Multi-layer cooperative hunting method for unmanned aerial vehicle group in three-dimensional unknown complex environment

Abstract

The invention discloses an unmanned aerial vehicle group multi-layer cooperative hunting method in a three-dimensional unknown complex environment. The method comprises the following steps: S1, establishing an unmanned aerial vehicle motion model and a motion model of a target hunting by an unmanned aerial vehicle group in an obstacle environment; s2, establishing a multi-layer surrounding model, wherein the multi-layer surrounding model comprises a three-dimensional simplified virtual stress surrounding model, an obstacle avoidance method for disturbing a fluid dynamic system and an interlayer motion model; s3, the unmanned aerial vehicle performs cross-layer motion between adjacent layers through the inter-layer motion model, and performs surrounding motion towards a target through a three-dimensional simplified virtual stress surrounding model or an obstacle avoidance method of a disturbed fluid dynamic system; and S4, when all the unmanned aerial vehicle individuals meet the set position conditions, ending the hunting. According to the method, multi-layer hunting is performed on the dynamic target, the target is not easy to escape, the principle is simple, the calculation amount is small, and the method is suitable for hunting of the target by the unmanned aerial vehicle group in a barrier-free environment and hunting of the target by the unmanned aerial vehicle group in an unknown complex dynamic environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicles, and particularly relates to a multi-layer cooperative hunting method for a swarm of unmanned aerial vehicles in a three-dimensional unknown complex environment. Background Art

[0002] In the military and civilian fields, unmanned aerial vehicles have been widely used due to their small size, strong concealment, low cost and other characteristics. With the complication of the application scenarios of unmanned aerial vehicles, the task requirements for unmanned aerial vehicles are also getting higher and higher, and a single unmanned aerial vehicle can no longer complete complex tasks. Therefore, it is necessary for multiple unmanned aerial vehicles to cooperate with each other to meet the task requirements. In recent years, the cooperative technology of unmanned aerial vehicle swarms has always been a research hotspot. The cooperative hunting of unmanned aerial vehicle swarms is a typical problem in the research of the cooperative technology of unmanned aerial vehicle swarms, and it is mainly applied to task scenarios such as formation control, cooperative search and rescue, and transportation.

[0003] At present, most of the research on the cooperative hunting of unmanned aerial vehicle swarms is the single-layer hunting of the target by the unmanned aerial vehicle swarm. When the hunting circumference of the target is determined, with the increase in the number of unmanned aerial vehicles, performing single-layer hunting on the target will make the unmanned aerial vehicles prone to collision on the hunting circumference. With the continuous complication of the cooperative tasks and cooperative hunting environments of unmanned aerial vehicle swarms, the cooperative multi-layer hunting of dynamic targets by unmanned aerial vehicle swarms in an obstacle-free environment can gradually no longer meet the requirements. At this time, it is necessary to consider the problem of how the unmanned aerial vehicles avoid obstacles during the hunting process in a complex environment. Summary of the Invention

[0004] Aiming at the above problems existing in the prior art, the purpose of the present invention is to provide a multi-layer cooperative hunting method for a swarm of unmanned aerial vehicles in a three-dimensional unknown complex environment, which performs multi-layer hunting on a dynamic target. Compared with single-layer hunting, the target is less likely to escape. The model algorithm only needs to consider the position information of the unmanned aerial vehicle individual and its two nearest neighbors, and based on the distances between the unmanned aerial vehicle individual and its two nearest neighbors, the inter-layer movement of the unmanned aerial vehicle is carried out to perform self-organized hunting of the unmanned aerial vehicle. The principle is simple and the calculation amount is small. It is not only applicable to the hunting of the target by the unmanned aerial vehicle swarm in an obstacle-free environment, but also applicable to the hunting of the target by the unmanned aerial vehicle swarm in an unknown complex dynamic environment.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] A multi-layer cooperative hunting method for a swarm of unmanned aerial vehicles in a three-dimensional unknown complex environment, comprising the following steps:

[0007] Step S1: Establish a motion model of the unmanned aerial vehicle and a motion model of the unmanned aerial vehicle swarm hunting the target in an obstacle environment;

[0008] Step S2: Establish a multi-layer hunting model, and the established multi-layer hunting model includes a three-dimensional simplified virtual force hunting model, an obstacle avoidance method for a perturbed fluid dynamic system, and an inter-layer movement model;

[0009] Step S3: The drone performs cross-layer movement between adjacent layers through the inter-layer movement model, and performs the encirclement movement towards the target through the obstacle avoidance method of the three-dimensional simplified virtual force encirclement model or the perturbed fluid dynamic system; among them, the obstacle avoidance methods of the three-dimensional simplified virtual force encirclement model and the perturbed fluid dynamic system are both based on spherical expansion of non-convex obstacles in the environment.

[0010] Step S4: When all drone individuals meet the set position conditions, the encirclement ends.

[0011] As a further improvement of the above technical solution:

[0012] In step S3, when a drone meets the condition that both of its two neighbors are obstacles and the distances between the two neighbors and the drone are both less than the set value, the velocity vector of the drone is calculated through the obstacle avoidance method of the perturbed fluid dynamic system, and the drone moves one time step according to the velocity vector; when the drone does not meet the said condition, the velocity vector of the drone is calculated through the three-dimensional simplified virtual force encirclement model, and the drone moves one time step according to the velocity vector.

[0013] The encirclement movement of the drone towards the target is a step-by-step movement. The drone moving one time step according to the calculated velocity vector is one step, and the current encirclement step number is the total number of steps that the drone has moved from the start of the encirclement to the current moment.

[0014] If the value of the current encirclement step number is greater than the set parameter, the drone swarm performs an inter-layer movement and then performs the encirclement movement, otherwise the drone directly performs the encirclement movement.

[0015] Multiple drones are arranged on multiple concentric circumferences or elliptical circumferences with different radii. The layers where the circumferences or elliptical circumferences are located from the innermost layer to the outermost layer are 1 to n respectively. The process of the inter-layer movement model is as follows:

[0016] Let a drone be the target drone. Determine whether both of the two neighbors of the target drone are drones. If not, there is no need to perform inter-layer movement; if so, determine whether the distances between the two neighbors and the target drone and the distance between the two neighbors both meet the set values.

[0017] Determine whether the distances between the two neighbors and the target drone and the distance between the two neighbors both meet the set values. If so, after the target drone moves out one layer, determine whether the current layer where the target drone is located is greater than 1; if not, directly determine whether the layer where the target drone is located is greater than 1.

[0018] Determine whether the layer where the target UAV is located is greater than 1. If not, the inter-layer movement ends; if so, determine whether the number of UAVs in the inner layer of the layer where the target UAV is currently located is not less than 2. The inner layer of the layer where the target UAV is located refers to the UAV layer that is 1 less than the layer where the target UAV is located.

[0019] Determine whether the number of UAVs in the inner layer of the layer where the target UAV is currently located is not less than 2. If so, calculate the two UAVs in this inner layer that are closest to the target UAV and the distance between these two UAVs. Let these two UAVs be the two closest neighbors in the inner layer, and the distance between these two UAVs is the distance between the two closest neighbors in the inner layer; if the number of UAVs in the inner layer of the layer where the target UAV is currently located is less than 2, artificially set a parameter as the distance between the two closest neighbors in the inner layer.

[0020] Determine whether the distance between the two closest neighbors in the inner layer is greater than the set value. If so, the target UAV moves in one layer inward; if not, the inter-layer movement ends.

[0021] The obstacle avoidance method for the disturbed fluid dynamic system is as follows: First, according to the position and velocity information of the UAV individuals and the position information of the pursuit target, construct the flow velocity of the UAV individuals in the obstacle-free environment as the initial flow velocity; then, according to the disturbance of the initial flow velocity by the static obstacles in the environment, construct a disturbance matrix, and obtain the velocity of the UAV individuals in the obstacle environment by correcting the initial flow velocity through the disturbance matrix. When there are dynamic obstacles in the environment, construct the flow velocity of the relative disturbance flow field relative to the initial flow field by introducing the motion information of the dynamic obstacles.

[0022] In step S4, the set positions satisfied by all UAV individuals include: the distance between the pursuit target and the UAV individuals satisfies the set value, and the distance between the two closest neighbors of the UAVs and the UAV individuals satisfies the set value.

[0023] In step S2, when establishing the three-dimensional simplified virtual force pursuit model, construct a relative coordinate system XOYZ. The UAV U i has coordinates (x i , y i , z i ) in the global coordinate system xoyz. Construct a relative coordinate system XOYZ with U i as the origin, the line connecting U i and t 1 ′ as the Y axis, and the axis parallel to the z axis of the global coordinate system as the Z axis, where t 1 ′ is the projection of the pursuit target t 1 on the plane passing through U i and parallel to the xoy plane.

[0024] The beneficial effects of the present invention are:

[0025] (1) Conduct multi-layer encirclement and capture of dynamic targets. Compared with single-layer encirclement and capture, it is more difficult for the target to escape.

[0026] (2) The model algorithm only needs to consider the position information of the UAV itself and its two nearest neighbors. Based on the distances between the UAV and its two nearest neighbors, the inter-layer movement of the UAV is carried out for self-organized encirclement and capture of the UAV. The principle is simple and the computational amount is small. It is applicable not only to the encirclement and capture of targets by UAV swarms in obstacle-free environments, but also to the encirclement and capture of targets by UAV swarms in unknown complex dynamic environments.

[0027] (3) For non-convex obstacles in three-dimensional complex environments, consider the spherical expansion of the UAV's own size and combine it with the perturbed fluid dynamic system for obstacle avoidance. It can not only effectively avoid convex and non-convex static and dynamic obstacles, but also generate a relatively smooth route.

[0028] (4) For the encirclement and capture of dynamic targets by UAVs, a three-dimensional simplified virtual force-based hunting model (3D-SVFH) is proposed. This model only considers the position information of the two nearest neighbors and the target, and decomposes the forces exerted on the UAV by the two nearest neighbors and the target in different directions, effectively avoiding the problem of UAVs falling into local minima.

[0029] (5) For the multi-layer encirclement and capture of dynamic targets by UAV swarms, an adaptive inter-layer movement strategy for UAVs is proposed. In this strategy, each UAV only considers the position information of its two nearest neighbors and adaptively performs inter-layer movement according to the distances between itself and the two nearest neighbor UAVs. Brief Description of the Drawings

[0030] Figure 1 It is a schematic diagram of the three-dimensional simplified virtual force-based hunting model of the present invention.

[0031] Figure 2 It is the UAV path planning based on the interference perturbed fluid dynamic system of the present invention.

[0032] Figure 3 It is the flow chart of the collaborative multi-layer encirclement and capture of UAV swarms of the present invention.

[0033] Figure 4 It is the flow chart of the inter-layer movement of UAVs of the present invention.

[0034] Figures 5(a) to 5(f) It is a schematic diagram of the collaborative multi-layer encirclement and capture process of UAV swarms in a three-dimensional unknown complex environment of the present invention.

[0035] Figures 6(a) to 6(d) It is a performance comparison chart of UAV swarms in three different modes. Detailed Embodiment

[0036] The following is a detailed description of the specific embodiments of the present invention in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only for the purpose of illustrating and explaining the present invention, and are not intended to limit the present invention.

[0037] For the sake of convenience of description, spatial relative terms such as "above", "over", "on the upper surface", "upper" etc. can be used here to describe the spatial positional relationship between a device or feature shown in the figure and other devices or features. It should be understood that the spatial relative terms are intended to encompass different orientations in use or operation in addition to the orientation described in the figure for the device. For example, if the device in the figure is inverted, the device described as "above other devices or structures" or "over other devices or structures" will then be positioned as "below other devices or structures" or "under other devices or structures". Thus, the exemplary term "above" can include both the orientations of "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and corresponding interpretations are made for the spatial relative descriptions used here.

[0038] A multi - layer collaborative encirclement method for a UAV swarm in a three - dimensional unknown complex environment, comprising the following steps:

[0039] Step S1: Establish a UAV motion model and a motion model of the UAV swarm encircling a target in an obstacle environment.

[0040] Step S2: Establish a multi - layer encirclement model, and the established multi - layer encirclement model includes a three - dimensional simplified virtual force - based encirclement model, an obstacle avoidance method for a disturbed fluid dynamic system, and an inter - layer motion model.

[0041] Among them, both the three - dimensional simplified virtual force - based encirclement model and the obstacle avoidance method for the disturbed fluid dynamic system are based on spherical expansion of non - convex obstacles in the environment. The so - called spherical expansion of non - convex obstacles in the environment means expanding the non - convex obstacles into spheres or converting the non - convex obstacles into a virtual spherical body for calculation.

[0042] Step S3: The UAVs perform cross - layer motion between adjacent layers through the inter - layer motion model, and perform encirclement motion towards the target through the three - dimensional simplified virtual force - based encirclement model or the obstacle avoidance method of the disturbed fluid dynamic system. Specifically as follows:

[0043] When a UAV meets the condition that both of its two nearest neighbors are obstacles and the distances between the two nearest neighbors and the UAV are both less than a set value, calculate the velocity vector of the UAV through the obstacle avoidance method of the disturbed fluid dynamic system, and move one time step according to the velocity vector; when a UAV does not meet the above conditions, calculate the velocity vector of the UAV through the three - dimensional simplified virtual force - based encirclement model, and move one time step according to the velocity vector.

[0044] Among them, multiple drones form a drone swarm, and the multiple drones are arranged in multiple layers. Specifically, the multiple drones are arranged on multiple concentric circumferences or elliptical circumferences with different radii. The number of the circumferences or elliptical circumferences is the number of layers. The layer relatively closer to the center is the inner layer, and the layer farther from the center is the outer layer. For example, for a certain layer (set as the target layer), the layers on one side of it are closer to the center than the target layer, which are the inner layers; the layers on the other side of it are farther from the center than the target layer, which are the outer layers.

[0045] The encirclement movement of the drones towards the target is a step-by-step movement. Each drone moves a time step according to the calculated velocity vector, which is one step. The current number of encirclement steps is the total number of steps that the drone has moved from the start of the encirclement to the current moment.

[0046] Step S4: When all drone individuals meet the set position conditions, the encirclement ends.

[0047] In step S1, the specific process of establishing the drone motion model is as follows:

[0048] The motion model of the drone at time t is:

[0049]

[0050] Among them: (x i , y i , z i ) is the position information of drone U i , v i is the linear velocity of drone U i , ω i is the angular velocity of the yaw angle of the drone. t is time, is the angle between the line OU i connecting the origin O and drone U i and the xoy plane, and θ is the angle between the projection of the line OU i in the xoy plane and the x-axis.

[0051] The limitations of the linear velocity and angular velocity of the drone are as follows:

[0052]

[0053] Among them: are the maximum linear velocity and maximum linear acceleration of the drone respectively, are the maximum angular velocity and maximum angular acceleration of the yaw angle of the drone respectively.

[0054] Considering that the drone is affected by the target and the forces of the two nearest neighbors (drones, static and dynamic obstacles) during the encirclement process. During the encirclement process, the force application function of the target on the drone individual is as follows:

[0055]

[0056] Where: d xy , d z are respectively the horizontal distance and the vertical distance between the UAV and the target t 1 , α 1 , β 1 are pursuit parameters greater than 0 and real numbers, r c is the encirclement radius of the target, r n is the layer where the UAV is located, r g is the distance between layers. sgn(χ) is the sign function, which is 1 when the target is above the UAV and -1 otherwise. n s is the current encirclement step, l s is a set parameter.

[0057] During the encirclement process, the force application function of the neighbor on the UAV individual is as follows:

[0058]

[0059] Where: b i , c 1 , a i are UAV obstacle avoidance distance parameters, i = 1, 2, 3 are respectively the parameters for avoiding UAVs, static obstacles, and dynamic obstacles, and d is the distance between the UAV and its neighbor.

[0060] It should be noted that the above "force" does not actually exist, but is a technical solution and means defined to prevent collisions between UAVs and UAVs, obstacles, targets, etc., and its function is equivalent to a repulsive force.

[0061] In step S1, the process of establishing the motion model of the UAV swarm to encircle the target in an obstacle environment is as follows:

[0062] In the finite three-dimensional space R 3 , the UAV swarm encircles the target environment K ∈ {U, T, S, V}, and the coordinates of K in the global coordinate system xoyz are (x k , y k , z k ). To better describe the magnitudes of the capabilities between the target and UAVs and obstacles in the environment, the concept of "potential" is introduced. Let the set of potentials in the environment be P ∈ {P U , P T , P S , P V}}.

[0063] 1) The UAV U ∈ {u i , i = 1, 2,..., n 1}, the potential of the individual drone is

[0064] 2) Target T∈{t j ,j=1}, the potential of the target is

[0065] 3) Static obstacle S∈{s i ,i=1,2,...,n 3}, the potential of the static obstacle is

[0066] 4) Dynamic obstacles The potential of the dynamic obstacle is

[0067] 5) Target j The set of UAVs in the potential domain is N UT ={i∈U:u i ∈G t}={i∈U:||u i -t j ||≤r t}, target t j The static obstacles and dynamic obstacles that need to be avoided are Dynamic obstacles The static obstacles and dynamic obstacles that need to be avoided are The total perceived potential is G t : Target potential domain, that is, in the target potential domain radius r t The area within. t s ,d t v ,d v s ,d v v They are the distances at which the target starts to avoid static obstacles, the distance at which the target starts to avoid dynamic obstacles, the distance at which dynamic obstacles start to avoid static obstacles, and the distance at which dynamic obstacles start to avoid dynamic obstacles. The potential relationships among individual drones, targets, static obstacles, and dynamic obstacles are as follows:

[0068]

[0069] In this paper, the total perceived potential is the sum of the apparent potentials, that is,

[0070] According to the above definition of potential, the total potential perceived by the target is the sum of the perceived explicit potentials of the target, as shown below:

[0071]

[0072]

[0073] Wherein: are the potentials of the UAV, static obstacle, and dynamic obstacle, respectively; are the angles between the lines connecting the UAV, static obstacle, dynamic obstacle, and the location of the target and the xoy plane, respectively; are the angles between the projections of the lines connecting the UAV, static obstacle, dynamic obstacle, and the location of the target on the xoy plane and the x-axis, respectively. is the angle between the projection of the line connecting the total perceived potential of the target and the origin on the xoy plane and the x-axis, is the angle between the line connecting the total perceived potential of the target and the origin and the xoy plane. The positive direction of the potential angle represents the direction with the weakest total perceived potential, called the escape direction; conversely, it represents the direction with the strongest total perceived potential, called the driving direction. c a (·) is the function for calculating the potential angle.

[0074] From the above description and the formulas for the total perceived potential and potential angle of the target, the motion equation of the target in the obstacle environment is as follows:

[0075]

[0076] Wherein, are the wandering speed and maximum speed of the target, respectively, is the maximum speed of the UAV, generally taking When the target does not perceive the potential the target wanders randomly, and the random wandering direction angle is When the total perceived potential of the target is greater than the individual potential of the target the target escapes, and the escape acceleration is the wandering speed of the target, and the escape direction angle is the direction with the weakest total perceived potential When the total perceived potential of the target is less than the individual potential of the target the target is driven, and at this time the target should decelerate, that is, the acceleration of the target is the difference between the wandering speed of the target and the current speed of the target, and the driving direction angle is the direction with the strongest total perceived potential

[0077] Thus, a motion model for a UAV swarm to surround and capture a target in an obstacle environment is established.

[0078] To achieve the encirclement and capture of dynamic targets by a drone swarm, it is first necessary to construct an encirclement and capture model. In step S2, based on a two-dimensional simplified virtual force model, a three-dimensional simplified virtual force encirclement and capture model in a three-dimensional unknown complex environment is established. In addition, for non-convex obstacles in the environment, spherical expansion considering the size of the drone itself is adopted, and obstacle avoidance is carried out in combination with an interference perturbation fluid dynamic system.

[0079] In step S2, the process of establishing a three-dimensional simplified virtual force encirclement and capture model is as follows:

[0080] Drone U i The coordinates in the global coordinate system xoyz are (x i , y i , z i ). Since the distributed control method is adopted in this paper, information can be exchanged between local areas and between local areas and the environment. Drone U i can obtain the position information of target t 1 and two nearest neighbor objects O pi , O qi . As Figure 1 shown, a relative coordinate system XOYZ is constructed with U i as the origin, the line connecting U i and t 1 ′ as the Y-axis, and the axis parallel to the z-axis of the global coordinate system as the Z-axis. Here, t 1 ′ is the projection of target t 1 on the plane passing through U i and parallel to the xoy plane. The position information of the two nearest neighbor objects O pi , O qi , target t 1 and t 1 ′ are (x pi , y pi , z pi ), (x qi , y qi , z qi ), In the relative coordinate system XOYZ, the position vectors p pi , p qi are respectively defined as:

[0081]

[0082] p pi =(x pi -x i )i+(y pi -y i )j+(z pi -z i )k,

[0083] p qi =(x qi -x i )i+(y qi -y i )j+(z qi -z i )k,

[0084]

[0085] Unmanned aerial vehicle U i is subjected to the forces from the target t 1 and two adjacent neighbors O pi 、O qi respectively as f pi and f qi . The direction of the position vector is the positive direction of the Y-axis. γ Y is the angle between the positive direction of the Y-axis and the x-axis. The angle between the positive direction of the X-axis and the x-axis is γ X =γ Y -π / 2. The positive direction of the z-axis is the positive direction of the Z-axis. γ Z is the angle between the positive direction of the Z-axis and the z-axis. When , the unmanned aerial vehicle is subjected to the gravitational force of the target. When , the unmanned aerial vehicle is subjected to the repulsive force of the target. The repulsive forces f pi and f qi projected onto the XOY plane are f Xpi and f Xqi respectively. The repulsive force angles are γ fXpi 、γ fXqi . γ fXpi is the angle between the X-axis and f Xpi ; γ fXqi is the angle between the X-axis and f Xqi . The repulsive force f i that U Xpqi receives on the X-axis is the sum of the projections f Xpi and f Xqi onto the X-axis, which are f Xpi φ(cos(γ fXpi )) and f Xqi φ(cos(γ fXqi )) respectively. When f Xpqi ≥0, its direction angle is γ fXpqi =γ X ; when f Xpqi <0, its direction angle is γ fXpqi =γ X ±π. U iThe resultant force f XYZi is composed of the component f Xpqi on the X-axis, the component on the Y-axis and the component on the Z-axis.

[0086] From the above description, when the target is stationary, the velocity of U is:

[0087]

[0088] where i, j, k are the unit vectors on the X, Y, and Z axes respectively; f Xpqi = f Xpi (||p pi ||)φ(cos(γ fXpi )) + f Xqi (||p qi ||)φ(cos(γ fXqi )); is the force application function of the target, calculated according to equations (4) and (3) respectively; f Xpi (||p pi ||) and f Xqi (||p qi ||) are the force application functions of two near neighbors, calculated according to equation (5). At the same time, this algorithm equivalently represents the velocities of the UAV on the X, Y, and Z axes as the component forces on these three axes, that is, v Xpqi = f Xpqi , v XYZi = v Xpqi + v Yi + v Zi .

[0089] In this paper, it is assumed that the UAV is a UAV with a fixed camera. The UAV needs to turn to the desired angle and rely on the information captured by the camera to perceive the surrounding environment information. However, during the movement of the UAV, it does not always move at the desired speed and desired angle. At this time, it is necessary to control the actual movement speed and angle of the UAV so that it moves in the desired direction at the desired speed. Let the desired speed of the UAV be v ie , and the desired angle be θ ie , and the movement period be T'. Among them, the desired speed v ie and the desired angle θ ie The calculation formulas are:

[0090]

[0091] where v it is the velocity vector of the UAV sensing the target. The UAV turns to the desired angle relying on the yaw angle. According to the kinematic model equation (1) of the UAV individual and the target motion equation (7), the motion of the UAV individual is designed:

[0092] When T′ < t it At this time, the UAV only performs angular motion within a time step and does not update its position. To reach the desired angle as quickly as possible, the angular acceleration is the limited angular acceleration, that is v i = 0.

[0093] When T′ ≥ t it At this time, the UAV first performs angular motion within a time step. After turning to the desired angle, it updates its position, that is:

[0094]

[0095]

[0096] where t it1 is the time required for the UAV to accelerate to the maximum angular velocity, t it2 is the time required for the UAV to rotate to the desired angle at the maximum angular velocity, θ itbef is the yaw angle of the UAV's previous motion, v ic is the speed for the UAV to compensate to reach the desired speed, v ia is the actual speed of the UAV.

[0097] In terms of UAV obstacle avoidance, an interference perturbation fluid dynamic system is used for static and dynamic obstacle avoidance. This paper assumes that there are a series of convex and non-convex static and dynamic obstacles in the enclosure environment. Considering the UAV's own size for non-convex obstacles, the safety domain is inflated into a spherical obstacle, and the inflated spherical obstacle is avoided using the interference perturbation hydrodynamic system method.

[0098] The obstacle avoidance method based on the interference perturbation fluid dynamic system first constructs the initial flow velocity, that is, the flow velocity v bef (u) of the UAV individual in a non-obstacle environment, according to the position and velocity information of the UAV individual and the position information of the target, as shown in Equation (12). Where: is the intersection point of the ray in the target motion direction and the enclosure circumference with the target as the center; d(u) is the distance between the UAV and .

[0099]

[0100] Secondly, this obstacle avoidance algorithm constructs a perturbation matrix (such as Equation (13)) according to the perturbation of the initial flow velocity by the static obstacles in the environment, and obtains the velocity of the UAV individual in the obstacle environment by correcting the initial flow velocity through the perturbation matrix, as shown in Equation (14). In addition, when there are dynamic obstacles in the environment, the flow velocity v of the relative perturbation flow field relative to the initial flow field is constructed by introducing the motion information of the dynamic obstaclesaft (u), since the dynamic obstacle in this paper is a spherical obstacle, rotating around the centroid will not change the motion space of the dynamic obstacle. Therefore, this paper only considers the translational motion of the centroid of the dynamic obstacle (as shown in Equation (15)).

[0101]

[0102] v aft (u) = P(u)v bef (u) (14)

[0103]

[0104] Assume that the UAV performs uniform motion within a period of time. The position of the UAV individual at the next moment can be updated according to the current position and speed of the UAV individual. The simulation results of path planning for static targets using IFDS (Interference Disturbance Fluid Dynamic System) are as Figure 2 shown (where the black lines represent the motion paths of the dynamic obstacles).

[0105] The flowchart of the multi-layer encirclement and capture of dynamic targets by the UAV swarm is as Figure 3 shown. In the figure, do is the emergency obstacle avoidance distance. After the UAV swarm moves for a period of time, considering the inter-layer motion of the UAV individuals, Figure 4 is the flowchart of the inter-layer motion of the UAVs. Figure 4 Before the UAVs perform inter-layer motion, it is necessary to re-determine the two nearest neighbors of the UAV individual (assuming this UAV individual is the target UAV): when the number of other UAVs in the current layer where the target UAV is located exceeds 2, use the UAVs in the same layer as the two nearest neighbors; when the number of other UAVs in the current layer where the target UAV is located is 1, use this UAV as the two nearest neighbors of the target UAV, that is, the relevant calculations of the two nearest neighbors of the target UAV all use the parameters of this UAV; when the number of UAVs in the current layer where the target UAV is located is 0, use the global two nearest neighbors as the two nearest neighbors of the current UAV. After the UAV determines the two nearest neighbor UAVs, it performs adaptive inter-layer motion based on the distance between the two nearest neighbor UAVs. Among them, d oc is the maximum distance between the two nearest neighbors in the same layer when allowing the UAV individual to move out one layer, d oc = 5; d ic is the minimum distance between the two nearest neighbors in the inner layer when allowing the UAV individual to move in one layer, d ic = 7.

[0106] The following will specifically explain the flowcharts of Figure 3 and Figure 4 :

[0107] The process of the UAV swarm's cooperative multi-layer encirclement and capture is as follows: as Figure 3As shown, first initialize the system parameters and the position and velocity information of the UAV swarm. Let \(n = 1\) at this time. If the value of \(n\) is greater than the set parameter \(l\) at this time, then each UAV performs an inter-layer movement and then a pursuit movement. Otherwise, the UAV directly performs a pursuit movement. During the pursuit movement, each UAV first determines two nearest neighbors. Taking one UAV as an example, let this UAV be the target UAV. If both of the target UAV's two nearest neighbors are obstacles and the distances between the target UAV and the two nearest neighbors are both less than the set parameter \(d_0\), then use the obstacle avoidance method of the perturbed fluid dynamic system to calculate the velocity vector of this UAV, and the UAV moves one time step according to this velocity vector; otherwise, calculate the velocity vector of this UAV through the three-dimensional simplified virtual force-based pursuit model and move one time step according to this velocity vector. When all UAV individuals meet the set position conditions, the pursuit ends; otherwise, judge whether the value of the current pursuit step \(n\) is greater than the set parameter \(l\), and repeat the above steps. Obviously, the current pursuit step \(n\) has increased by one step. s If at this time \(n\) s is greater than the set parameter \(l\) s , then each UAV performs an inter-layer movement and then a pursuit movement. Otherwise, the UAV directly performs a pursuit movement. During the pursuit movement, each UAV first determines two nearest neighbors. Taking one UAV as an example, let this UAV be the target UAV. If both of the target UAV's two nearest neighbors are obstacles and the distances between the target UAV and the two nearest neighbors are both less than the set parameter \(d_0\), then use the obstacle avoidance method of the perturbed fluid dynamic system to calculate the velocity vector of this UAV, and the UAV moves one time step according to this velocity vector; otherwise, calculate the velocity vector of this UAV through the three-dimensional simplified virtual force-based pursuit model and move one time step according to this velocity vector. When all UAV individuals meet the set position conditions, the pursuit ends; otherwise, judge whether the value of the current pursuit step \(n\) s is greater than the set parameter \(l\) s , and repeat the above steps. Obviously, the current pursuit step \(n\) s has increased by one step.

[0108] In this embodiment, when all UAV individuals meet the following set position conditions, the pursuit ends:

[0109]

[0110] \(\vert\vert p\) pi \(\vert\vert-\vert\vert p\) qi \(\vert\vert\vert\lt\varepsilon\) 3

[0111] where \(\varepsilon\) 1 , \(\varepsilon\) 2 , \(\varepsilon\) 3 are the parameter values set by humans.

[0112] The process of the UAV inter-layer movement is as follows:

[0113] As Figure 4 shown, taking one UAV as an example, let this UAV be the target UAV, and from the center outwards, the layers where each UAV is located are the 1st, 2nd, …, \(n\)th layers respectively;

[0114] First, judge whether both of the target UAV's two nearest neighbors are UAVs. If not, then there is no need to perform an inter-layer movement; if so, then judge whether the distances between the two nearest neighbors and the target UAV and the distance between the two nearest neighbors both meet the set values;

[0115] Judge whether the distances between two neighboring drones and the target drone, as well as the distance between the two neighboring drones, all meet the set values. If so, after the target drone moves out one layer, judge whether the current layer where the target drone is located is greater than 1; if not, directly judge whether the layer where the target drone is located is greater than 1.

[0116] Judge whether the layer where the target drone is located is greater than 1. If not, the inter-layer movement ends; if so, judge whether the number of drones in the inner layer of the layer where the target drone is currently located is not less than 2. The inner layer of the layer where the target drone is located refers to the drone layer that is 1 less than the layer where the target drone is located. For example, if the layer where the target drone is located is the 3rd layer, then the inner layer of the layer where the target drone is located is the 2nd layer.

[0117] Judge whether the number of drones in the inner layer of the layer where the target drone is currently located is not less than 2. If so, calculate the two drones that are closest to the target drone in this inner layer (let these two drones be the two neighboring drones in the inner layer) and the distance between these two drones (i.e., the distance between the two neighboring drones in the inner layer); if the number of drones in the inner layer of the layer where the target drone is currently located is less than 2, artificially set a parameter as the distance between the two neighboring drones in the inner layer.

[0118] Judge whether the distance between the two neighboring drones in the inner layer is greater than the set value. If so, the target drone moves in one layer; if not, the inter-layer movement ends.

[0119] It should be noted that each drone can obtain its own and other drones' position information through communication, and judge the position information of two neighboring drones through existing technologies such as image processing technology. If the position information of a neighboring drone is not the position information of any drone, then this neighboring drone is an obstacle.

[0120] The stability analysis of the system is carried out in three parts: The first part first shows that the adaptive inter-layer movement algorithm of the drone swarm is stable and reasonable; the second part conducts a stability analysis on the multi-layer encirclement system of the drone swarm after determining its specific encirclement circumference layer in an obstacle environment that does not meet the disturbed fluid dynamic system or in a non-obstacle environment; the third part explains the stability of the multi-layer encirclement system of the drone swarm in an obstacle environment that meets the use of the disturbed fluid dynamic system for obstacle avoidance.

[0121] When the drone swarm conducts multi-layer encirclement, it needs to adaptively perform inter-layer movement so as to achieve an appropriate number of drones on each encirclement circumference from the inside to the outside, and in an obstacle environment, the effective movement between layers can pass through a narrow environment.

[0122] There are four basic situations for realizing inter-layer movement: First, the "wide-in wide-out" strategy; Second, the "wide-in strict-out" strategy; Third, the "strict-in wide-out" strategy; Fourth, the "strict-in strict-out" strategy. Here, "in" and "out" respectively refer to moving inwards into a layer of the encirclement circumference and moving outwards from a layer of the encirclement circumference; Here, "wide" and "strict" respectively refer to relatively easy and difficult, which can be achieved by setting parameters.

[0123] The following analyzes the characteristics of these four strategies. First, the "wide-in wide-out" strategy can cause individual drones to move frequently between layers or the number of drones on any layer of the encirclement circumference to change frequently. It can be seen that this strategy will cause excessive energy consumption of the drones and is also not conducive to the formation of a multi-layer encirclement formation. Second, the "wide-in strict-out" strategy can cause the drone swarm to gather massively on the inner-layer encirclement circumference, reducing energy consumption. However, when the drone swarm avoids obstacles, due to the excessive density of drones on the same layer and the difficulty of drones moving outwards, it is not conducive to obstacle avoidance. Third, the "strict-in wide-out" strategy can cause the drone swarm to be scattered on the encirclement circumferences of more layers, which is conducive to passing through narrow channels to a certain extent, but it needs to move on a larger-radius encirclement circumference, wasting energy. Fourth, the "strict-in strict-out" strategy can effectively control the movement of drones between layers, which can not only ensure a certain number of drones on each layer but also maintain the relative stability of dynamic movement and reduce energy consumption. Therefore, the fourth strategy is adopted in this paper.

[0124] d oc is the maximum distance between the two nearest neighbors on the same layer when allowing an individual drone to move out one layer, and d ic is the minimum distance between the two nearest neighbors on the inner layer when allowing an individual drone to move in one layer. Here, taking d ic as the reference standard, 3 < d ic < 7 is the "easy" interval. If d oc > d ic at this time, it is the "wide-in wide-out" interval; if d oc < d ic at this time, it is the "wide-in strict-out" interval. d ic ≥ 7 is the "difficult" interval. If d oc > d ic at this time, it is the "strict-in wide-out" interval; if d oc < d ic at this time, it is the "strict-in strict-out" interval.

[0125] The following analyzes the stability of the model algorithm in an obstacle-free environment as follows:

[0126] In an obstacle-free environment, the system deviation is the distance deviation between the individual and the target as and half of the distance deviation δ between the individual and its two nearest neighbor UAVs Xpqi =(s fXpi ||p pi || + s fXqi ||p qi ||) / 2. Where s fXpi = sgn(cosγ fXpi ), s fXqi = sgn(cosγ fXqi ), s fXpi and s fXqi are functions to judge whether the two nearest neighbors are on the left or right of the individual, and sgn(·) is a sign judgment function.

[0127] When δ Zi = 0, δ Yi = 0, δ Xpqi = 0 (i = 1, 2,..., n 1 ), a formation for ideal encirclement is formed. Therefore, when δ Zi → 0, δ Yi → 0, δ Xpqi → 0 (i = 1, 2,..., n 1 ), the conditions are the stability conditions of the encirclement system. Discretizing the above system deviation gives:

[0128]

[0129] δ Xpqi (k) = (s fXpi (k)||p pi (k)|| + s fXqi (k)||p qi (k)||) / 2

[0130] Let the dynamic disturbance of the system Based on the three-dimensional simplified virtual force-based encirclement model, the deviation equation of the individual's self-organized movement is obtained:

[0131] δ Zi (k + 1) = δ Zi (k) - v Zi (k)T′ (16)

[0132] δ Yi (k + 1) = δ Yi (k) - v Yi (k)T′ (17)

[0133] δ Xpqi (k + 1) = δ Xpqi (k) - v Xpqi (k)T′ (18)

[0134] Where, vZi (k), v Yi (k), v Xpqi (k) are respectively v Zi , v Yi , v Xpqi in discretized form, so:

[0135]

[0136] Theorem 1 In an obstacle-free environment, if each UAV individual satisfies Equation (16) and -2 < β 1 T′ < 2, then the origin equilibrium state of the system is globally asymptotically stable.

[0137] Proof: Substitute Equation (19) into Equation (16) to get

[0138]

[0139] Construct the Lyapunov function as It is easy to know that Δ Z (k) ≠ 0, V Z (Δ Z (k)) > 0 and V Z (0) = 0, and further derivation can be carried out

[0140]

[0141] As can be easily seen from the above, when -2 < β 1 T′ < 2, V Z (Δ Z (k)) is negative definite. When ||Δ Z (k)|| → ∞, V Z (Δ Z (k)) → ∞. Therefore, according to the Lyapunov stability theorem for discrete systems, it can be obtained that the origin equilibrium state is globally asymptotically stable.

[0142] Theorem 2 In an obstacle-free environment, if each UAV individual satisfies n s > l s , Equation (17) and 0 < α 1 T′ < 2, then the origin equilibrium state of the system is globally asymptotically stable.

[0143] Proof: Substitute Equation (20) into Equation (17) to get

[0144]

[0145] When the UAV moves for a period of time, that is, n s > l s when,

[0146]

[0147] Construct the Lyapunov function as It is easy to know that Δ Y (k)≠0, V Y (Δ Y (k))>0 and V Y (0)=0. Furthermore, it can be deduced that:

[0148]

[0149] As is easy to know from the above, when 0<α 1 T′<2, V Y (Δ Y (k)) is negative definite. When ||Δ Y (k)||→∞, V Y (Δ Y (k))→∞. Therefore, according to the Lyapunov stability theorem of discrete systems, it can be obtained that the origin equilibrium state is globally asymptotically stable.

[0150] According to Theorem 1 and Theorem 2, it is known that each UAV individual in the group needs to satisfy Theorem 1 and Theorem 2 to converge to the encirclement circle. However, to achieve successful encirclement, the UAV individuals also need to be evenly distributed on the encirclement circle, that is, it is also necessary to prove the convergence of δ Xpqi .

[0151] Theorem 3 In an obstacle-free environment, if each UAV individual satisfies Equation (18) and then the origin equilibrium state of the system is globally asymptotically stable. Among them,

[0152] ζ=maxζ i (k), {i=1,2,...,n 1 ; k=1,2,...,l 1}

[0153]

[0154] Proof Substitute Equation (21) into Equation (18) to get

[0155] δ Xpqi (k + 1)=δ Xpqi (k)

[0156] -(f Xpi (||p pi (k)||)·φ(cos(γ fXpi (k)))

[0157] +fXqi (||p qi (k)||)·φ(cos(γ fXqi (k))))T′

[0158] Construct the Lyapunov function as It is easy to know that Δ Xpqi (k)≠0, V Xpqi (Δ Xpqi (k))>0 and V Xpqi (0)=0, and further it can be deduced that:

[0159]

[0160] where it is assumed that ζ reaches the maximum value at step l 1 , that is, ζ=maxζ i (k) (i=1,2,…,n 1 , k=1,2,...,l 1 ). If ζ does not reach the maximum value at step l 1 , then it will also reach the maximum value at step l 1 +n, that is, ζ=maxζ i (k) (i=1,2,…,n 1 , k=1,2,…,l 1 +n). When , V Xpqi (Δ Xpqi (k)) is negative definite. When ||Δ Xpqi (k)||→∞, V Xpqi (Δ Xpqi (k))→∞, so according to the Lyapunov stability theorem of discrete systems, it can be obtained that: the origin equilibrium state is globally asymptotically stable.

[0161] Therefore, for the UAV swarm to successfully surround the target in an obstacle-free environment, it is necessary to satisfy Theorem 1, Theorem 2, and Theorem 3 simultaneously. At the same time, the three theorems further limit the relationship between the motion period T′ and some parameters. The motion period T′ needs to satisfy:

[0162]

[0163] Since β 1 >0, the motion period T′ needs to satisfy:

[0164]

[0165] Given the relationship between the time period and the relevant parameters, when the system is unstable, the parameters β 1 , α 1 , c 1Stabilize it. The above stability conditions exist on the premise that the system perturbation is constantly 0, that is, the target remains stationary. In fact, as long as the time period meets the above conditions, when the target is moving, the UAV swarm can also converge to the encirclement circle and be evenly distributed on the encirclement circle. At this time, the lower limit of the motion period T′ needs to satisfy two conditions simultaneously: one is the time required for the maximum rotation angle of 180° of the UAV individual; the other is the time required for the compensation speed v of the UAV ic to reach the lowest speed (the target's wandering speed). According to Eqs. (9) - (11), we can obtain:

[0166]

[0167] According to Eq. (22), it is obtained that T′ > max(t mit , t mah ), where:

[0168]

[0169] Combining the above conditions that the motion period needs to satisfy, a sufficient condition for the UAV swarm to successfully encircle a moving target is obtained as

[0170]

[0171] Eq. (23) is a sufficient condition for the UAV swarm to successfully encircle a target escaping at a wandering speed. The above assumes that the target rotates 180° at each step during escape, and the UAV also rotates the maximum angle of 180° at each step. However, in actual situations, the UAV does not need to rotate 180° at each step. Therefore, Eq. (23) is also applicable to encirclements with a lower limit smaller than the given value.

[0172] The stability analysis of the algorithm in an unknown complex environment is as follows:

[0173] In an unknown complex environment, the system deviation is also divided into two parts: the distance deviation between the individual and the target and half of the distance deviation between the individual and two neighboring UAVs or obstacles δ′ Xpqi =(s fXpi ||p pi || + s fXqi ||p qi || + d Xoi ) / 2. In the three-dimensional simplified virtual force-based encirclement model, the force of the obstacle on the individual does not affect the gravitational or repulsive force of the target on the individual. Therefore, the analysis of the distance deviation between the individual and the target is the same as that in the obstacle-free environment, that is, Theorem 1 and Theorem 2. At this time, only the distance deviation δ′ Xpqi between the individual and two neighbors needs to be analyzed. s fXpi = sgn(cos(γ fXpi )) and s fXqi = sgn(cos(γfXqi ))),s fXpi and s fXqi is a function to determine whether two neighbors are on the left or right side of an individual, sgn(·) is a sign judgment function, d Xoi =-s fXpoi ||p Xpoi (k)||-s fXqoi ||p Xqoi ||, ||p Xpoi ||and ||p Xqoi || is the distance between the UAV U i at the force balance point U io to two neighbors O pi and O qi respectively.

[0174] Discretize the distance deviation δ′ Xpqi between an individual and two neighbors to get

[0175] δ′ Xpqi (k)=(s fXpi (k)||p pi (k)||+s fXqi (k)||p qi (k)||+d Xoi (k)) / 2

[0176] Where:

[0177] d Xoi (k)=-s fXpoi (k)||p Xpoi (k)||-s fXqoi (k)||p Xqoi (k)||

[0178] Let the dynamic disturbance of the system Based on the three-dimensional simplified virtual force-based pursuit and capture model, the individual self-organized motion deviation equation is obtained:

[0179] δ′ Xpqi (k + 1)=δ′ Xpqi (k)-v Xpqi (k)T′ (24)

[0180] Where, v Xpqi (k) is the discrete form of v Xpqi

[0181] Theorem 4 Under the condition that the obstacle condition of the disturbance fluid dynamic system is not satisfied, if each UAV individual satisfies Equation (24) and 0 < T′c 1 ζ′ < 2, then the origin equilibrium state of the system is globally asymptotically stable. Where, ​

[0182] ζ′ = maxζ i ′(k), i = 1, 2, …, n 1 , k = 1, 2,, l 1

[0183]

[0184] Proof: Substituting Equation (21) into Equation (24) gives

[0185] δ′ Xpqi (k + 1) = δ′ Xpqi (k)

[0186] -(f Xpi (||p pi (k)||)·φ(cos(γ fXpi (k)))

[0187] + f Xqi (||p qi (k)||)·φ(cos(γ fXqi (k))))T′

[0188] Construct the Lyapunov function as It is easy to know that Δ′ Xpqi (k) ≠ 0, V X ′ pqi (Δ′ Xpqi (k)) > 0 and V X ′ pqi (0) = 0. Then it can be deduced that

[0189]

[0190] Among them, assume that ζ′ reaches the maximum value at step l, that is, ζ′ = maxζ 1 ′(k), {i = 1, 2,..., n i ; k = 1, 2,..., l 1}, if ζ′ does not reach the maximum value at step l, then it will also reach the maximum value at step l 1} If ζ′ does not reach the maximum value at step l 1 step, then it will also reach the maximum value at step l 1 + n, that is, ζ′ = maxζ i ′(k) (i = 1, 2,…, n 1 , k = 1, 2…, l 1 + n). When 0 < T′c 1 ζ′ < 2, V X ′ pqi (Δ′ Xpqi (k)) is negative definite. When ||Δ′ Xpqi (k)|| → ∞, V X ′pqi (Δ′ Xpqi (k)) approaches infinity. Therefore, according to the Lyapunov stability theorem for discrete systems, it can be obtained that is globally asymptotically stable.

[0191] Therefore, when the target is stationary in an unknown complex environment, for the UAV swarm to converge to the encirclement circle and be evenly distributed on the circle, Theorems 1, 2, and 4 need to be satisfied. According to the three theorems, the motion period is limited, that is, 0 < T′ < min(2 / β 1 , 2 / α 1 , 2 / c 1 ζ′). When the target is moving, for the UAV swarm to successfully encircle the target, only Equation (22) and 0 < T′ < min(2 / β 1 , 2 / α 1 , 2 / c 1 ζ′) need to be satisfied. That is, the sufficient condition for a target escaping at a wandering speed to be successfully encircled by the UAV swarm is

[0192] max(t mit , t mah ) < T′ < min(2 / β 1 , 2 / α 1 , 2 / c 1 ζ′) (25)

[0193] where the specific calculations of t mit and t mah are shown in Equation (22).

[0194] Based on the above perturbation fluid dynamic system and three-dimensional simplified virtual force-based encirclement model, a simulation experiment on multi-layer cooperative encirclement of UAV swarms in a three-dimensional unknown complex environment is carried out. According to the above stability analysis, there are certain limitations on the parameters for the UAV swarm to successfully encircle a dynamic target. Therefore, the system parameters in the simulation are set as shown in Table 1 below.

[0195] Table 1 Encirclement system parameters

[0196]

[0197]

[0198] To verify the feasibility of the algorithm in this paper, a multi-layer cooperative pursuit experiment of UAV swarms is carried out in a three-dimensional unknown complex environment, considering complex static, dynamic convex and non-convex obstacles. Taking the number of UAVs as 35 as an example, the simulation experiment process of multi-layer cooperative pursuit of UAV swarms based on IFDS is demonstrated, as shown in Figure 5. The red represents the target, the blue represents the UAVs, the black represents the static obstacles, the purple represents the spherical obstacles after the expansion of non-convex obstacles, and the green represents the dynamic obstacles. Among them, Figure 5(a) shows the initial position (1 step), Figure 5(b) shows the pursuit (16 steps), Figure 5(c) shows the avoidance of static obstacles by IFDS (36 steps), Figure 5(d) shows the formation of the initial layer of UAVs for pursuit (102 steps), Figure 5(e) shows the avoidance of dynamic obstacles by IFDS (260 steps), and Figure 5(f) shows the success of multi-layer pursuit (446 steps).

[0199] Initially, no potential is sensed within the potential field range of the target, and the target moves randomly while the UAVs pursue the dynamic target. When the UAVs are far from the obstacles, a three-dimensional simplified virtual force-based pursuit model is adopted for collision avoidance between UAVs and between UAVs and obstacles, considering the action of the forces of the two nearest neighbor objects, so as to avoid collisions between UAVs during the pursuit process.

[0200] When an individual UAV is close to an obstacle, the UAV adopts the obstacle avoidance principle based on the perturbed fluid dynamic system to avoid the obstacle after the obstacle is expanded into a sphere, as shown in Figure 5(c). U 12 、U 14 Adopt the perturbed fluid dynamic system to avoid the spherical obstacle after the expansion of the non-convex cylinder and generate a smooth path. As the individual UAV moves, after the individual UAV gradually moves away from the obstacle, a three-dimensional simplified virtual force-based pursuit model is adopted for movement.

[0201] When there are many obstacles in the environment, the UAVs increase their layers at this time to pass through narrow channels, as shown in Figure 5(d). In this paper, d oc <d ic That is, when an individual UAV moves out one layer, the maximum distance between the two nearest neighbor UAVs in the same layer should be less than the minimum distance between the two nearest neighbor UAVs in the inner layer when the individual UAV moves in one layer, forming a strict entry and strict exit strategy. Similarly, this strategy is beneficial for the individual UAVs to first form a stable inner layer pursuit of the target and then conduct an outer layer pursuit. In Figure 5(d), the first layer of pursuit is carried out on the dynamic target first, and the remaining UAVs move in the remaining layers.

[0202] The drones perform multi-layer collaborative encirclement outside the target potential field range. When the two nearest neighbors of a drone individual are dynamic obstacles and the distance to the dynamic obstacles is far, the drone individual uses a three-dimensional simplified virtual force-based encirclement model to avoid the dynamic obstacles at this time; conversely, the drone individual uses a perturbed fluid dynamic system to avoid the dynamic obstacles. As shown in Fig. 5(e), when the drone U 20 is close to the dynamic obstacle, it uses a perturbed fluid dynamic system to avoid the obstacle. The blue circles in the figure are the drones U 20 During the obstacle avoidance process, the drone U 20 successfully avoids the dynamic obstacle. From step 102 to step 260, the target senses the presence of dynamic obstacles within the potential field range and also successfully avoids the dynamic obstacles. At the same time, as can be seen from From Figure 5(d) to Figure 5(e) , when the environment changes from relatively crowded to relatively loose, the drones will automatically reduce the number of encirclement circular layers at this time. During the subsequent movement process, the drones continuously perform multi-layer encirclement on the target outside the target potential field range and gradually distribute evenly in each layer. From the above analysis, it can be seen that the multi-layer encirclement algorithm proposed in this paper greatly improves the flexibility and scalability of the encirclement system.

[0203] Next, a comparative experiment analysis is carried out. To conduct the comparative experiment analysis, three encirclement model algorithms are set for comparison, and the three encirclement model algorithms are shown in Table 2.

[0204] Table 2 Multi-layer encirclement algorithm for drone swarms

[0205]

[0206] In Model 1, an expansion algorithm combining hemisphere expansion and spherical expansion and a three-dimensional simplified virtual force-based encirclement model are used to encircle dynamic targets; in Model 2, after spherical expansion of non-convex obstacles in the environment, a three-dimensional CC and a spherical crown of velocity obstacles in space (VOSC) are combined with a three-dimensional simplified virtual force-based encirclement model to encircle dynamic targets; in Model 3, after spherical expansion of non-convex obstacles in the environment, the 3D-MLH method proposed in this paper is used for encirclement. Using the above three modes, 20 independent simulation experiments are carried out on a certain number of drone swarms in the same encirclement environment. When the drone swarms multi-layer encircle dynamic targets, the time consumption (T U ), path consumption (S U ), total number of turning angles (N ro ), and total turning angle (R d ) of the system are respectively recorded. And the average value, maximum value, and minimum value are calculated. The obtained data are shown in Table 3, and the statistical chart is shown in Fig. 6. Among them, Fig. 6(a) represents the time consumption, Fig. 6(b) represents the path consumption, Fig. 6(c) represents the total number of turning angles, and Fig. 6(d) represents the total turning angle.

[0207] Table 3 Performance Comparison of UAV Swarms in 3 Different Modes

[0208]

[0209]

[0210]

[0211]

[0212] As can be seen from Figure 6, with the increase in the number of UAVs, the path loss, the number of turning angles, and the total turning angle all increase. When the scale of the number of UAVs is 5, Model 3 reduces the time consumption, path loss, total number of turning angles, and total turning angle by 4.54%, 2.83%, 0.02%, and 9.28% respectively compared to Model 2; when the number of UAVs is 25, Model 3 reduces the time consumption, path loss, total number of turning angles, and turning angle by 0.74%, 1.54%, 2.04%, and 1.46% respectively compared to Model 1. Compared with Model 1, the 3D-MLH algorithm (i.e., Model 3) proposed in this paper reduces the time consumption, path loss, total number of turning angles, and total turning angle by 3.16%, 3.09%, 5.32%, and 7.12% on average respectively; compared with Model 2, Model 3 reduces the time consumption, path loss, total number of turning angles, and total turning angle by 2.65%, 2.78%, 2.97%, and 5.32% on average respectively. When using Model 1 to avoid obstacles, this model uses two nearest neighbor objects to avoid obstacles by the action of the force on the UAV individual. As the UAV individual moves, the action of the obstacle's near neighbor point on the UAV's force will cause the UAV to generate a non-smooth path near the obstacle, resulting in greater consumption; Model 2 uses the method of three-dimensional collision cone and obstacle spherical crown to avoid static and dynamic obstacles. During the obstacle avoidance process, the UAV individual changes the movement direction towards the circumferential circle of the multi-layer capture of the dynamic target due to obstacle avoidance, increasing the time consumption, path loss, etc. of the UAV individual for the multi-layer capture of the dynamic target; when Model 3 uses a three-dimensional simplified virtual force capture model based on the interference perturbation fluid dynamic system to avoid obstacles, it performs corresponding obstacle avoidance according to the shape of the obstacle and moves towards the circumferential circle where the target is located at the same time. It can not only effectively avoid obstacles but also reduce the time consumption, path loss, etc. during the process of capturing the target. The obstacle avoidance path of this method is smoother.

[0213] Finally, it is necessary to clarify here that: the above embodiments are only used to further illustrate the technical solutions of the present invention in detail, and cannot be understood as a limitation on the protection scope of the present invention. Some non-essential improvements and adjustments made by those skilled in the art based on the above content of the present invention all belong to the protection scope of the present invention.

Claims

1. A multi-layer collaborative capture method for drone swarms in a three-dimensional unknown complex environment, characterized in that: The steps include: Step S1: Establishing the UAV motion model and the motion model of the UAV swarm encircling the target in the obstacle environment; Step S2: establishing a multi-layer capture model, wherein the established multi-layer capture model includes a three-dimensional simplified virtual force capture model, an obstacle avoidance method for a disturbed fluid dynamic system, and an inter-layer motion model; Step S3: the UAV performs cross-layer motion between adjacent layers through the inter-layer motion model, and performs capture motion toward the target through a three-dimensional simplified virtual force capture model or an obstacle avoidance method of a perturbed fluid dynamic system; wherein the three-dimensional simplified virtual force capture model and the obstacle avoidance method of the perturbed fluid dynamic system are both based on spherical expansion of non-convex obstacles in the environment; Step S4: When all drone individuals meet the set position conditions, the roundup ends.

2. The method for trapping according to claim 1, characterized in that: In step S3, when a drone meets the conditions that both its two neighbors are obstacles and the distances between the two neighbors and the drone are less than a set value, the velocity vector of the drone is calculated by the obstacle avoidance method of the perturbed fluid dynamic system, and the drone moves one time step according to the velocity vector; when the drone does not meet the conditions, the velocity vector of the drone is calculated by a three-dimensional simplified virtual force capture model, and the drone moves one time step according to the velocity vector.

3. The method for trapping according to claim 2, characterized in that: The drone's encirclement and capture movement towards the target is a step-by-step movement. The drone moves one time step according to the calculated velocity vector, which is one step. The current encirclement and capture step number is the total number of steps the drone has moved from the start of the encirclement and capture to the current moment.

4. The method for trapping according to claim 3, characterized in that: If the current capture step value is greater than the set parameter, the drone group will perform an inter-layer movement before performing the capture movement, otherwise the drones will directly perform the capture movement.

5. The method for trapping according to claim 1 or 2, characterized in that: Multiple drones are arranged on multiple concentric circles or ellipses with different radii. The number of layers from the innermost to the outermost circles or ellipses is 1 to n. The process of the inter-layer motion model is as follows: Assume that a drone is the target drone, and determine whether the two neighbors of the target drone are both drones. If not, there is no need to perform inter-layer motion. If yes, determine whether the distances between the two neighbors and the target drone and the distances between the two neighbors meet the set values. Determine whether the distances between the two nearest neighbors and the target drone and the distances between the two nearest neighbors meet the set values. If so, the target drone moves one layer outward and determines whether the current layer of the target drone is greater than 1; if not, directly determine whether the layer of the target drone is greater than 1; Determine whether the number of the layer where the target drone is located is greater than 1. If not, the inter-layer movement ends; if so, determine whether the number of drones in the inner layer of the layer where the target drone is currently located is not less than 2. The inner layer of the layer where the target drone is located refers to the drone layer that is 1 smaller than the layer where the target drone is located; Determine whether the number of drones in the inner layer of the layer where the current target drone is located is not less than 2. If so, calculate the two drones in the inner layer that are closest to the target drone and the distance between the two drones. Let the two drones be the two nearest neighbors of the inner layer, and the distance between the two drones is the distance between the two nearest neighbors of the inner layer. If the number of drones in the inner layer of the layer where the current target drone is located is less than 2, artificially set a parameter as the distance between the two nearest neighbors of the inner layer. Determine whether the distance between the two neighbors in the inner layer is greater than the set value. If so, the object drone moves one layer inward; if not, the inter-layer movement ends.

6. The method for trapping according to claim 1, characterized in that: The obstacle avoidance method of the perturbed fluid dynamic system is as follows: first, according to the position and speed information of the individual drone and the position information of the encirclement target, the flow velocity of the individual drone in an obstacle-free environment is constructed as the initial flow velocity; then, according to the disturbance of the initial flow velocity by the static obstacles in the environment, a perturbation matrix is ​​constructed, and the speed of the individual drone in the obstacle environment is obtained by correcting the initial flow velocity with the perturbation matrix. When there are dynamic obstacles in the environment, the flow velocity of the relative perturbation flow field under the relative initial flow field is constructed by introducing the motion information of the dynamic obstacles.

7. The method for trapping according to claim 1, characterized in that: In step S4, the set positions satisfied by all individual drones include: the distance between the capture target and the individual drone meets the set value, and the distance between the two nearest neighbors of the drone and the individual drone meets the set value.

8. The method for trapping according to claim 1, characterized in that: In step S2, a relative coordinate system XOYZ is constructed when establishing a three-dimensional simplified virtual force capture model. i The coordinates in the global coordinate system xoyz are (x i ,y i ,z i ), build with U i is the origin, U i The line connecting t1′ is the Y axis, and the line parallel to the global coordinate system z axis is the relative coordinate system XOYZ of the Z axis, where t1′ is the target t1 after passing through U i And the projection on the plane parallel to the xoy plane.

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