Method for assigning time coordination hunting of aircraft cluster to high maneuvering target

Abstract

The application discloses a method for time-specified cooperative hunting of a high-maneuvering target by a cluster of aircrafts, and belongs to the technical field of aerospace.The application solves the problem of time-specified cooperative hunting of a high-maneuvering target by a cluster of fixed-wing aircrafts, considering the motion capability constraints such as the upper limit of the normal overload of the fixed-wing aircrafts.The method comprises the following steps: step one, based on a Dubins trajectory planning algorithm, a mathematical model for calculating the hunting domain of the cluster of fixed-wing aircrafts and the escape domain of the high-maneuvering target is established; step two, based on a PSO algorithm, an optimal hunting formation planning algorithm is designed; and step three, based on a time-varying high-gain algorithm, a time-specified space-time cooperative guidance law is designed.The application is applied to the cooperative hunting of a high-maneuvering target by a cluster of fixed-wing aircrafts, and is flexible while improving the execution efficiency of the hunting task.

Description

TECHNICAL FIELD

[0001] The present application relates to an aircraft hunting method, in particular to a specified time cooperative hunting method of an aircraft cluster for a high-maneuverability target, and belongs to the technical field of aerospace. BACKGROUND

[0002] In recent years, the international situation changes rapidly, and high-tech military capabilities are increasingly valued by governments around the world. High-maneuverability targets such as all-terrain vehicles and spherical wheel vehicles are constantly emerging, and the hunting problem for such targets has attracted close attention from scholars and researchers inside and outside the field. As a representative of hypersonic aircraft, fixed-wing aircraft are favored in the military field for their low consumption, high speed, and large payload. Although their maneuverability is inferior to that of quadcopters, in traditional low-speed hunting problems, fixed-wing aircraft have an absolute advantage in speed over the target, so there is no need to plan and design the hunting formation. However, with the widespread application of high-maneuverability targets, the speed advantage of hypersonic aircraft gradually diminishes, while their lack of maneuverability becomes more prominent. Therefore, there is an urgent need to design an efficient hunting formation planning and design algorithm and a multi-aircraft cooperative guidance law to improve the execution efficiency of hunting tasks for high-maneuverability targets.

[0003] When performing a hunting task, a hunting formation should be planned and designed first to ensure efficient coverage of the target escape domain by the hunting domain of the aircraft cluster while minimizing the cluster's movement distance, thereby improving the execution efficiency of the hunting task. However, traditional hunting formation planning and design algorithms only use simple geometric methods such as "square enclosure" and "circular enclosure" to plan and design hunting formations. Although these methods are simple to calculate, they have low coverage and uneven distribution, and their mathematical models do not fully consider the task requirements of minimizing the cluster's movement distance. Although hunting formation planning and design algorithms based on intelligent algorithms such as reinforcement learning take into account performance indicators such as coverage efficiency and movement distance, they have complex algorithm structures and slow calculation speeds.

[0004] In addition, for a specific hunting formation, a cooperative guidance law needs to be designed to enable each aircraft to achieve the desired hunting formation within a specified time. Due to the finite time characteristics of the guidance problem, traditional proportional guidance laws cannot achieve formation deployment within a finite time. To address this deficiency, scholars have proposed a finite-time cooperative guidance law to achieve formation deployment of multiple aircraft within a finite time. However, the formation deployment time of this method varies with the initial scene, and for some scenes, it cannot complete the formation deployment task. SUMMARY

[0005] The present application provides a kind of aircraft cluster specified time cooperative hunting method for high maneuverability target to solve the deficiencies of prior art, which designs specified time guidance law to make multiple aircraft complete formation deployment within any specified time, and the deployment time can be arbitrarily specified and is not dependent on initial scene, thus greatly improving the success rate of multiple aircraft cooperative formation deployment, and then completing the hunting of high maneuverability target at the specified time.

[0006] A kind of aircraft cluster specified time cooperative hunting method for high maneuverability target, comprising the following step content:

[0007] Step one: based on Dubins trajectory planning algorithm, the mathematical model for calculating fixed-wing aircraft cluster hunting domain and high maneuverability target escape domain is established;

[0008] Step two: based on PSO algorithm, optimal hunting formation planning design algorithm is designed;

[0009] Step three: based on time-varying high gain algorithm, specified time space cooperative guidance law is designed.

[0010] The above-mentioned aircraft cluster specified time cooperative hunting method for high maneuverability target can achieve the following task requirements: (1) efficient planning and design of optimal hunting formation;(2) make fixed-wing aircraft cluster complete the hunting of high maneuverability target under the specified time index;(3) maintain high cooperative position and angle accuracy.

[0011] Specifically achieved by the following content: a mathematical model for calculating high maneuverability target escape domain is established, and a mathematical model for calculating fixed-wing aircraft hunting domain is established;Design particle swarm position and velocity information update strategy, set particle value range and optimize performance index function based on actual task requirements, simultaneously design cross trajectory unwinding, constantly update feasible solution set through optimization, and finally obtain the optimal feasible solution;Finally, based on time-varying high gain algorithm, specified time space cooperative guidance law is designed, including line-of-sight normal guidance law design and line-of-sight direction guidance law design, so that each aircraft reaches the corresponding position indicated in the hunting formation at a high cooperative position accuracy at the preset time point, and maintains the corresponding orientation angle indicated in the hunting formation at a high cooperative angle accuracy.

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

[0013] The method proposed in the present application has certain degree of innovation breakthrough in theory innovation and engineering application compared with the traditional method in the field:

[0014] (1) In the aspect of the algorithm for planning and designing the encircling formation: compared with the algorithm for planning and designing the encircling formation based on the traditional geometric method such as the "square encircling" and "circular encircling", the application comprehensively considers the performance indexes such as the encircling formation coverage rate, coverage efficiency and multi-vehicle cooperative guidance task execution efficiency to design the performance index function of the PSO algorithm; compared with the algorithm for planning and designing the encircling formation based on the reinforcement learning and other machine learning methods, the application 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 index function according to the task requirements, thus solving the problems of low reasoning speed and difficulty in defining the reward function.

[0015] (2) In the aspect of the time-space cooperative guidance law, the application innovatively improves the limitations of different guidance methods: first, compared with the defect that the convergence time of the traditional proportional guidance law tends to infinity, the application uses the finite time control method to significantly improve the convergence speed of the system; second, aiming at the strong dependence of the finite time cooperative guidance law on the initial scene, the application effectively enhances the robustness of the time-space cooperative guidance by introducing the time-varying high gain feedback mechanism; finally, compared with the problem that the convergence time is complexly coupled with the system parameters in the fixed time guidance law, the method proposed by the application realizes the independent adjustment of the convergence time without changing other system parameters, thus greatly simplifying the design process of the time-space cooperative guidance law.

[0016] The method proposed in the application can calculate the optimal encircling formation considering the coverage task and the multi-vehicle cooperative guidance task under any reasonable set of initial conditions such as the initial position of the cluster, the attack capability of the vehicle and the movement capability of the vehicle and the target, and then make each vehicle reach the corresponding position indicated in the encircling formation at a higher cooperative position accuracy at the preset time point and keep the corresponding orientation angle indicated in the encircling formation at a higher cooperative angle accuracy through the specified time-space cooperative guidance law.

[0017] The execution time of the encircling task can be arbitrarily specified and the cooperative position and angle accuracy is high, so the method proposed in the application improves the execution efficiency of the encircling task while maintaining flexibility.

[0018] The application will be further described below in combination with the drawings and embodiments: BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 is a Dubins trajectory diagram;

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

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

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

[0023] Figure 5 is the schematic diagram of the working principle of the encirclement formation planning and design algorithm;

[0024] Figure 6 is the schematic diagram of the performance of the encirclement formation planning and design algorithm (pursuit formation);

[0025] Figure 7 is the schematic diagram of the performance of the encirclement formation planning and design algorithm (encirclement formation);

[0026] Figure 8 is the schematic diagram of the performance of the proportional guidance law (pursuit formation);

[0027] Figure 9 is the schematic diagram of the performance of the proportional guidance law (encirclement formation);

[0028] Figure 10 is the schematic diagram of the performance of the specified time cooperative space-time guidance law (pursuit formation);

[0029] Figure 11 is the schematic diagram of the performance of the specified time cooperative space-time guidance law (encirclement formation);

[0030] Figure 12 is the schematic diagram of the coverage effect of the cooperative guidance task execution result (pursuit formation);

[0031] Figure 13 is the schematic diagram of the coverage effect of the cooperative guidance task execution result (encirclement formation). DETAILED DESCRIPTION

[0032] Embodiment I: The embodiment provides a fixed-wing aircraft cluster specified time cooperative encirclement method for a high-maneuverability target, which comprises the following steps:

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

[0034] Step 2: Based on the classical particle swarm optimization (PSO) algorithm, an optimal encirclement formation planning and design algorithm is designed;

[0035] Step 3: Based on the time-varying high-gain algorithm, a specified time space-time cooperative guidance law is designed.

[0036] Embodiment II: The embodiment is different from embodiment I in that step 1 is specifically:

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

[0038] Dubins trajectory planning algorithm is an effective method for solving the shortest path of a particle between two points considering the motion ability constraints such as limited turning radius, Dubins trajectory can be roughly divided into three categories: (1) straight path; (2) path formed by always driving with the minimum turning radius; (3) motion path formed by the combination of the above two paths, Dubins trajectory is shown in Figure 1 In the task background of the present application, 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 high-maneuvering target

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

[0041] The equal length of the Dubins trajectory ensures the consistency of the description of the reachable range under the same time limit, and the involute composed of the endpoints of the equal length Dubins trajectory fully considers the influence of the minimum turning radius and other constraints on the motion trajectory, therefore, the reachable set obtained by calculating the involute of the left and right turning radius circles can more truly represent the complex maneuvering situation of the object in the actual motion scene, the relationship between the reachable set and the minimum turning radius is shown in Figure 2 .

[0042] Then the reachable set front RSF i of the motion particle i at time t, with the current position p i (t) = (x i , y i ) as the base point, within the time range of Δt is calculated as shown in equation (1).

[0043]

[0044] Where, V i max is the maximum speed of the motion particle i, Ny i is the normal overload capability coefficient, Let be the maximum normal acceleration of the moving particle i, and g be the acceleration due to gravity. The reachable front is calculated from the RSF obtained by passing through the involute curves for right and left turns respectively. i,R RSF i,L It consists of two parts, the right half of the reachable domain front, RSF. i,R The calculation method is shown in equation (2), and the left half is RSF. i,L It is symmetrical to it;

[0045]

[0046] Where, θ i Let r be the velocity and heading angle of the moving particle i. i o =(V i max ) 2 / Ny i Minimum turning radius, These are the coordinates of the center of the right-turn circle with the minimum turning radius.

[0047] Since the minimum velocity of a highly maneuverable target can be approximated as zero, if it is treated as a moving point mass, the following calculation can be obtained using this method: Figure 3 The reachable region shown is the escape region of the target (where, Figure 3 (a) represents the outer contour of the reachable domain. Figure 3 (b) for Figure 3 (a) fills in the area to indicate reachable regions.

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

[0049] Due to the inherent motion characteristics of fixed-wing aircraft, they cannot maintain a continuous hovering state in the air, meaning their minimum speed is not zero. This constraint directly leads to a more complex structure in their reachability set. The reachability set has a leading edge and a trailing edge, and the sides are no longer composed of minimum turning arcs. Specifically, the set of Dubins trajectory endpoints constructed based on the fixed-wing aircraft's maximum flight speed defines the leading edge of the reachability set. This boundary acts like the outermost expansion limit of a capture net, determining the maximum coverage area of ​​the target under ideal high-speed conditions. The set of Dubins trajectory endpoints constructed based on the minimum flight speed determines the trailing edge of the reachability set, defining the boundary of the area that the aircraft can still cover at its slowest speed; it is the inward contraction limit of the capture net. As the aircraft's speed gradually increases from minimum to maximum, the edges of the reachability set do not change linearly during this dynamic process, but gradually evolve into two unique curves. These two curves form the two side boundaries of the capture domain.

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

[0051]

[0052] Among them, V i max V is the maximum velocity of the moving particle i. i min Let Ny be the minimum velocity of moving particle i. i For normal overload, RSF imax Represents the reachable frontier, RSF imin Represents the trailing edge of the reachable region, boundary(RSF) iV ) represents the two endpoints of the reachable front of the region with velocity V.

[0053] The reachable domain of the aircraft calculated using this method is as follows: Figure 4 As shown (the upper left figure represents the reachable domain of the aircraft at its maximum and minimum speeds, with the red line indicating the boundary of the actual reachable domain; the upper right figure represents the reachable domain of the aircraft at its speeds between the maximum and minimum speeds, with the upper and lower edges of the actual reachable domain boundary being the upper edges of the outer contours of the reachable domains corresponding to the maximum and minimum speeds, respectively; the left and right edges of the actual reachable domain boundary are formed by sequentially connecting the two endpoints of the upper edges of the outer contours of all reachable domains generated by the particle during the process of fine interpolation from the minimum speed to the maximum speed; the figure below is the actual reachable domain itself), the capture domain of the aircraft swarm is the union of the reachable domains of all the aircraft within it.

[0054] Specific Implementation Method Three: This implementation method further specifies that step two is specifically as follows:

[0055] The working principle of the encirclement formation planning and design algorithm proposed in this invention is as follows: Figure 5 As shown, the core ideas of each key design stage are as follows:

[0056] Step 2.1: Design a strategy for updating particle swarm position and velocity information

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

[0058]

[0059] Where, N p For the number of particles, Coord ac Let Θ be the set of coordinates of the aircraft cluster. ac For the set of orientation angles of the aircraft cluster, Here are the coordinates of the i-th aircraft. Let N be the heading angle of the i-th aircraft. ac This represents the total number of aircraft.

[0060] particle p k speed v k(t+1) and position x k The updating strategy of (t+1) information in the tth iteration process is shown in equation (5) :

[0061]

[0062] Where ω(t) is the inertia factor of the particle swarm in the tth iteration process, c1 and c2 are respectively the individual and group experience learning rate, pbest k (t) is the optimal position of the particle p k in the first t iteration rounds, gbest(t) is the group optimal position of the particle swarm in the first t iteration rounds, iter max is the maximum iteration number.

[0063] In order to improve the convergence speed of the algorithm, the linear weight decreasing strategy is used to dynamically update the inertia factor ω, so that the particle swarm maintains a larger inertia factor in the early stage of the iteration process, so as to expand the group search range and avoid falling into the local optimal position; a smaller inertia factor is maintained in the late stage of the iteration process, so as to search the global optimal position in detail, and the calculation method of the inertia factor ω(t) in the tth iteration process is shown in equation (6).

[0064]

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

[0066] In the optimization process, only the coordinate information Coord ac of the aircraft cluster is iteratively updated with the particle position x ac In order to improve the execution efficiency of the subsequent attack task, the orientation angle Θ -1 of each aircraft is always in the direction pointing to the center of the target escape domain, and the updating strategy of the orientation angle Θ of the jth aircraft is shown in equation (7).

[0067]

[0068] Where tan target (E) is a function for calculating the angle between the vector E and the coordinate axis x, coord target is the reference coordinate of the target, which is set as the origin in this project to simplify the calculation, and accordingly, while is the relative coordinate of the jth aircraft relative to the reference coordinate coord target of the target, where and coord targetTrue are respectively the actual coordinates of the jth aircraft and the target.

[0069] Step 2.2: Particle value range setting

[0070] Through the analysis of the calculation method of the aircraft cluster trapping domain and the target escape domain mentioned in step one, it can be known that the schematic diagram of both is approximately axisymmetric, therefore, in order to further improve the convergence efficiency of the optimization process, the present application combines theoretical analysis with the kinematic characteristics of both, and designs the particle group value range as a circular ring area with the target current position as the center, the inner circle radius r min and the outer circle radius r max The calculation method is shown in formula (8).

[0071]

[0072] Wherein, distance hit is the radius of the aircraft strike range, indicating that when the target is in the range, there is a certain guidance law that can make the aircraft complete the strike task on the target, is the maximum speed of the aircraft, is the maximum speed of the target, and constants Δr min and Δr max are the inner circle and outer circle value margins added to consider the cooperative position accuracy of the guidance process;

[0073] In order to reduce the travel of the aircraft cluster and improve the execution efficiency of the trapping task, and also to speed up the convergence by limiting the particle update range, the present application limits the coordinate value range of each aircraft to the circular ring area of the quadrant where its initial position is located, if its initial position is on the coordinate axis, the coordinate value range is limited to the circular ring area of the two adjacent quadrants of the coordinate axis. If the updated coordinate of the particle after the current iteration exceeds the value range, the position is randomly initialized again, and the heading angle always points to the center of the target escape domain.

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

[0075] In order to meet the following practical requirements of the trapping task: (1) ensure the successful completion of the trapping task, 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 escape domain of the target; (3) indirectly improve the execution efficiency of the multi-aircraft cooperative guidance task, that is, minimize the motion travel of the cluster and the variance of the motion travel of each aircraft, the present application designs the optimization performance index (fitness) function of the particle swarm optimization iteration process according to the initial quadrant distribution of each aircraft, for the "pursuit" and "encirclement" two trapping array forms, as shown in formula (9), and the optimization goal is to minimize the fitness.

[0076]

[0077] Wherein, w ii = 1, 2, …, 7 are the weight gains of each performance index, the weight is negative, the optimization goal is to maximize it, otherwise the optimization goal is to minimize it, flag surround is the "surrounding formation" flag bit, which is set to "true" when the initial positions of the aircrafts in the cluster are in 3 or more quadrants. The meanings of each performance index and the optimization goal are:

[0078] (1) area cover is the coverage area of the cluster trapping domain to the target escape domain, which should be maximized to ensure the successful completion of the trapping task. Since improving the coverage rate is the most core optimization goal, its weight gain w1 is the largest, and its calculation method is shown in equation (10).

[0079]

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

[0081] (2) is the variance of the formation side length, which should be minimized to make the trapping formation more symmetrical, and its calculation method is shown in equation (11).

[0082]

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

[0084] (3) is the sum of the motion distances of each aircraft, which should be minimized to reduce the distance of the aircraft (the straight-line distance from the initial position to the corresponding position in the optimized trapping formation), and its calculation method is shown in equation (12).

[0085]

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

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

[0088]

[0089] (5) The sum of the variance of the distance from each vehicle in the swarm to the center of the target escape region should be minimized to improve the symmetry of the "pursuit formation" around the target. The calculation method is shown in equation (14).

[0090]

[0091] wherein fix(A) is a function of calculating the integer part of real number A, is the coordinate of the center of the target escape region.

[0092] (6) The sum of the distance from each vehicle to the center of the target escape region should be maximized to indirectly reduce the motion distance of each vehicle while expanding the "encirclement formation" capture area, thereby improving the execution efficiency of the capture task. The calculation method is shown in equation (15).

[0093]

[0094] (7) The distance from the center of the swarm capture formation to the center of the target escape region should be minimized to improve the symmetry of the "encirclement formation" capture formation. The calculation method is shown in equation (16).

[0095]

[0096] wherein, is the coordinate of the center of the swarm capture formation.

[0097] Step 2.4: Cross-track unwinding method design

[0098] In the optimization process, the random initialization characteristics of the PSO algorithm for particle swarm position and speed may cause the flight trajectories of different vehicles to cross each other, so it is necessary to detect the trajectory crossing phenomenon after updating the particle swarm position each time, and to perform unwinding processing on the crossed trajectories to avoid the phenomenon of "vehicle collision" in the subsequent cooperative guidance process. This process consists of the following two key modules:

[0099] (1) Cross case detection module. This module judges whether two line segments intersect by vector cross product method. Cross product reveals the relative direction between vectors in geometry, and its sign can effectively distinguish the lateral relationship between points and straight lines. By calculating the cross product value of the end points of a line segment relative to another line segment, the relative position relationship between line segments can be accurately captured. According to the basic principles of plane geometry, if the two end points of a line segment are on the opposite sides of another line segment, and vice versa, there must be an intersection point between the line segments. The advantage of this method is that it does not need to calculate the intersection point explicitly, but can efficiently obtain the result by symbolic judgment.

[0100] (2) Cross trajectory unwrapping module. This module continuously adjusts the initial line segments generated by the given point set according to the trajectory intersection situation output by the cross case detection module until there is no trajectory intersection. The specific working principle is as follows: first, generate the initial connection between points by simple rules, and form a line segment between each adjacent two points; then detect the line segment set, and correct it by exchanging the end points of the line segments when the intersection phenomenon is found, so as to ensure that the final line segment set is independent in geometry and has no intersection point.

[0101] Specific implementation method four: this implementation method is further limited as follows:

[0102] Step 3.1: system modeling

[0103] The present application comprehensively considers the following performance indicators: (1) spatiotemporal coordination accuracy; (2) aircraft overload constraint; (3) aircraft speed constraint; (4) surround formation coverage rate, and constructs a specified time spatiotemporal coordination guidance law design method based on time-varying high gain algorithm.

[0104] The design goal of the multi-aircraft surround guidance law is to make each aircraft track the desired surround angle and the desired surround coordinate in a limited time. First, the aircraft guidance mathematical model is established. Considering that the pitch and yaw of the aircraft can be decoupled and analyzed, the guidance law design in the yaw plane is similar to that in the pitch plane. Therefore, without loss of generality, the relative motion model of multi-aircraft cooperative surround in a two-dimensional plane is established. 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 surround target, is the acceleration of the aircraft relative to the desired surround target, is the line-of-sight angular rate of the aircraft and the target, is the line-of-sight angular acceleration rate of 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.q 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 line-of-sight normal guidance law is to track the desired pursuit angle φ d in a finite time. Due to the target's maneuver, there is a complicated functional relationship between the desired line-of-sight angle q d and the desired pursuit angle φ d . There is a constraint relationship at the end of the guidance as shown in equation (18):

[0108]

[0109] where, denotes the missile heading angle, denotes the target heading angle,

[0110] The desired line-of-sight angle q d can be expressed as equation (19):

[0111]

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

[0113] The state variables are chosen as q denotes the line-of-sight angle of the vehicle and the target, q d denotes the line-of-sight angle of the vehicle and the target in the normal direction, denotes the line-of-sight angle rate of the vehicle and the target in the normal direction; then the line-of-sight normal mathematical model 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 pursuit guidance problem is further converted into the specified time stabilization problem of the above second-order system, that is, to design a guidance law u q so that x1, x2 converges to zero in a specified time.

[0116] The design objective of the line-of-sight direction guidance law is to make the vehicle track the desired pursuit coordinates in a finite time. Define Rd = V d (T-t) is the virtual relative distance, where T is the desired time-to-capture. The state variable is chosen as z1= R-R d , The mathematical model in the line-of-sight direction can be represented 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, 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 time-to-capture, 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 , where γ(t) is a time-varying high gain parameter, γ(t) is designed in the following,

[0127] (2) Design the time-varying function φ1(x)

[0128] The design of φ1(x) is shown in equation (23):

[0129]

[0130] where λ > 0 is a tunable parameter,

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

[0132] The design of the line-of-sight normal acceleration command is shown in equation (24):

[0133]

[0134] where b = [0, 1] T , x = [x1, x2] T , g 1(x) = 1 / R, t ∈ [0, T), σ c is a constant, where 0 < s < 1 is a tunable parameter. The above acceleration command can guarantee that the state variables x1, x2 converge to zero at any specified time, thereby realizing that the aircraft tracks the desired pursuit angle φ at any specified time d .

[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 the line-of-sight normal method, which can be designed according to the following steps:

[0137] (1) Solve P(γ)

[0138] Solve the parametric Lyapunov equation

[0139] A T P + PA - Pbb T P = -γP

[0140] The unique positive definite solution P(γ) = γ(t)L n P n L n , where γ(t) is designed later,

[0141] (2) Design the time-varying function φ2(x)

[0142] The design of φ2(x) is shown in equation (25):

[0143]

[0144] where λ > 0 is a tunable parameter,

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

[0146] The design of the line-of-sight direction acceleration command is shown in equation (26):

[0147]

[0148] where b = [0, 1] T , z = [z1, z2] T , g 2(z) = 1 / R, t ∈ [0, T), σc where 0 < s < 1 is a tunable parameter. The above acceleration command can guarantee that the state variables z1, z2 converge to zero at any specified time, and thus the aircraft can achieve the desired pursuit coordination in finite time.

[0149] Step 3.4: Acceleration solution

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

[0151]

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

[0153]

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

[0155] Embodiment

[0156] Suppose that the aircraft swarm is composed of N ac = 3 fixed-wing aircrafts with identical flight speed and performance parameters: minimum flight speed maximum flight speed normal overload capability coefficient Ny ac = 0.32, and the gravitational acceleration g ≈ 9.81 m / s 2 ; the high-maneuverability target is a maneuverable trolley with the following motion capability parameters: maximum motion speed normal overload capability coefficient Ny target = 0.189. It is assumed that any aircraft in the swarm can use a certain guidance law to complete the attack task within a target distance distance hit = 0.4 km.

[0157] In the optimal pursuit formation planning and design algorithm: the number of particles N p = 50, the individual experience learning rate c1 = 1.5, the group experience learning rate c2 = 1.5, the maximum number of iterations iter max = 5, the maximum value of the inertia factor ω max = 0.9, the minimum value of the inertia factor ω min = 0.4, the inner circle value margin Δr min = 2 m / s, and the outer circle value margin Δr max= -2 m / s, w1 = 4.5, w2 = 1.5, w3 = 0.0001, w4 = 0.1, w5 = 1.5, w6 = 1000, w7 = 1; the parameters in the proportional guidance law are N = 3; the parameters in the specified time cooperative time-space guidance law 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 Select the initial heading angle of the target To verify the performance of the swarm in "pursuit formation" (flag flag surround = 0) to surround the target, the initial position of the swarm is selected as Select the initial heading angle of the swarm To verify the performance of the swarm in "encirclement formation" (flag flag surround = 1) to surround the target, the initial position of the swarm is selected as Select the initial heading angle of the swarm Both the aircraft and the target are treated as moving particles, and the target performs a sinusoidal maneuver as in formula a t = 7cos (0.8t), first, the optimal encirclement formation planning and design algorithm proposed in the application is used to calculate the optimal encirclement formation, and then the specified time cooperative time-space guidance law is used to perform the cooperative guidance task of multiple aircrafts, and finally the encirclement task of the high-maneuvering target is completed.

[0159] In addition, the encirclement formation is designed by directly making the center of each flight reachable domain coincide with the center of the target escape domain as a control group to verify the performance of the optimal encirclement formation planning and design algorithm proposed in the application; the proportional guidance law is used to perform the cooperative guidance task of multiple aircrafts as a control group to verify the performance of the specified time cooperative time-space guidance law proposed in the application. Two groups of simulation experiments are carried out for the two cases of "pursuit formation" and "encirclement formation", combined with the above comparison verification method, and the experimental results are as shown in Figures 6-13

[0160] Figure 6 , Figure 7 ​The performance of the optimal encirclement formation planning and design algorithm when the cluster encircles the target in the "pursuit formation" and "encirclement formation" is recorded respectively, wherein the "relative position" is represented as the position of the aircraft relative to the target when the target is placed at the origin (the true position in the remaining figures) to facilitate the design and operation of the optimization algorithm. As can be seen from the figure, when the cluster encircles the target in the "pursuit formation" or "encirclement formation", compared with directly making the center of the reachable region of each aircraft coincide with the center of the target escape region, the encirclement formation calculated by using the optimal encirclement formation planning and design algorithm can achieve more complete and efficient coverage of the target escape region, while also reducing the motion travel of the cluster and the variance of the motion travel of each aircraft, thereby indirectly improving the execution efficiency of the multi-aircraft cooperative guidance task. Figure 8 、 Figure 9 The performance of the proportional guidance law when the cluster encircles the target in the "pursuit formation" and "encirclement formation" is recorded respectively. As can be seen from the figure, when the cluster encircles the target in the "pursuit formation" or "encirclement formation", the encirclement formation is relatively loose and cannot achieve effective encirclement. Figure 10 、 Figure 11 The performance of the specified time cooperative space-time guidance law when the cluster encircles the target in the "pursuit formation" and "encirclement formation" is recorded respectively. As can be seen from the figure, when the cluster encircles the target in the "pursuit formation" or "encirclement formation", it can form a relatively effective encirclement formation. The three lines in the above Figures 8-11 represent the motion trajectories of the three aircrafts. Figure 12 、 Figure 13 The coverage effect when the corresponding position and orientation angle of the target are encircled by the cluster according to the use of the proportional guidance law and the specified time cooperative space-time guidance law to execute the cooperative guidance task when the cluster encircles the target in the "pursuit formation" and "encirclement formation" is recorded respectively. As can be seen from the figure, when the cluster encircles the target in the "pursuit formation" or "encirclement formation", compared with the proportional guidance law, the coverage effect of the final encirclement formation obtained by using the specified time cooperative space-time guidance law to execute the cooperative guidance task is closer to the ideal state, that is, the coverage effect of the encirclement formation calculated by using the optimal encirclement formation planning and design algorithm.

[0161] In summary, whether the cluster encircles the target in the "pursuit formation" or "encirclement formation", the encirclement formation calculated by using the optimal encirclement formation planning and design algorithm can achieve efficient coverage of the high-maneuvering target, and the specified time cooperative space-time 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 encirclement method proposed by the present application has certain theoretical significance and application value for the encirclement task of high-maneuvering targets.

[0162] The application has been disclosed above with the preferred embodiments, however, it is not intended to limit the application, any skilled in the art can make some changes or modifications to the equivalent embodiments with the equivalent changes within the scope of the application without departing from the technical solutions of the application, which still belong to the scope of the technical solutions of the application.

Claims

1. A method for assigning time-coordinated encirclement of a high-maneuvering target by a cluster of aircraft, characterized in that: Comprising the following steps: Step one: based on Dubins trajectory planning algorithm, the establishment of the mathematical model of the calculation of fixed-wing aircraft cluster hunting domain and high maneuverability target escape domain; The specific process is: The high maneuverability target and the fixed-wing aircraft are regarded as a particle, and the reachable set can be regarded as the set of positions that the particle can reach within a certain time; Step 1.1: establish the mathematical model for calculating the escape domain of high maneuverability target then the moving mass point i at time t, with the current position p i (t) = (x i ,y i ) as the base point, the reachable set front RSF i As shown in equation (1); where V i max is the maximum velocity of moving mass i, Ny i is the normal overload capability coefficient, is the maximum normal acceleration of moving mass i, g is the gravity acceleration, the reachable set frontiers are composed of two parts, the right half RSF i,R , RSF i,L , and the left half RSF i,R , as shown in equation (2), the left half RSF i,L is symmetric to the right half. where θ i is the velocity heading angle of the moving mass point i, r i o = (V i max ) 2 / Ny i is the minimum turning radius, is the center coordinate of the right turning circle. Since the minimum speed of the high-maneuvering target is zero, the reachable region boundary is obtained by calculating the arc length of the reachable region front and left and right minimum turning circle arcs, and the reachable region is indirectly solved. The reachable region obtained in this way is the escape region of the target; Step 1.2: establish the mathematical model for calculating the hunting domain of fixed-wing aircraft The set of Dubins trajectory endpoints made on the basis of the maximum flight speed of fixed-wing aircraft defines the front of its reachable set; The set of Dubins trajectory endpoints constructed on the basis of the minimum flight speed determines the rear of the reachable set, and the reachable set R of fixed-wing aircraft is shown in formula (3); where V i max is the maximum velocity of the moving mass i, V i min is the minimum velocity of the moving mass i, Ny i is the normal overload capability factor, RSF imax denotes the frontiers of the reachable set, RSF imin denotes the reariers of the reachable set, boundary(RSF iV ) denotes the two end points of the frontiers of the reachable set with velocity V, and the trapping region of the fixed-wing aircraft cluster is the union of all the reachable sets of the fixed-wing aircrafts. Step two: based on PSO algorithm, design optimal hunting formation planning algorithm; Step three: based on time-varying high gain algorithm, design space-time cooperative guidance law at specified time.

2. The method for assigning time-coordinated encirclement of a high-maneuverability target by a cluster of aircrafts according to claim 1, characterized in that: Step two based on PSO algorithm, the process of designing optimal hunting formation planning algorithm is: Step 2.1: design particle swarm position and speed information update strategy The position and speed information of particle swarm is shown in formula (3): where N p is the number of particles, Coord ac is the set of coordinates of the swarm of vehicles, Θ ac is the set of orientation angles of the swarm of vehicles, is the coordinate information of the i-th vehicle, is the orientation angle of the i-th vehicle, N ac is the total number of vehicles; Particle p k Velocity v k (t+1) and position x k (t+1) information is updated in the tth round of iteration process as shown in equation (5): Where ω(t) is the inertia factor of the particle swarm in the t-th iteration, c1 and c2 are the individual and group experience learning rates, respectively, and pbest k (t) represents particle p k The best position of an individual particle in the first t iterations, gbest(t), is the best position of the swarm as a whole in the first t iterations. max This represents the maximum number of iterations. The calculation of inertia factor ω(t) in the tth round of iteration process is shown in formula (6): ω max ω min are respectively preset maximum and minimum values of the inertia factor; The coordinates Coord of the cluster of vehicles are updated in the optimization process ac The orientation angle Θ of the cluster of vehicles is updated iteratively with the particle position x ac The orientation angle Θj of the jth vehicle is always the direction pointing to the center of the target escape region in the optimization process The update strategy of Θj is shown in equation (7): where tan -1 (E) is a function of the angle between the vector E and the coordinate axis x, coord target is the reference coordinate of the target, is the relative coordinate of the jth aircraft with respect to coord target , and coord targetTrue are the actual coordinates of the jth aircraft and the target, respectively; Step 2.2: set the value range of particle Based on the hunting area of the aircraft cluster and the escape area of the high-maneuvering target, the particle swarm value range is a circular ring area with the current position of the target as the center, the inner circle radius r min and the outer circle radius r max as shown in formula (8). where distance hit is the radius of the striking range of the aircraft, indicating that when the target is in this range, there is a certain guidance law that can make the aircraft complete the striking task of the target, is the maximum speed of the aircraft, is the maximum speed of the target, and Δr min is the constant Δr max is the inner and outer circle value margin added to consider the cooperative position accuracy of the guidance process; Step 2.3: design optimization performance index function According to the initial quadrant distribution of each aircraft, for the "pursuit" and "encirclement" two hunting formation patterns, the optimization performance index function of particle swarm optimization iteration process is shown in formula (9): wherein w i i = 1, 2,..., 7 is the weight gain of each performance index, the weight is negative, the optimization goal is to maximize the target, otherwise the optimization goal is to minimize the target, flag surround is the "surrounding formation" flag bit; When the initial position of the aircraft in the cluster is in 3 or more quadrants, it is set to "true", the meaning of each performance index and the optimization goal is: (1) area cover To maximize the coverage area of the cluster trapping domain to the target escape domain, its calculation is shown as formula (10): wherein area(A) is a function to calculate the area of the region object A, is the reachable set of the i-th aircraft, zone target is the escape set of the target; (2) The variance of the array pattern side length should be minimized, and its calculation is shown in equation (11): Where, var(B) is the function of calculating the element variance of vector B, length(B,C) is the function of calculating the straight line distance from point B to point C in the parentheses; (3) The sum of the motion travel of each vehicle should be minimized, and its calculation is shown in equation (12): wherein, with being the initial coordinates for the i-th aircraft; (4) The variance of each aircraft motion trajectory should be minimized, which is calculated as shown in equation (13): (5) The sum of the variances of the distances of the vehicles in the swarm from the center of the target escape region for symmetric positions relative to the target should be minimized, which is calculated as shown in equation (14): where fix(D) is a function that computes the integer part of the real number D, is the center coordinate of the target escape domain. (6) The sum of the distances of each vehicle to the center of the target escape region should be maximized, which is calculated as shown in equation (15): (7) To make the distance from the center of the cluster hunting formation to the center of the target escape domain minimum, the calculation is shown in equation (16): wherein, is the center coordinate of the cluster encirclement formation; Step 2.4: design cross trajectory unwinding method In the optimization process, it is necessary to detect the trajectory intersection phenomenon after updating the position of particle swarm each time, and to process the unwinding of the intersecting trajectory, which consists of two modules: (1) Intersection detection module, which judges whether two line segments intersect by vector cross product method, and captures the relative position relationship between line segments by calculating the cross product value of the end points of the line segment relative to another line segment; (2) Cross trajectory unwinding module, which constantly adjusts the initial line segment generated by the given point set according to the output of the intersection detection module, until there is no trajectory intersection phenomenon, first generate the initial connection between points by simple rules, and each adjacent two points form a line segment; Then detect the line segment set, and modify it by exchanging the end points of the line segment when the intersection phenomenon is found, so as to ensure that the final line segment set is independent in geometry and there is no intersection point.

3. The method for assigning time-coordinated encirclement of a high-maneuverability target by a cluster of aircrafts according to claim 1, characterized in that: Step three based on time-varying high gain algorithm, the process of designing space-time cooperative guidance law at specified time is: Step 3.1: system modeling First, establish the mathematical model of aircraft guidance, and establish the relative motion model of multi-aircraft cooperative hunting in two-dimensional plane, and the relative motion equation of aircraft and target in plane is shown in formula (17): where R is the distance of the aircraft from the desired target, is the acceleration of the aircraft relative to the desired target, is the angular rate of the line of sight of the aircraft to the target, is the angular acceleration of the line of sight of the aircraft to the target, d R and u R are the components of the target acceleration and the aircraft acceleration in the line of sight direction, d q and u q are the components of the target acceleration and the aircraft acceleration in the line of sight normal direction; The constraint relationship at the end of guidance is shown as equation (18): wherein, represents the missile heading angle, represents the target heading angle, Thus, the line-of-sight angle q d may be expressed as equation (19): where ξ = V t / V m , V t denotes the target velocity, V m denotes the missile velocity, is an intermediate variable, φ d is the desired angle of pursuit; The state variable is selected as x1 = q - q d , q represents the line-of-sight angle of the aircraft to the target, q d represents the line-of-sight angle in the normal direction of the aircraft to the target, represents the line-of-sight angular rate in the normal direction of the aircraft to the target; The mathematical model of the line-of-sight normal is a second-order system as shown in equation (20): where u q is the control input in the direction of the line of sight, d q is the system disturbance in the direction of the line of sight, and u q is designed such that x1, x2converge to zero at a specified time. Definition of R d = V d (T-t) is the virtual relative distance, where T is the desired time-to-capture, and the state variable is chosen as z1= R-R d , The mathematical model in the line-of-sight direction is then a second order system as shown in equation (21): where 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: Design of the line-of-sight normal guidance law Let T>0 be the desired time of capture, (1) Solve P(γ) Consider the parameter Lyapunov equation as shown in equation (22): A T P+PA-Pbb T P=-γP (22) Where, The unique positive definite solution P(y) = y(t)L is obtained n P n L n where y(t) is a time-varying high gain parameter, (2) Design the time-varying function φ1(x) φ1(x) is designed as shown in equation (23): where λ > 0 is a tunable parameter, (3) Design the line-of-sight normal acceleration command The line-of-sight normal acceleration command is designed as shown in equation (24): where b = [0, 1] T , x = [x1, x2] T , g 1(x) = 1 / R, σ c is a constant, 0 < s < 1 is a tunable parameter, the above acceleration command can guarantee that the state variables x1, x2 converge to zero at any specified time, and thus the aircraft can track the desired pursuit angle φ at any specified time d ; Step 3.3: Design of the line-of-sight direction guidance law Let T>0 be the desired time of capture, (1) Solve P(γ) Solve the parameter Lyapunov equation A T P+PA-Pbb T P=-γP The unique positive definite solution P(y) = y(t)L n P n L n where y(t) is a time-varying high gain parameter, (2) Design the time-varying function φ2(x) φ2(x) is designed as shown in equation (25): where λ > 0 is a tunable parameter, (3) Design the line-of-sight direction acceleration command The line-of-sight direction acceleration command is designed as shown in equation (26): where b = [0, 1] T , z = [z1, z2] T , g 2(z) = 1 / R, σ c is a constant, and 0 < s < 1 is a tunable parameter. The above acceleration command can guarantee that the state variables z1, z2 converge to zero at any specified time, thereby achieving finite-time reaching of the desired pursuit coordinates for the aircraft. Step 3.4: Acceleration calculation The normal acceleration a of the aircraft m The tangential acceleration a t Can be calculated respectively as: The acceleration components of the aircraft along the x-axis and y-axis can be calculated as: where θ m is the heading angle of the aircraft.

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