinσ i ) c =u ψi V i cosγ i (25)

[0177] Finally, based on the inherent properties of reentry gliding, the actual control inputs for each aircraft can be given by the following formula:

[0178]

[0179] The calculated α i and σ i are substituted into the motion equation to obtain the trajectory of each follower by numerical integration.

[0180] As another aspect, the application also provides a multi-sail glider cooperative formation reentry trajectory rapid planning system, as shown in the figure, comprising a rendezvous segment planning module and a formation keeping segment trajectory planning module. Figure 6 The rendezvous segment trajectory planning module adopts a coordination-execution two-layer architecture for trajectory planning.

[0181] The coordination layer comprises a space-time capability boundary prediction submodule and a coordination information adaptive solver submodule; the space-time capability boundary prediction submodule is configured to predict the arrival time, heading angle and position adjustable range of each aircraft virtual rendezvous point based on a space-time capability boundary prediction method; the coordination information adaptive solver submodule is configured to determine the constraints of each aircraft real rendezvous point according to the arrival time, heading angle, position and formation configuration of each aircraft virtual rendezvous point; and to adaptively solve the constraint values of each aircraft real rendezvous point based on the coordination information and the arrival time, heading angle and position adjustable range of each aircraft virtual rendezvous point; and the execution layer comprises a rendezvous trajectory planning submodule configured to take the constraint values of each aircraft real rendezvous point as terminal constraints, and to plan the rendezvous segment trajectory of each aircraft based on a semi-analytical algorithm considering obstacle avoidance constraints.

[0182] The formation keeping segment trajectory planning module adopts a leader-follower cooperative architecture for trajectory planning.

[0183] The leader comprises a leader trajectory planning submodule configured to plan the trajectory of the leader based on a semi-analytical algorithm considering obstacle avoidance constraints; and the follower layer comprises a follower trajectory planning submodule configured to generate formation instructions based on the altitude and heading angle of the proximate communicable aircraft by using a gradual consistency control algorithm, and to realize formation keeping segment trajectory planning based on the formation instructions.

[0184] The above multi-sail glider cooperative formation reentry trajectory rapid planning method is simulated and verified, and the specific process is as follows:

[0185] In an exemplary embodiment, a CAV-H is used as a model to carry out a lead plane formation task scenario simulation to verify the feasibility, rapidity and multi-task applicability of the proposed flight scheme and algorithm framework. The number of formation aircraft N is set to 3, the formation configuration is an isosceles triangle with a bottom side length of 10 km and a height of 3 km, and the formation range S FMS = 800 km, wherein aircraft 1 is the leader, and aircraft 2 and 3 are the followers, and the communication topology between the aircraft is as shown in the figure.

[0186] Figure 4 ​The initial and terminal position constraints of each vehicle are shown in Table 1, and the initial state of each vehicle is set as: t0=0s, h0=75km, V0=6500m / s, γ0=-0.1°, and ψ0 is the azimuth angle of the virtual rendezvous point relative to the reentry point. The terminal state constraint of the leader is set as: The process constraint is set as q max =100kPa and n max =3. The preset angle of attack profile and angle of attack constraint are set as α min =5°, α maxLD =10°, α max =20°, V a =5000m / s, V b =4000m / s. The roll angle constraint is σ min =0°, σ max =80°, and |σ0|=5°. The mid-final handover distance is 30km. All simulations are completed on a desktop computer equipped with an Intel Core i7-8700 3.20GHz Intel processor, and the simulation environment is Visual Studio 2019 platform.

[0187] Table 1 Initial and terminal position constraints of each vehicle

[0188]

[0189] Based on the above simulation conditions, the multi-sail vehicle cooperative formation trajectory planning results are shown in Figure 5 Figures 3(a) and 3(b). As can be seen from Figure 5 Figures 3(a) and 3(b), in the case of rendezvous formation in different height planes, each vehicle can still achieve high-precision rendezvous before formation, and maintain the basic formation configuration during the formation maintaining segment until the leader accurately reaches the mid-final handover position. As can be seen from Figure 5 Figures 3(c) and 3(d), the follower can closely track the leader's altitude and heading angle throughout the formation maintaining segment, thereby maintaining effective formation flight.

[0190] Other embodiments of the application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. It is intended that the specification and examples be considered as exemplary only, with the true scope and spirit of the application being indicated by the following claims.

[0191] It should be understood that the application is not limited to the precise construction which has been described above and which shown in the drawings, and that various modifications and changes can be made by those skilled in the art without departing from the scope of the application. The scope of the application should be determined by the claims appended hereto.

Claims

1. A method for rapid planning of reentry trajectory of a multi-slug aircraft cooperative formation, characterized in that, The method comprises rendezvous and assembly section trajectory planning and formation keeping section trajectory planning. The rendezvous and assembly section trajectory planning comprises: The virtual rendezvous point arrival time, heading angle and position adjustable range of each aircraft are predicted based on a time-space capability boundary prediction method; the real rendezvous point constraints of each aircraft are determined according to the virtual rendezvous point arrival time, heading angle, position and formation configuration of each aircraft; the real rendezvous point constraint values of each aircraft are adaptively solved based on coordination information and the virtual rendezvous point arrival time, heading angle and position adjustable range of each aircraft; and the real rendezvous point constraint values of each aircraft are taken as terminal constraints, and the rendezvous and assembly section trajectory of each aircraft is planned based on a semi-analytical algorithm considering obstacle avoidance constraints. The semi-analytical algorithm considering obstacle avoidance constraints is specifically: the lateral planning part of a near-analytical gliding trajectory planning method considering time-space full-state constraints is improved, one of the trajectories is selected as a to-be-adjusted trajectory, and collision is avoided by adjusting the once-inclination-reversal time before the collision point, comprising: a flight trajectory between the collision point and the position of the once-inclination-reversal before the collision point is defined as a collision avoidance adjustment section. By analyzing the characteristics of the aircraft collision process and the collision avoidance adjustment section, the collision avoidance adjustment section range S c , the average height , the average speed , the average amplitude of the roll angle , the minimum safety distance p safe , and the reverse timing adjustment amount are selected as key parameters; Traverse S c , and As a simulation condition, the position change amount Δp of the adjusted trajectory at the original collision point energy is obtained by the trajectory simulation method. The interpolation table is constructed with input S c , p safe and output ; finally, when trajectory adjustment is required, input S c , p safe and find and output that meet the requirement of Δp≥p safe , that is, the reverse opportunity adjustment amount that meets the collision avoidance constraint can be obtained. The formation keeping section trajectory planning comprises: The leader is trajectory planned based on the semi-analytical algorithm considering obstacle avoidance constraints; the formation instructions of each follower are generated based on the height and heading angle of the adjacent communicable aircraft through a gradual consistency control algorithm, and the formation keeping section trajectory planning is realized based on the formation instructions.

2. The method of claim 1, wherein, The virtual rendezvous point arrival time adjustable range of each aircraft comprises: The flight range and time adjustable range of the aircraft is approximately a rhombus, the rendezvous and assembly section target flight range is determined under the condition of the virtual rendezvous point position being determined, and the flight time adjustable range is simplified into a straight line parallel to the time axis under the condition, the intersection of the straight line and the upper and lower boundaries of the rhombus is the virtual rendezvous point arrival time adjustable range of each aircraft under the condition of the virtual rendezvous point position being determined.

3. The method of claim 2, wherein, The virtual rendezvous point heading angle adjustable range of each aircraft comprises: The line-of-sight angle change of the segment point compared to the reentry point depends on the size of the inclination reversal time, and the heading angle adjustable range is obtained by planning the reentry trajectory corresponding to the maximum inclination reversal time under the condition of different initial inclination angle signs sgn (σ0).

4. The method of claim 3, wherein, The virtual rendezvous point position adjustable range of each aircraft comprises: The virtual rendezvous point position adjustable range of each aircraft is determined based on the formation azimuth angle, and the following formula is used: wherein (λ VRP ,φ VRP ) is a virtual rendezvous point position, A VRP is a formation azimuth, S FMS is a formation range, R e is an earth radius, φ f is a terminal latitude, and λ f is a terminal longitude.

5. The method of claim 4, wherein, The real rendezvous point constraints of each aircraft comprise height, speed, longitude, latitude, local ballistic inclination angle, heading angle, heading angle error and time constraints, and the specific form is as follows: wherein the subscript VRP represents virtual rendezvous point related information, and the subscript RRP represents real rendezvous point related information, and are the virtual rendezvous state corresponding altitude, velocity, longitude, latitude, local ballistic angle, heading angle and time constraint values, respectively, is the normalized energy at the real rendezvous point, and f h,i (Γ), f λ,i (Γ), f φ,i (Γ) are the altitude, longitude, latitude correction values caused by the formation configuration Γ, respectively, and ψ RRPLOS,i and are the line-of-sight angle and line-of-sight angle error constraint values at the real rendezvous point, respectively.

6. The method of claim 1, wherein, The leader is trajectory planned based on the semi-analytical algorithm considering obstacle avoidance constraints, and the terminal time and heading angle constraints do not need to be considered.

7. A multi-slug aircraft cooperative formation reentry trajectory rapid planning system, characterized in that, The method comprises a rendezvous and assembly section planning module and a formation keeping section trajectory planning module. The rendezvous and assembly section trajectory planning module adopts a coordination-execution double-layer architecture for trajectory planning. The rendezvous and assembly section trajectory planning module adopts a coordination-execution double-layer architecture for trajectory planning. The coordination layer comprises a space-time capability boundary prediction submodule and a coordination information adaptive solver submodule; the space-time capability boundary prediction submodule is configured to predict the arrival time, heading angle and position adjustable range of each aircraft virtual rendezvous point based on a space-time capability boundary prediction method; the coordination information adaptive solver submodule is configured to determine the real rendezvous point constraint of each aircraft according to the arrival time, heading angle, position and formation configuration of each aircraft virtual rendezvous point; and to adaptively solve the real rendezvous point constraint value of each aircraft based on the coordination information and the arrival time, heading angle and position adjustable range of each aircraft virtual rendezvous point; the execution layer comprises a rendezvous trajectory planning submodule configured to take the real rendezvous point constraint value of each aircraft as a terminal constraint, and to plan the rendezvous and meeting segment trajectory of each aircraft based on a semi-analytical algorithm considering obstacle avoidance constraints; The semi-analytical algorithm considering obstacle avoidance constraints is specifically: improving the lateral planning part of a near-analytical gliding trajectory planning method considering space-time full-state constraints, selecting one of the trajectories as an adjusted trajectory, and avoiding collision by adjusting the time of the previous roll reversal before the collision point, comprising: defining the flight trajectory between the collision point and the previous roll reversal position as a collision avoidance adjustment segment; By analyzing the characteristics of the aircraft collision process and the collision avoidance adjustment section, the collision avoidance adjustment section range S c , the average height , the average speed , the average amplitude of the roll angle , the minimum safety distance p safe , and the reverse timing adjustment amount are selected as key parameters; Traverse S c , and As a simulation condition, the position change amount Δp of the adjusted trajectory at the original collision point energy is obtained by the trajectory simulation method. Construct input S c , p safe and The output is The interpolation table; finally, when trajectory adjustment is needed, input S. c , p safe and Find and output the expression Δp≥p safe Required This allows us to obtain the reversal timing adjustment amount that satisfies the collision avoidance constraints; The formation keeping segment trajectory planning module adopts a leader-follower collaborative architecture for trajectory planning; The leader comprises a leader trajectory planning submodule configured to plan the trajectory of the leader based on the semi-analytical algorithm considering obstacle avoidance constraints; and the follower layer comprises a follower trajectory planning submodule configured to generate formation instructions based on the height and heading angle of the adjacent communicable aircraft by using a gradual consistency control algorithm, and to realize formation keeping segment trajectory planning based on the formation instructions.

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