Aircraft cluster specified time cooperative hunting method for high maneuvering target

Abstract

The invention discloses an aircraft cluster specified time cooperative hunting method for a high maneuvering target, belongs to the technical field of aerospace, and solves the problem of specified time cooperative hunting of a fixed-wing aircraft cluster for the high maneuvering target in consideration of motion capability constraint conditions such as a normal overload upper limit of a fixed-wing aircraft. The method comprises the following steps: 1, based on a Dubins trajectory planning algorithm, establishing a mathematical model for calculating a fixed-wing aircraft cluster hunting domain and a high-maneuvering target escape domain; 2, designing an optimal hunting formation planning design algorithm based on a PSO algorithm; and step 3, based on a time-varying high-gain algorithm, designing a specified time space-time cooperative guidance law. The method is applied to cooperative hunting of a fixed-wing aircraft cluster on a high-maneuvering target, and flexibility is kept while hunting task execution efficiency is improved.

Description

Technical Field

[0001] The present invention relates to a method for a flying vehicle to conduct an encirclement and capture operation, specifically to a method for a cluster of flying vehicles to conduct a collaborative encirclement and capture operation at a specified time for a highly maneuverable target, belonging to the field of aerospace technology. Background Art

[0002] In recent years, the international situation has been changing rapidly, and high-tech military capabilities have been increasingly valued by governments of various countries. Highly maneuverable targets such as all-terrain vehicles and spherical wheeled vehicles have emerged continuously, and the problem of encircling and capturing such targets has attracted the close attention of scholars and researchers inside and outside the field. As a representative of hypersonic flying vehicles, fixed-wing flying vehicles are highly favored in the military industry due to their advantages such as low consumption, high speed, and large payload. Although their maneuverability is relatively poor compared to quadrotor flying vehicles, in traditional low-speed encirclement and capture problems, fixed-wing flying vehicles have an absolute speed advantage over the target. Therefore, there is no need to plan and design the encirclement formation, and only the classical guidance law can be used to directly pursue the target. However, with the wide application of highly maneuverable targets, the speed advantage of hypersonic flying vehicles has gradually faded, while the defects in maneuverability have become more prominent. Therefore, there is an urgent need to design an efficient encirclement formation planning algorithm and a multi-flying vehicle cooperative guidance law to improve the execution efficiency of the encirclement and capture task for highly maneuverable targets.

[0003] When performing an encirclement and capture task, an encirclement formation should be planned and designed first to ensure that the encirclement area of the flying vehicle cluster efficiently covers the target escape area while minimizing the movement distance of the cluster, thereby improving the execution efficiency of the encirclement and capture task. However, traditional encirclement formation planning algorithms only plan and design encirclement formations through simple geometric methods such as "square encirclement" and "circular encirclement". Although these methods have a simple calculation process, they have problems such as low coverage rate and uneven distribution, and their mathematical models do not fully consider task requirements such as minimizing the movement distance of the cluster; the encirclement formation planning algorithms designed based on intelligent algorithms such as reinforcement learning take into account performance indicators such as coverage efficiency and movement distance, but have problems such as a relatively complex algorithm structure and a slow calculation speed.

[0004] In addition, for a specific encirclement formation, a cooperative guidance law needs to be designed to enable each flying vehicle to achieve the desired encirclement formation within a specified time. Due to the finite-time characteristic of the guidance problem, the traditional proportional navigation law cannot achieve the formation deployment within a finite time. To address this defect, scholars have proposed a finite-time cooperative guidance law to achieve the formation deployment of multiple flying vehicles within a finite time. However, the formation deployment time of this method will change with the change of the initial scenario, and for some scenarios, it cannot complete the formation deployment task. Summary of the Invention

[0005] To solve the deficiencies of the prior art, the present invention provides a method for collaborative encirclement of a high-maneuver target by an aircraft cluster at a specified time. This method designs a specified-time guidance law to enable multiple aircraft to complete formation deployment within any specified time. The deployment time can be arbitrarily specified without relying on the initial scenario, thus greatly improving the success rate of collaborative formation deployment of multiple aircraft. Furthermore, at the specified time, the target can be encircled according to the specified index for high-maneuver targets.

[0006] A method for collaborative encirclement of a high-maneuver target by an aircraft cluster at a specified time includes the following steps:

[0007] Step 1: Based on the Dubins trajectory planning algorithm, establish a mathematical model for calculating the encirclement domain of a fixed-wing aircraft cluster and the escape domain of a high-maneuver target.

[0008] Step 2: Based on the PSO algorithm, design an optimal encirclement formation planning algorithm.

[0009] Step 3: Based on the time-varying high-gain algorithm, design a specified-time space-time collaborative guidance law.

[0010] The above method for collaborative encirclement of a high-maneuver target by an aircraft cluster at a specified time can achieve the following task requirements: (1) Efficiently plan and design the optimal encirclement formation; (2) Enable the fixed-wing aircraft cluster to complete the encirclement of the high-maneuver target under the specified time index; (3) Maintain a high collaborative position and angle accuracy.

[0011] Specifically, it is achieved through the following steps: Establish a mathematical model for calculating the escape domain of a high-maneuver target and a mathematical model for calculating the encirclement domain of a fixed-wing aircraft; Design a particle swarm position and velocity information update strategy, set the particle value range based on the actual task requirements, design an optimized performance index function, and synchronously perform cross-trajectory unwinding design. Continuously update the set of feasible solutions through optimization until the optimal feasible solution is obtained; Finally, based on the time-varying high-gain algorithm, design a specified-time space-time collaborative guidance law, including the design of the line-of-sight normal guidance law and the line-of-sight direction guidance law, so that each aircraft can reach the corresponding position indicated in the encirclement formation with high collaborative position accuracy at the preset time point and maintain the corresponding orientation angle indicated in the encirclement formation with high collaborative angle accuracy.

[0012] The beneficial effects of the present invention compared with the prior art are:

[0013] The method proposed in this application has certain innovative breakthroughs in both theoretical innovation and engineering application compared with the traditional methods in this field:

[0014] (1) In terms of the algorithm for planning and designing the encirclement formation: Compared with traditional geometric method-based algorithms for planning and designing encirclement formations such as "square encirclement" and "circular encirclement", the present invention comprehensively considers performance indicators such as the coverage rate of the encirclement formation, the coverage efficiency, and the execution efficiency of the multi-aircraft cooperative guidance mission to design the performance indicator function of the PSO algorithm; compared with the algorithm for planning and designing encirclement formations based on machine learning methods such as reinforcement learning, the present invention uses the PSO algorithm of the heuristic optimization algorithm, and uses the linear weight decreasing strategy to dynamically update the inertia factor to accelerate the convergence process, and comprehensively designs the performance indicator function according to various task requirements, solving problems such as low inference speed and difficult definition of the reward function.

[0015] (2) In terms of the time-space collaborative guidance law, the present invention has made innovative improvements to the limitations existing in different guidance methods: First, compared with the defect that the convergence time of the traditional proportional guidance law approaches infinity, the present invention adopts the finite-time control method, significantly improving the convergence speed of the system; Second, aiming at the strong dependence of the finite-time cooperative guidance law on the initial scenario, the present invention effectively enhances the robustness of the time-space collaborative guidance by introducing a time-varying high-gain feedback mechanism; Finally, compared with the problem of complex coupling between the convergence time and system parameters in the fixed-time guidance law, the method proposed by the present invention realizes independent adjustment of the convergence time without changing other system parameters, thus greatly simplifying the design process of the time-space collaborative guidance law.

[0016] The method proposed in this application can, under any reasonably set initial conditions such as the initial positions of the cluster, the strike capabilities of the aircraft, and the motion capabilities of the aircraft and the target, calculate the optimal encirclement formation that takes into account the coverage task and the multi-aircraft cooperative guidance task through the algorithm for planning and designing the encirclement formation, and then make each aircraft reach the corresponding position indicated in the encirclement formation with a relatively high cooperative position accuracy at a preset time point through the specified time cooperative time-space guidance law, and maintain the corresponding orientation angle indicated in the encirclement formation with a relatively high cooperative angle accuracy.

[0017] For the method proposed in this application, the execution time of the encirclement task can be arbitrarily specified and relatively high cooperative position and angle accuracies can be maintained. Therefore, the method proposed in this application improves the execution efficiency of the encirclement task while not losing flexibility.

[0018] The following further describes the present invention in conjunction with the drawings and embodiments: Description of the Drawings

[0019] Figure 1 It is a schematic diagram of the Dubins trajectory;

[0020] Figure 2 It is a relationship diagram between the reachable domain and the minimum turning radius;

[0021] Figure 3It is a schematic diagram of the target escape domain;

[0022] Figure 4 It is a schematic diagram of the reachable domain of the aircraft;

[0023] Figure 5 It is a flow chart of the working principle of the algorithm for planning and designing the encirclement formation;

[0024] Figure 6 It is a schematic diagram of the performance of the algorithm for planning and designing the encirclement formation (chasing formation);

[0025] Figure 7 It is a schematic diagram of the performance of the algorithm for planning and designing the encirclement formation (surrounding formation);

[0026] Figure 8 It is a schematic diagram of the performance of the proportional navigation law (chasing formation);

[0027] Figure 9 It is a schematic diagram of the performance of the proportional navigation law (surrounding formation);

[0028] Figure 10 It is a schematic diagram of the performance of the specified-time coordinated spatio-temporal guidance law (chasing formation);

[0029] Figure 11 It is a schematic diagram of the performance of the specified-time coordinated spatio-temporal guidance law (surrounding formation);

[0030] Figure 12 It is a schematic diagram of the coverage effect of the execution result of the cooperative guidance mission (chasing formation);

[0031] Figure 13 It is a schematic diagram of the coverage effect of the execution result of the cooperative guidance mission (surrounding formation). Specific implementation manners

[0032] Specific implementation manner 1: This implementation manner provides a method for specified-time cooperative encirclement of a fixed-wing aircraft cluster for a highly maneuverable target, which includes the following steps:

[0033] Step 1: Based on the Dubins trajectory planning algorithm, establish a mathematical model for calculating the encirclement domain of the fixed-wing aircraft cluster and the escape domain of the highly maneuverable target;

[0034] Step 2: Based on the classical Particle Swarm Optimization (PSO) algorithm, design an optimal algorithm for planning and designing the encirclement formation;

[0035] Step 3: Based on the time-varying high-gain algorithm, design a specified-time spatio-temporal cooperative guidance law.

[0036] Specific implementation manner 2: The difference between this implementation manner and Specific implementation manner 1 is that Step 1 is specifically:

[0037] Step 1.0: Consider the practical application of the Dubins trajectory planning algorithm in this task context

[0038] The Dubins trajectory planning algorithm is an effective method for solving the shortest path between two points for a particle considering motion ability constraints such as limited turning radius. Dubins trajectories can be roughly divided into three categories: (1) straight paths; (2) paths formed by always traveling at the minimum turning radius; (3) motion paths formed by combining the above two paths. Dubins trajectories are as shown Figure 1 in the figure. In the task context of the present invention, the motion trajectory of the aircraft is a Dubins trajectory, and the Dubins trajectory can be used to solve the limit position that the particle can reach within a specified time

[0039] Step 1.1: Establish a mathematical model for calculating the escape domain of a highly maneuverable target

[0040] If both the target and the aircraft are regarded as particles, the reachable domain can be regarded as the set of positions that the particle may reach within a certain time. Since this point set is continuously distributed, it is also a connected domain. As the key characterization of the reachable domain, the front of the reachable domain is a curve formed by the ordered connection of the limit positions that the particle can reach within a certain time. Therefore, the reachable domain of the particle can be obtained by calculating the front of its reachable domain and the left and right minimum turning arcs to obtain the boundary of the reachable domain, thereby indirectly solving the reachable domain

[0041] The isochronicity of the Dubins trajectory ensures a consistent description of the reachable range under the same time limit, and the involute formed by the endpoints of the isochronic Dubins trajectories fully considers the influence of constraints such as the minimum turning radius on the motion trajectory. Therefore, the reachable domain obtained by calculating the involutes of the left and right turning radius circles can more realistically characterize the complex maneuvering situation of the object in the actual motion scenario. The relationship between the reachable domain and the minimum turning radius is as shown Figure 2 in the figure

[0042] Then, for the moving particle i at time t, with the current position p i (t) = (x i , y i ) as the base point, the calculation method of the reachable domain front RSF i within the time range of Δt is shown in Equation (1)

[0043]

[0044] Among them, V i max is the maximum speed of the moving particle i, Ny i is the normal overload capacity coefficient is the maximum normal acceleration of the moving particle i, and g is the acceleration due to gravity. The leading edge of the reachable domain consists of RSF i,R , RSF i,L which are calculated from the right and left turning involutes respectively. The right half part RSF i,R of the leading edge of the reachable domain is calculated as shown in Equation (2), and the left half part RSF i,L is symmetric to it;

[0045]

[0046] where θ i is the velocity course angle of the moving particle i, r i o =(V i max ) 2 / Ny i is the minimum turning radius, is the center coordinate of the right turning circle of the minimum turning radius.

[0047] Since the minimum speed of a highly maneuverable target can be approximated as zero, if it is regarded as a moving particle, the reachable domain calculated according to this method is the escape domain of the target as shown in Figure 3 (where, Figure 3 (a) represents the outer contour of the reachable domain, Figure 3 (b) is the filling of Figure 3 (a), representing the reachable domain).

[0048] Step 1.2: Establish a mathematical model for calculating the reachable domain of a fixed-wing aircraft

[0049] Limited by the motion characteristics of a fixed-wing aircraft, it cannot hover in the air continuously, that is, the minimum speed is not zero. This limitation directly leads to a more complex structure of its reachable set. Its reachable set has a leading edge and a trailing edge, and the two sides are no longer composed of minimum turning arcs. Specifically, the set of the endpoints of the Dubins trajectory made based on the maximum flight speed of the fixed-wing aircraft defines the leading edge of its reachable set. This boundary is like the outermost expansion limit of a fishing net, determining the maximum coverage range of the target in the ideal high-speed state; the set of the endpoints of the Dubins trajectory constructed with the minimum flight speed determines the trailing edge of the reachable set, which delimits the boundary of the area that the aircraft can still cover at the slowest speed and is the inner contraction limit of the fishing net. When the speed of the aircraft gradually increases from the minimum to the maximum, in this dynamic change process, the edge of the reachable set does not change linearly but gradually evolves into two unique curves. These two curves form the two side boundaries of the enclosing domain.

[0050] The calculation method of the reachable domain R of a fixed-wing aircraft is shown in Equation (3).

[0051]

[0052] Among them, V i max is the maximum speed of the moving particle i, V i min is the minimum speed of the moving particle i, Ny i is the normal overload, RSF imax represents the leading edge of the reachable domain, RSF imin represents the trailing edge of the reachable domain, boundary(RSF iV ) represents the two end points on both sides of the leading edge of the reachable domain with speed V.

[0053] The reachable domain of the aircraft calculated in this way is as Figure 4 shown (the upper left figure shows the reachable domain of the aircraft at the maximum and minimum speeds, and the red line represents the boundary of the actual reachable domain; the upper right figure shows the reachable domain of the aircraft at the speeds between the maximum and minimum speeds. The upper and lower sides of the boundary of the actual reachable domain are the upper outlines of the reachable domains corresponding to the maximum and minimum speeds respectively. The left and right sides of the boundary of the actual reachable domain are formed by connecting successively the two end points of the upper outlines of all reachable domains generated during the process of the particle interpolating finely from the minimum speed to the maximum speed; the lower figure is the actual reachable domain itself). The encirclement domain of the aircraft cluster is the union of the reachable domains of all aircraft.

[0054] Specific Embodiment 3: What this embodiment further defines is that: Step 2 is specifically:

[0055] The working principle of the encirclement formation planning and design algorithm proposed by the present invention is as Figure 5 shown, among which, the core ideas of each key design link are as follows:

[0056] Step 2.1: Design the update strategy of the particle swarm position and velocity information

[0057] The position and velocity information of the particle swarm are shown in Equation (4).

[0058]

[0059] Among them, N p is the number of particles, Coord ac is the coordinate set of the aircraft cluster, Θ ac is the set of the orientation angles of the aircraft cluster, is the coordinate information of the i-th aircraft, is the orientation angle of the i-th aircraft, N ac is the total number of aircraft.

[0060] The velocity v k of the particle p k(t + 1) and position x k The update strategy of the (t + 1) information in the t-th iteration process is shown in Equation (5):

[0061]

[0062] Among them, ω(t) is the inertia factor of the particle swarm in the t-th iteration process, c 1 and c 2 are the individual and group experience learning rates respectively, pbest k (t) is the individual optimal position of particle p k in the previous t iteration rounds, gbest(t) is the group optimal position of the particle swarm in the previous t iteration rounds, and iter max is the maximum number of iterations.

[0063] To improve the convergence speed of the algorithm, the present invention uses a linear weight decreasing strategy to dynamically update the inertia factor ω, so that the particle swarm maintains a larger inertia factor at the beginning of the iteration process to expand the group search range and avoid falling into the local optimal position; at the end of the iteration process, it maintains a smaller inertia factor to refine the search for the global optimal position. The calculation method of the inertia factor ω(t) in the t-th iteration process is shown in Equation (6).

[0064]

[0065] Among them, ω max and ω min are the preset maximum and minimum values of the inertia factor respectively.

[0066] During the optimization process, only the coordinate information Coord of the aircraft cluster ac is iteratively updated with the particle position x. In order to improve the execution efficiency of subsequent strike missions, the orientation angle Θ of each aircraft ac is always in the direction pointing to the center of the target escape domain during the optimization process. The update strategy of the orientation angle of the j-th aircraft is shown in Equation (7).

[0067]

[0068] Among them, tan -1 (E) is a function for calculating the angle between the vector E and the x-axis of the coordinate axis, coord target is the reference coordinate of the target. In this project, it is set to the origin to simplify the calculation. Correspondingly, is the relative coordinate of the j-th aircraft with respect to the target reference coordinate coord target , where and coord targetTrue are the actual coordinates of the j-th aircraft and the target respectively.

[0069] Step 2.2: Setting the value range of particles

[0070] By analyzing the calculation methods of the capture area and the target escape area of the aircraft cluster mentioned in Step 1, it can be seen that the schematic diagrams of both are approximately axisymmetric. Therefore, to further improve the convergence efficiency of the optimization process, the present invention combines theoretical analysis with the kinematic characteristics of both, and designs the value range of the particle swarm as a circular ring area with the current position of the target as the center, an inner circle radius r min and an outer circle radius r max The calculation method is shown in Equation (8).

[0071]

[0072] where distance hit is the radius of the strike range of the aircraft, indicating that when the target is within this range, there must be a certain guidance law that enables the aircraft to complete the strike mission against the target, is the maximum speed of the aircraft, is the maximum speed of the target, and the constants Δr min and Δr max are the inner and outer circle value margins added to consider the cooperative position accuracy during the guidance process;

[0073] To reduce the travel distance of the aircraft cluster and improve the execution efficiency of the capture mission, and at the same time, the convergence can be accelerated by restricting the particle update range. The present invention limits the coordinate value range of each aircraft to the circular ring area in the quadrant where its initial position is located. If its initial position is on the coordinate axis, its coordinate value range is limited to the circular ring area in the two adjacent quadrants of the coordinate axis. If the coordinates of the particle exceed the value range after being updated in the current iteration round, the position is randomly initialized again, and the orientation angle always points to the center of the target escape area.

[0074] Step 2.3: Design of the optimization performance index function

[0075] To meet the actual requirements of the following capture missions: (1) Ensure the successful completion of the capture mission, that is, maximize the coverage area; (2) Improve the coverage efficiency, that is, while ensuring the maximum coverage rate, make the coverage areas of each aircraft evenly distributed on the target escape area; (3) Indirectly improve the execution efficiency of the multi-aircraft cooperative guidance mission, that is, minimize the variance of the travel distance of the cluster and the travel distances of each aircraft. The present invention designs the optimization performance index (fitness) function for the particle swarm optimization iteration process as shown in Equation (9) according to the initial quadrant distribution of each aircraft, and the optimization goal is to minimize the fitness.

[0076]

[0077] Among them, w i , i = 1, 2, ..., 7 are the weight gains of each performance index. The weights are negative, and the optimization goal is to maximize it. Conversely, the optimization goal is to minimize it. flag surround is the "surround formation" flag bit, which is set to "true" when the initial positions of the aircraft in the cluster are in 3 or more quadrants. The meanings and optimization goals of each performance index are as follows:

[0078] (1) area cover is the coverage area of the cluster's capture domain over the target's escape domain, and it should be maximized to ensure the successful completion of the capture task. Since increasing the coverage rate is the most core optimization goal, its weight gain w 1 is the largest, and its calculation method is shown in Equation (10).

[0079]

[0080] Among them, area(A) is the function for calculating the area of the calculation region object A, is the reachable domain of the i-th aircraft, and zone target is the escape domain of the target.

[0081] (2) is the variance of the formation side length, and it should be minimized to make the capture formation more symmetrical. Its calculation method is shown in Equation (11).

[0082]

[0083] Among them, var(B) is the function for calculating the variance of the elements of vector B, and length(B, C) is the function for calculating the straight-line distance from point B to point C within the parentheses.

[0084] (3) is the sum of the movement distances of each aircraft, and it should be minimized to reduce the travel distance of the aircraft (the straight-line distance from the initial position to the corresponding position in the optimized capture formation). Its calculation method is shown in Equation (12).

[0085]

[0086] Among them, and are the initial coordinates (coordinates before optimization) of the i-th aircraft.

[0087] (4) is the variance of the movement distances of each aircraft, and it should be minimized to make the movement distances of each aircraft close, reduce the complexity of the cooperative guidance process, and thus improve the cooperative position accuracy. Its calculation method is shown in Equation (13).

[0088]

[0089] (5) It is the sum of variances of the distances from the aircraft at the symmetric position relative to the target in the cluster (when the number of aircraft is even, the 2 aircraft at the central position do not participate in the calculation of this link) to the center of the target escape domain, and it should be minimized to improve the symmetry of the "chasing formation" encirclement formation with respect to the target. Its calculation method is shown in Equation (14).

[0090]

[0091] Among them, fix(A) is a function to calculate the integer part of the real number A. is the central coordinate of the target escape domain.

[0092] (6) It is the sum of the distances from each aircraft to the center of the target escape domain, and it should be maximized to indirectly reduce the movement distances of each aircraft while expanding the encirclement area of the "encirclement formation", thereby improving the execution efficiency of the encirclement mission. Its calculation method is shown in Equation (15).

[0093]

[0094] (7) It is the distance from the center of the cluster encirclement formation to the center of the target escape domain, and it should be minimized to improve the symmetry of the "encirclement formation" encirclement formation. Its calculation method is shown in Equation (16).

[0095]

[0096] Among them, is the central coordinate of the cluster encirclement formation.

[0097] Step 2.4: Design of the cross-trajectory unwinding method

[0098] During the optimization process, the random initialization characteristic of the PSO algorithm for the positions and velocities of the particle swarm may cause the flight trajectories of different aircraft to cross each other. Therefore, it is necessary to detect the trajectory crossing phenomenon after each update of the particle swarm positions and perform unwinding processing on the crossed trajectories to avoid the phenomenon of "aircraft collision" during the subsequent cooperative guidance process. This process consists of the following two key modules:

[0099] (1) Cross - situation detection module. This module determines whether two line segments intersect by using the method of vector cross - product. Cross - product reveals the relative direction between vectors in geometry, and its sign can effectively distinguish the lateral relationship between a point and a line. By calculating the cross - product values of the endpoints of a line segment with respect to another line segment, the relative position relationship between line segments can be accurately captured. When the two endpoints of a line segment are on the opposite sides of another line segment and vice versa, according to the basic principles of plane geometry, there must be an intersection point between the line segments. The advantage of this method is that it does not require explicit calculation of the intersection point and can efficiently obtain the result only through sign judgment.

[0100] (2) Cross - trajectory unwinding module. This module continuously makes global adjustments to the initial line segments generated from a given point set according to the trajectory intersection situation output by the cross - situation detection module until there is no trajectory intersection phenomenon. The specific working principle is as follows: First, initial connections between points are generated through simple rules, and a line segment is formed between every two adjacent points; then the set of line segments is detected. When an intersection phenomenon is found, it is corrected by swapping the endpoints of the line segments to ensure that the final set of line segments is geometrically independent and has no intersection points.

[0101] Specific implementation method four: What is further defined in this implementation method is that: Step three is specifically:

[0102] Step 3.1: System modeling

[0103] The present invention comprehensively considers: (1) spatio - temporal collaborative accuracy; (2) aircraft overload constraint; (3) aircraft speed constraint; (4) coverage rate of the encirclement formation, etc. performance indicators, and constructs a spatio - temporal collaborative guidance law design method at a specified time based on a time - varying high - gain algorithm.

[0104] The design goal of the multi - aircraft encirclement guidance law is to enable each aircraft to perform finite - time tracking of the desired encirclement angle and the desired encirclement coordinates. First, an aircraft guidance mathematical model is established. Considering that the pitch and yaw of the aircraft can be decoupled for analysis, and the guidance law design in the yaw plane is similar to that in the pitch plane. Therefore, without loss of generality, this project establishes a relative motion model of multi - aircraft collaborative encirclement in a two - dimensional plane. The relative motion equation of the aircraft and the target in the plane is shown in Equation (17):

[0105]

[0106] where, R is the distance between the aircraft and the desired encirclement target, is the acceleration of the aircraft relative to the desired encirclement target, is the line - of - sight angular rate between the aircraft and the target, is the line - of - sight angular acceleration between the aircraft and the target, d R and u R are the components of the target acceleration and the aircraft acceleration in the line - of - sight direction respectively, dq and u q are the components of the target acceleration and the vehicle acceleration in the line-of-sight normal direction, respectively;

[0107] The design objective of the guidance law in the line-of-sight normal direction is to track the desired encirclement angle φ within a finite time d . Due to the maneuver of the target, there is a relatively complex functional relationship between the desired line-of-sight angle q d and the desired encirclement angle φ d . There is a constraint relationship at the end of the guidance as shown in Equation (18):

[0108]

[0109] where represents the missile course angle, represents the target course angle,

[0110] Thus, the desired line-of-sight angle q d can be expressed as Equation (19):

[0111]

[0112] where ξ = V t / V m , V t represents the target velocity, V m represents the missile velocity, is an intermediate variable. It can be seen from the above equation that the desired line-of-sight angle q d is a function of the target and vehicle velocities and flight angles.

[0113] Select the state variables as q represents the line-of-sight angle between the vehicle and the target, q d represents the line-of-sight angle between the vehicle and the target in the normal direction, represents the line-of-sight angular rate between the vehicle and the target in the normal direction; then the mathematical model in the line-of-sight normal direction can be expressed as a second-order system as shown in Equation (20):

[0114]

[0115] where u q is the control input in the line-of-sight normal direction, d q is the system disturbance in the line-of-sight normal direction. Then the multi-vehicle encirclement guidance problem is further transformed into the specified-time stabilization problem of the above second-order system, that is, design the guidance law u q such that x 1 , x 2 converges to zero at the specified time.

[0116] The design objective of the guidance law in the line-of-sight direction is to enable the aircraft to track the desired rendezvous coordinates in finite time. Define R d =V d (T - t) as the virtual relative distance, where T is the desired rendezvous time. Select the state variable as z 1 =R - R d 、 Then the mathematical model in the line-of-sight direction can be expressed as a second-order system as shown in Equation (21):

[0117]

[0118] where, u R is the control input in the line-of-sight direction, and d R is the system disturbance in the line-of-sight direction.

[0119] Step 3.2: Design of the line-of-sight normal guidance law

[0120] Let T > 0 be the desired rendezvous time, then the line-of-sight normal acceleration command can be designed according to the following steps:

[0121] (1) Solve P(γ)

[0122] Consider the parametric Lyapunov equation as shown in Equation (22):

[0123] A T P + PA - Pbb T P = -γP (22)

[0124] where,

[0125]

[0126] Its unique positive definite solution P(γ) = γ(t)L n P n L n can be solved, where γ(t) is a time-varying high-gain parameter, and γ(t) will be designed later.

[0127] (2) Design the time-varying function φ 1 (x)

[0128] φ 1 (x) is designed as shown in Equation (23):

[0129]

[0130] where, λ > 0 is an adjustable parameter.

[0131] (3) Design the line-of-sight normal acceleration command

[0132] The line-of-sight normal acceleration command is designed as shown in Equation (24):

[0133]

[0134] where \(b = [0, 1]\) T , \(x = [x 1 , x 2 \) T , g 1 \(\rho(x)=1 / R\), \(t\in[0, T)\), \(\sigma c is a constant, and here \(0 < s < 1\) is an adjustable parameter. The above acceleration command can ensure that the state variables \(x 1 \), \(x 2 \) converge to zero at any specified time, and then the aircraft can track the desired enclosing angle \(\varphi d \) at any specified time.

[0135] Step 3.3: Design of the line-of-sight direction guidance law

[0136] The design of the line-of-sight direction acceleration command is similar to that of the line-of-sight normal, and can be designed according to the following steps:

[0137] (1) Solve for \(P(\gamma)

[0138] Solve the parametric Lyapunov equation

[0139] A T P + PA - Pbb T P = -\gamma P

[0140] for the unique positive definite solution \(P(\gamma)=\gamma(t)L n P n L n \), where \(\gamma(t)\) will be designed later,

[0141] (2) Design the time-varying function \(\varphi 2 (x)

[0142] \(\varphi 2 (x)\) is designed as shown in Equation (25):

[0143]

[0144] where \(\lambda>0\) is an adjustable parameter,

[0145] (3) Design the line-of-sight direction acceleration command

[0146] The line-of-sight direction acceleration command is designed as shown in Equation (26):

[0147]

[0148] where b = [0, 1] T , z = [z 1 , z 2 T , g 2 ψ(z) = 1 / R, t ∈ [0, T), σ c is a constant, where 0 < s < 1 is an adjustable parameter. The above acceleration command can ensure that the state variables z 1 , z 2 converge to zero at any specified time, and then the aircraft can reach the desired enclosing coordinates in a finite time.

[0149] Step 3.4: Acceleration calculation

[0150] The normal acceleration a m and the tangential acceleration a t of the aircraft can be calculated separately as

[0151]

[0152] The acceleration components of the aircraft along the x-axis and y-axis can be calculated as

[0153]

[0154] where θ m is the heading angle of the aircraft.

[0155] Embodiment

[0156] Assume that the aircraft swarm consists of N ac = 3 fixed-wing aircraft with exactly the same performance parameters such as flight speed: minimum flight speed maximum flight speed normal overload capacity coefficient Ny ac = 0.32, gravitational acceleration g ≈ 9.81 m / s 2 ; the high-maneuver target is a mobile vehicle, and its motion ability parameters are: maximum motion speed normal overload capacity coefficient Ny target = 0.189. Assume that any aircraft in the swarm can complete the strike mission within the target distance distance hit = 0.4 km using a certain guidance law.

[0157] In the optimal enclosing formation planning and design algorithm: the number of particles N p = 50, individual experience learning rate c 1 ​= 1.5, swarm experience learning rate c 2 = 1.5, maximum number of iterations iter max = 5, maximum value of inertia factor ω max = 0.9, minimum value of inertia factor ω min = 0.4, inner circle value margin Δr min = 2 m / s, outer circle value margin Δr max = -2 m / s, w 1 = 4.5, w 2 = 1.5, w 3 = 0.0001, w 4 = 0.1, w 5 = 1.5, w 6 = 1000, w 7 = 1; in the proportional navigation law, the parameter is N = 3; in the specified-time coordinated space-time guidance law, the parameters are λ = 0.01, σ c = 6.83, s = 0.01, V d = 50 m / s, T = 80 s.

[0158] Select the initial position of the target Initial heading angle To verify the performance of the swarm surrounding the target in the "chasing formation" (flag bit flag surround = 0), select the initial position of the swarm Initial orientation angle To verify the performance of the swarm surrounding the target in the "encircling formation" (flag bit flag surround = 1), select the initial position of the swarm Initial orientation angle Regard both the aircraft and the target as moving particles, and consider the target performing a sinusoidal maneuver such as equation a t = 7cos(0.8t). First, use the optimal surrounding formation planning and design algorithm proposed in this application to calculate the optimal surrounding formation, then use the specified-time coordinated space-time guidance law to execute the multi-aircraft cooperative guidance task, and finally complete the surrounding task of the highly maneuverable target.

[0159] In addition, the present invention designs the surrounding formation by directly making the center of the reachable domain of each flight coincide with the center of the target escape domain as a control group to verify the performance of the optimal surrounding formation planning and design algorithm proposed in the present invention; uses the proportional navigation law to execute the multi-aircraft cooperative guidance task as a control group to verify the performance of the specified-time coordinated space-time guidance law proposed in the present invention. For the two cases of the swarm in the "chasing formation" and the "encircling formation", combined with the above comparison and verification method, two groups of simulation experiments are carried out, and the experimental results are as Figures 6 - 13As shown (in the figure, the trajectories of the same aircraft, the starting and ending points of the aircraft, and the reachable area of the aircraft, etc. are all expressed in the same color. The covered area of the escape area is uniformly represented by the same color. The transparency of each sub-region in this area can reflect its coverage thickness, that is, as the number of aircraft covering the sub-region increases, the transparency gradually decreases and the color also deepens accordingly. In this embodiment, 3 aircraft are given).

[0160] Figure 6 , Figure 7 respectively record the performance of the optimal capture formation planning and design algorithm when the cluster captures the target in the "chasing formation" and "surrounding formation". Among them, "relative position" means that for the convenience of the design and operation of the optimization algorithm, when the target is placed at the origin, the position of the aircraft relative to the target (the positions in the other figures are all real positions). It can be seen from the figure that: whether the cluster captures the target in the "chasing formation" or the "surrounding formation", compared with directly making the centers of the reachable areas of each aircraft coincide with the center of the target's escape area, the capture formation calculated by using the optimal capture formation planning and design algorithm can achieve a more complete and efficient coverage of the target's escape area, and at the same time, it can also reduce the movement distance of the cluster and the variance of the movement distances of each aircraft, thereby indirectly improving the execution efficiency of the multi-aircraft cooperative guidance mission; Figure 8 , Figure 9 respectively record the performance of the proportional navigation law when the cluster captures the target in the "chasing formation" and "surrounding formation". It can be seen from the figure that: whether the cluster captures the target in the "chasing formation" or the "surrounding formation", its capture formation is relatively loose and cannot achieve effective capture; Figure 10 , Figure 11 respectively record the performance of the specified-time cooperative spatio-temporal guidance law when the cluster captures the target in the "chasing formation" and "surrounding formation". It can be seen from the figure that: whether the cluster captures the target in the "chasing formation" or the "surrounding formation", it can form a relatively effective capture formation. The three lines in the above Figures 8 - 11 respectively represent the movement trajectories of three aircraft. Figure 12 , Figure 13 respectively record the coverage effects when the cluster captures the target according to the corresponding positions and orientation angles in the results of the cluster executing the cooperative guidance mission using the proportional navigation law and the specified-time cooperative spatio-temporal guidance law when capturing the target in the "chasing formation" and "surrounding formation". It can be seen from the figure that: whether the cluster captures the target in the "chasing formation" or the "surrounding formation", compared with the proportional navigation law, the coverage effect of the final capture formation obtained by using the specified-time cooperative spatio-temporal guidance law to execute the cooperative guidance mission is closer to the ideal state, that is, the coverage effect of the capture formation calculated by using the optimal capture formation planning and design algorithm.

[0161] In summary, whether the cluster pursues the target in a "chase formation" or an "encirclement formation", the pursuit formation calculated by the optimal pursuit formation planning and design algorithm proposed by the present invention can achieve efficient coverage of highly maneuverable targets. The proposed specified-time cooperative spatio-temporal guidance law can complete the multi-aircraft cooperative guidance task with high cooperative position and angle accuracy under the specified task execution time index. Therefore, the fixed-wing aircraft cluster specified-time cooperative pursuit method proposed by the present invention has certain theoretical significance and application value for the pursuit task of highly maneuverable targets.

[0162] The present application has been disclosed above with preferred embodiments. However, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the equivalent embodiments with equivalent changes within the scope of the technical solutions of the present application by using the disclosed structures and technical contents. All of them still fall within the scope of the technical solutions of the present application.

Claims

1. A method for collaboratively capturing a high-maneuverable target by a cluster of aircraft at a specified time, characterized in that: The following steps are involved: Step 1: Based on the Dubins trajectory planning algorithm, a mathematical model is established to calculate the fixed-wing aircraft cluster capture area and the high-maneuverability target escape area; Step 2: Based on the PSO algorithm, design the optimal capture formation planning algorithm; Step 3: Based on the time-varying high-gain algorithm, design the space-time coordinated guidance law for the specified time.

2. The method for collaboratively capturing a high-maneuverability target by a cluster of aircraft at a designated time according to claim 1, characterized in that: Step 1 Based on the Dubins trajectory planning algorithm, the specific process of establishing a mathematical model for calculating the fixed-wing aircraft cluster capture area and the high-maneuverability target escape area is as follows: If both the high-maneuverability target and the fixed-wing aircraft are regarded as point masses, the reachable domain can be regarded as the set of positions that the point mass may reach within a certain period of time; Step 1.1: Develop a mathematical model to calculate the escape zone of a highly maneuverable target Then the moving particle i at time t is at its current position p i (t) = (x i ,y i ) as the base point, the RSF of the reachable domain frontier within the time range of Δt i As shown in formula (1); Among them, V i max is the maximum velocity of the moving particle i, Ny i is the normal overload capacity coefficient, is the maximum normal acceleration of the moving particle i, g is the gravitational acceleration, and the frontier of the reachable domain is the RSF calculated by the right and left turning involutes respectively. i,R 、RSF i,L It consists of two parts, the right half of the frontier of the reachable domain RSF i,R As shown in formula (2), the left half of RSF i,L It is symmetrical with it; Among them, θ i is the velocity heading angle of the moving particle i, is the minimum turning radius, is the center coordinate of the right turning circle with the minimum turning radius; since the minimum speed of a high maneuverable target is zero, the reachable domain boundary is obtained by calculating the frontier of the reachable domain and the arc length of the left and right minimum turning circles, and the reachable domain is indirectly solved. The reachable domain calculated in this way is the escape domain of the target; Step 1.2: Build a mathematical model to calculate the capture area of ​​fixed-wing aircraft The set of Dubins trajectory endpoints based on the maximum flight speed of the fixed-wing aircraft defines the front edge of its reachable set; the set of Dubins trajectory endpoints constructed with the minimum flight speed determines the back edge of the reachable set. The reachable domain R of the fixed-wing aircraft is shown in formula (3); Among them, V i max is the maximum velocity of the moving particle i, V i min is the minimum velocity of the moving particle i, Ny i is the normal overload, RSF imax Represents the reachable domain frontier, RSF imin Represents the back edge of the reachable domain, boundary(RSF iV ) represents the two end points of the frontier of the reachable domain with a speed of V. The capture domain of the fixed-wing aircraft cluster is the union of the reachable domains of all fixed-wing aircraft.

3. The method for collaboratively capturing a high-maneuverability target by a cluster of aircraft at a designated time according to claim 2, characterized in that: Step 2 Based on the PSO algorithm, the process of designing the optimal capture formation planning design algorithm is as follows: Step 2.1: Design a strategy for updating particle swarm position and velocity information The position and velocity information of the particle group is shown in formula (3): Among them, N p is the number of particles, Coord ac is the coordinate set of the aircraft cluster, Θ ac is the set of heading angles of the aircraft cluster, is the coordinate information of the i-th aircraft, is the heading angle of the i-th aircraft, N ac is the total number of aircraft. Particle p k The speed v k (t+1) and position x k The update strategy of (t+1) information in the tth round of iteration is shown in formula (5): Among them, ω(t) is the inertia factor of the particle swarm in the tth round of iteration, c1 and c2 are the individual and group experience learning rates, pbest k (t) is particle p k The individual best position in the first t iterations, gbest(t) is the group best position of the particle swarm in the first t iterations, iter max is the maximum number of iterations; The calculation of the inertia factor ω(t) during the tth iteration is shown in formula (6): Among them, ω max With ω min are respectively the preset maximum and minimum values ​​of the inertia factor; During the optimization process, the coordinates of the aircraft cluster Coord ac As the particle position x is iteratively updated, the orientation angle Θ of the aircraft cluster ac During the optimization process, the direction always points to the center of the target escape zone, and the jth aircraft faces the angle The update strategy is shown in formula (7): Among them, tan -1 (E) is the function for calculating the angle between vector E and the x-axis, coord target is the reference coordinate of the target, is the jth aircraft relative to coord target The relative coordinates of With coord targetTrue are the actual coordinates of the jth aircraft and target respectively; Step 2.2: Particle value range setting Based on the aircraft cluster capture domain and the high-maneuverability target escape domain, the particle swarm value range is designed to be a circle with the current position of the target as the center and the inner radius r min With outer radius r max The circular area as shown in formula (8); Among them, distance hit is the radius of the aircraft's strike range, indicating that when the target is within this range, there must be a certain guidance law that enables the aircraft to complete the strike mission against the target. is the maximum speed of the aircraft, is the target maximum speed, constant Δr min With Δr max The inner circle and outer circle value margin added to consider the coordinated position accuracy of the guidance process; Step 2.3: Optimize performance indicator function design According to the initial quadrant distribution of each aircraft, the optimization performance index function of the particle swarm optimization iterative process is designed for the two capture formation forms of "chasing" and "encirclement" as shown in formula (9): Among them, w i ,i=1,2,...,7 is the weight gain of each performance index. If the weight is negative, the optimization goal is to maximize the target. Otherwise, the optimization goal is to minimize the target. surround It is the flag position of "encirclement formation"; When the initial position of the aircraft in the cluster is in 3 or more quadrants, it is set to "true". The meaning and optimization goals of each performance indicator are: (1)area cover The coverage area of ​​the cluster capture area to the target escape area should be maximized, and its calculation is shown in formula (10): Among them, area(A) is the function for calculating the area of ​​region object A. is the reachable area of ​​the i-th aircraft, zone target The escape zone of the target; (2) is the variance of the formation side length, which should be minimized. Its calculation is shown in formula (11): Among them, var(B) is the function for calculating the variance of the elements of vector B, and length(B,C) is the function for calculating the straight-line distance from point B to point C in the brackets; (3) is the sum of the motion strokes of each aircraft, which should be minimized. Its calculation is shown in formula (12): in, and are the initial coordinates of the i-th aircraft; (4) is the variance of the motion range of each aircraft, which should be minimized. Its calculation is shown in formula (13): (5) is the sum of the variances of the distances from the aircraft in the cluster that are symmetrically located relative to the target to the center of the target escape zone, which should be minimized. Its calculation is shown in formula (14): Where fix(D) is a function that calculates the integer part of a real number D. is the center coordinate of the target escape zone; (6) is the sum of the distances from each aircraft to the center of the target escape zone, which should be maximized. Its calculation is shown in formula (15): (7) The distance from the center of the cluster capture formation to the center of the target escape area should be minimized. Its calculation is shown in formula (16): in, is the center coordinate of the cluster capture formation; Step 2.4: Cross-track unwinding method design During the optimization process, it is necessary to detect the trajectory crossing phenomenon after each update of the particle swarm position and detangle the crossing trajectories. This process consists of two modules: (1) Intersection detection module: This module uses the vector cross product method to determine whether two line segments intersect. By calculating the cross product value of the end point of a line segment relative to another line segment, the relative position relationship between the line segments can be captured. (2) The intersection trajectory disentanglement module continuously adjusts the initial line segments generated by the given point set according to the trajectory intersection situation output by the intersection detection module until there is no trajectory intersection phenomenon. First, the initial connection between points is generated through simple rules, and each two adjacent points form a line segment; then the line segment set is detected, and when the intersection phenomenon is found, it is corrected by exchanging the endpoints of the line segment to ensure that the final line segment set is geometrically independent of each other and has no intersection points.

4. The method for collaboratively capturing a high-maneuverability target by a cluster of aircraft at a designated time according to claim 1, characterized in that: Step 3 Based on the time-varying high gain algorithm, the process of designing the time-space coordinated guidance law for a specified time is as follows: Step 3.1: System Modeling First, the aircraft guidance mathematical model is established, and the relative motion model of multi-aircraft cooperative capture is established in a two-dimensional plane. The relative motion equation between the aircraft and the target in the plane is shown in formula (17): Where R is the distance between the aircraft and the desired target. is the acceleration of the aircraft relative to the desired target, is the line-of-sight angular velocity between the aircraft and the target, is the line-of-sight angular acceleration rate between the aircraft and the target, d R and u R are the components of target acceleration and aircraft acceleration in the line of sight direction, d q and u q are the components of target acceleration and vehicle acceleration in the normal direction of the line of sight, respectively; There is a constraint relationship at the end of guidance as shown in formula (18): in, represents the missile heading angle, represents the target heading angle, So the expected sight angle q d It can be expressed as formula (19): Where ξ=V t / V m , V t represents the target speed, V m represents the missile speed, is the intermediate variable, φ d To round up the angle for expectation; Select the state variable as x1=qq d , q represents the line of sight angle between the aircraft and the target, q d It represents the sight angle between the aircraft and the target in the normal direction. Indicates the line-of-sight angular rate between the aircraft and the target in the normal direction; Then the mathematical model in the normal direction of the line of sight is expressed as a second-order system as shown in formula (20): Among them, u q is the control input in the normal direction of the line of sight, d q is the system perturbation in the normal direction of the line of sight, and u q Make x1 and x2 converge to zero at the specified time; Define R d =V d (Tt) is the virtual relative distance, where T is the expected capture time, and the state variable is z1 = RR d , Then the mathematical model in the line of sight direction is expressed as a second-order system as shown in formula (21): Among them, u R is the control input in the line of sight direction, d R is the system disturbance in the line of sight direction; Step 3.2: Line of sight normal guidance law design Let T>0 be the expected roundup time, (1) Solve P(γ) Consider the parametric Lyapunov equation, as shown in equation (22): A T P+PA-Pbb T P=-γP (22) in, The only positive solution is P(γ)=γ(t)L n P n L n , where γ(t) is the time-varying high gain parameter, (2) Design time-varying function φ1(x) φ1(x) is designed as shown in formula (23): Among them, λ>0 is an adjustable parameter, (3) Design the line of sight normal acceleration command The line of sight normal acceleration command is designed as follows: Where b = [0, 1] T , x=[x1,x2] T , g1(x)=1 / R, t∈[0,T), σ c is a constant, 0<s<1 is an adjustable parameter. The above acceleration command can ensure that the state variables x1 and x2 converge to zero at any specified time, thereby achieving the desired capture angle φ of the aircraft at any specified time tracking. d ; Step 3.3: Line of sight guidance law design Let T>0 be the expected roundup time, (1) Solve P(γ) Solving the parametric Lyapunov equation A T P+PA-Pbb T P=-γP The only positive solution is P(γ)=γ(t)L n P n L n , where γ(t) is the time-varying high gain parameter, (2) Design time-varying function φ2(x) φ2(x) is designed as shown in formula (25): Among them, λ>0 is an adjustable parameter, (3) Design the acceleration command in the line of sight direction The line of sight acceleration command is designed as follows: Where b = [0, 1] T , z=[z1,z2] T , g2(z)=1 / R, t∈[0,T), σ c is a constant, 0<s<1 is an adjustable parameter, the above acceleration instruction can ensure that the state variables z1 and z2 converge to zero at any specified time, thereby achieving the desired capture coordinates of the aircraft in a limited time; Step 3.4: Acceleration calculation The normal acceleration of the aircraft is a m With tangential acceleration a t Can be solved as: The acceleration components of the aircraft along the x-axis and y-axis can be solved as: Among them, θ m is the heading angle of the aircraft.

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