A multi-UAV formation obstacle avoidance method based on disturbed fluid

Abstract

The present invention discloses a multi-UAV formation obstacle avoidance method based on disturbed fluid, belonging to the field of UAV navigation, guidance, and control. Specifically, the method comprises the following steps: obtaining the current airspace comprehensive information of all UAVs participating in the formation collision avoidance flight mission; calculating the convergent flow velocity for each UAV; and predicting the collision risk of each UAV based on the current flight status of each UAV and the intruder aircraft; then calculating the appropriate avoidance maneuver criterion for each UAV, thereby optimizing the IFDS parameters of each UAV; combining the convergent flow velocity and IFDS parameters of each UAV, calculating the respective disturbed flow velocity, and applying kinematic constraints to obtain the planned overload and planned speed. Finally, using the planned speed, the next desired waypoint corresponding to each UAV is obtained; and the above operation is repeated at the next sampling moment to obtain the UAV formation collision avoidance flight path plan at each moment. The present invention improves the formation collision avoidance performance and meets the real-time requirements of the formation collision avoidance flight algorithm.

Description

Technical Field

[0001] The invention relates to a multi-UAV formation obstacle avoidance method based on disturbed fluid, belonging to the technical field of UAV navigation, guidance and control. Background Art

[0002] Formation flight is one of the key approaches to further enhancing drone autonomy. This involves multiple drones moving together toward a specific target or direction while maintaining a pre-defined spatial geometry. Formation flight can significantly improve mission efficiency and robustness. With the booming low-altitude economy, drones may increasingly operate in low-altitude environments, where densely distributed and diverse obstacles pose a serious threat. To ensure safe formation flight, multiple drones must not only avoid collisions with other members of the formation but also circumvent obstacles in the external environment.

[0003] Many studies have focused on collision avoidance within a formation, without considering external environmental constraints. Typical approaches can be broadly categorized as leader-follower, virtual structure, behavior-based, and consensus-based. These approaches drive agents to converge to an equilibrium point—the desired relative position and velocity between agents—to avoid internal collisions. Building on this foundation, collision avoidance methods can be further integrated to enable agents to avoid external obstacles during formation motion.

[0004] Typical collision avoidance methods can be broadly categorized into geometric methods, optimization-based methods, stochastic programming methods, artificial potential field methods, and the perturbed fluid dynamic system (IFDS) method. The IFDS method, inspired by the phenomenon of turbulence in nature, consists of two components: an initial flow field (confluence) and a perturbed flow field (perturbation). The confluence guides the drone toward the target point, while the perturbation created by obstacles creates a perturbation that allows the drone to circumvent the obstacle. The quality of the planned path depends on the IFDS parameters. The IFDS method can uniformly handle multiple obstacles of different types in a simple manner. Its advantages include low computational complexity, smooth planned paths, and the avoidance of oscillations and local minima common in traditional potential field methods.

[0005] Although scholars have achieved rich results in the field of formation collision avoidance, the existing technologies still commonly have the following problems:

[0006] (1) Many studies assume that the solution space is two-dimensional and build problem models based on it, including relative geometric relationships, motion models, and obstacle models. Therefore, the corresponding methods proposed are usually not directly applicable to three-dimensional environments. Compared with the two-dimensional plane, higher motion space dimensions help improve task performance and expand application scenarios. However, due to the increase in dimensionality, the complexity of motion constraints and the computational burden will increase significantly;

[0007] (2) Research on fluid-based formation maintenance methods is relatively insufficient. Since confluence is only applicable to a single agent, most existing IFDS methods cannot be directly used for formation collision avoidance. Based on the hemispherical area division of the airspace, some scholars proposed a confluence flow velocity adjustment strategy. However, due to the different formation maintenance rules in different hemispherical areas, the form of this strategy is relatively complicated; in addition, it cannot fundamentally eliminate the static error of formation tracking;

[0008] (3) The coupling between formation maintenance and collision avoidance places high demands on the selection of IFDS parameters, but this requirement may be difficult to meet due to the shortcomings of existing parameter optimization methods. Currently widely used optimization-based methods such as RHC have high requirements for computing and communication capabilities, which affects their application in engineering practice. To improve the real-time performance of algorithms, learning-based parameter optimization methods have been proposed in recent years, but their generalization ability and interpretability are generally difficult to guarantee. Summary of the Invention

[0009] In order to solve the above problems, the present invention proposes a multi-UAV formation obstacle avoidance method based on disturbed fluid in a three-dimensional low-altitude environment with densely distributed and diverse obstacles. A formation disturbed fluid dynamical system (FIFDS) based on fluid characteristics is established as the basic framework of multi-UAV formation collision avoidance flight, and a moderate evasive maneuver strategy (MEMS) is designed to further improve the formation collision avoidance performance. The method enables the UAVs to take moderate evasive maneuvers that match the current collision risk during formation flight to reasonably balance flight safety and collision avoidance costs, and can better meet the real-time requirements of the formation collision avoidance flight algorithm.

[0010] The multi-UAV formation obstacle avoidance method based on disturbed fluid specifically comprises the following steps:

[0011] Step 1: N u The drones are divided into 1 pilot and N u -1 follower, numbered in sequence and set to the desired formation configuration;

[0012] The navigator is designated manually based on actual conditions.

[0013] Step 2: Acquire current airspace comprehensive information during the multi-UAV formation collision avoidance flight mission;

[0014] The comprehensive airspace information includes: the position and ground speed vector of each UAV in the formation, the position, shape and size of each environmental obstacle, the relative motion information between the UAV and the intruder, and the formation collision avoidance performance index.

[0015] The relative motion information includes: the distance r between the jth intruder and the ith drone ij and speed and the relative direction angle and relative elevation angle

[0016] The formation collision avoidance performance indicators include: formation tracking error index J f , collision avoidance index J c , route length index J l , route smoothness index J s , overload index J is required o .

[0017] Step 3: At the current sampling moment, determine whether the formation collision avoidance flight mission is completed. If so, the algorithm ends; otherwise, proceed to step 4.

[0018] The mission is completed when the navigator reaches the target point with R d In the neighborhood of radius R d is the target point distance threshold.

[0019] Step 4: For the i-th UAV, calculate the expected speed of the UAV without considering collision avoidance, that is, the confluence flow velocity;

[0020] The reference flow lines are planned by the navigator;

[0021] The navigator's cruising speed is V1 and its position is p1 = [x1, y1, z1] T , the position of the target point is p g =[x g ,y g ,z g ] T ; The confluence velocity u(p1) is the velocity from the pilot position p1 to the target point position p g The vector is expressed as:

[0022]

[0023] After correcting the confluence flow velocity u(p1), the planned speed v1 of the navigator is obtained.

[0024] For the i-th follower drone (i=2,...,N u ), whose corresponding streamline is parallel to the planned velocity v1 and passes through the desired position of the UAV The expression is:

[0025]

[0026] Among them, l i is any point on the streamline of the i-th UAV, Δl is the straight line parameter, indicating that the point l i Relative to the desired position distance.

[0027] The desired speed required for the follower to maintain the formation is the convergence flow velocity u(p i ) is expressed as:

[0028]

[0029] Among them, p i is the position of the i-th UAV, k1 and k2 are constant positive numbers, is the expected formation change rate, is a vector parallel to v1, is a vector orthogonal to v1, is the position p i The projection on the corresponding streamline, v c It is the navigator motion compensation item.

[0030] Step 5: For the i-th UAV, predict the collision risk of the UAV based on the current flight status of the UAV and the intruder;

[0031] i=1,...,N u ;The minimum safe distance of the drone is d min .

[0032] Specifically, it includes the following three three-dimensional dynamic collision zone models:

[0033] 1) When the intruder is in the no-maneuver collision zone, if the UAV does not perform an evasive maneuver, a potential collision will occur. The boundary condition of the no-maneuver collision zone is that the potential collision will occur when the relative distance between the UAV and the intruder reaches the minimum, that is, the CPA distance is equal to the safety warning distance d s .

[0034] According to the relative motion information, and After that, the complete boundary value of the no-maneuver collision zone can be obtained according to the following formula:

[0035]

[0036] in:

[0037]

[0038]

[0039] and V i are the ground speed amplitudes of the intruder and drone respectively, and γ i are the climb angles of the intruder and drone respectively, It is the angle between the projection of the intruder ground speed vector on the horizontal plane and the x-axis of the relative system.

[0040] In engineering practice, when the relative velocity amplitude If is small enough, the two objects can be regarded as approximately stationary relative to each other; that is, if make Where V th is the speed threshold. In the present invention, V th Set to 0.1V i .

[0041] 2) When the intruder is in the maximum maneuver collision zone, if the UAV takes a certain maneuver from zero to the maximum average overload maneuver, a potential collision will occur.

[0042] n nmax is the maximum average normal overload of the UAV, n ymax and n zmax are the maximum overload components of the UAV along the y-axis and z-axis of the trajectory system, respectively.

[0043] Assume that the horizontal and vertical accelerations of the i-th UAV during collision avoidance maneuvers are and Its positive direction is respectively r y r and O r z r The positive direction of is the same. Therefore, and in is the average normal overload of the UAV, μ i is the speed roll angle, when the drone rolls to the right, μ i >0.

[0044] For the following five typical maneuvers: horizontal left turn, climb and turn left, vertical climb, climb and turn right, horizontal right turn; speed roll angle μ i The values ​​of

[0045] Similar to the non-maneuverable collision zone, the boundary condition of the maximum maneuverable collision zone can be expressed as:

[0046]

[0047] in, Can be expanded to:

[0048]

[0049] Obtain the unknown quantity r by iterative method ij and numerical solutions of Δt.

[0050] Traversal and Then the complete maximum collision zone boundary value can be obtained.

[0051] 3) The non-avoidable zone can be divided into a one-way non-avoidable zone and a completely non-avoidable zone, which represents the dividing line where the drone can avoid potential collisions under certain conditions.

[0052] One-way unavoidable zone It is the intersection of the no-maneuver collision zone and the maximum maneuver collision zone, where the subscript s∈S represents a specific maneuver direction, and S is the set of optional maneuver directions.

[0053] Completely unavoidable area is the intersection of all one-way unavoidable areas.

[0054] When the intruder is in a one-way non-avoidable zone If the UAV can only perform evasive maneuvers along direction s, a potential collision will occur.

[0055] When the intruder is in a completely unavoidable area When the intruder is in the area and moving towards the drone, no matter what possible maneuvers the drone takes, it cannot avoid the potential collision.

[0056] Step 6: Based on the predicted collision risk of the i-th UAV, calculate the appropriate avoidance maneuver criterion for the UAV;

[0057] The escape distance can be divided into local one-way escape distance Local complete escape distance Global one-way escape distance and the global complete escape distance in and The arrival of the jth intruder aircraft is and The remaining distance.

[0058] The criterion for moderate evasive maneuver is the global complete escape distance and global one-way escape distance

[0059] Since the UAV should avoid collision with any intruder, the global one-way / complete escape distance should be the minimum of the local one-way / complete escape distances, that is:

[0060]

[0061] Among them, the local complete escape distance The calculation formula is:

[0062]

[0063] Step 7: Based on the appropriate avoidance maneuver criterion of the i-th UAV, optimize the IFDS parameters of the UAV;

[0064] IFDS parameters include: reaction coefficient ρ i and the directional coefficient θ i ,

[0065] ρ i It can be expressed as:

[0066]

[0067] θ i It can be expressed as:

[0068]

[0069] Directivity coefficient θ i Can be discretized into N θ sampling values, each sampling value corresponds to a planned overload n i , optimal overload and planning overload i The angle ζ between them is expressed as:

[0070]

[0071] Step 8: Combine the confluence velocity and IFDS parameters of the i-th UAV to calculate the disturbance velocity of the UAV, that is, the expected velocity of the UAV considering collision avoidance;

[0072] The reaction coefficient and direction coefficient of each obstacle are taken to be the same value, that is, Considering the case of obstacle motion, use the sum perturbation matrix Corrected confluence velocity The following disturbed flow field velocity can be obtained

[0073]

[0074] in, is the weighted sum of obstacle velocities;

[0075] Step 9: Perform kinematic constraints on the flow velocity of the disturbed flow field, and obtain the constrained overload as the control input to plan the overload n i , and then get the feasible actual planning speed v of the UAV i .

[0076] First, the pre-planned motion variables Vi that have not yet considered kinematic constraints are p and V i p Limit the speed to the allowable range [V min ,V max ]Inside;

[0077] Assuming the planning step size is ΔT, calculate the motion variable V at the current moment i , χ i , γ i the expected rate of change;

[0078] Then, the maximum turning rate and maximum climbing angular rate of the UAV are respectively and Perform clipping;

[0079] According to the available overload range, the expected required overload is limited to obtain the constrained and Substituting back into the UAV kinematic model, the expected overload can be calculated Limit it to get a practical control input in:

[0080]

[0081] Actual planned speed v i Expressed as:

[0082]

[0083] Step 10: Use the planned speed v of the i-th UAV i Get the next desired waypoint corresponding to the UAV;

[0084] The next expected waypoint of drone i is denoted as p i,next , whose expression is:

[0085] p i,next =p i +v i ·ΔT (17)

[0086] Step 11: Return to step 2 to plan the UAV formation collision avoidance flight route for the next sampling moment.

[0087] The advantages of the present invention are:

[0088] (1) The present invention proposes a multi-UAV formation obstacle avoidance method based on disturbed fluid. Based on the simulation of fluid properties, the disturbed fluid method, which was originally only applicable to single-UAV collision avoidance, is naturally extended to formation collision avoidance. Compared with the existing fluid-based formation maintenance methods, it has a simpler form and better formation maintenance performance.

[0089] (2) The present invention provides a multi-UAV formation obstacle avoidance method based on disturbed fluid, which can guide UAVs to perform moderate avoidance maneuvers, thereby reasonably balancing flight safety and collision avoidance costs;

[0090] (3) The present invention provides a multi-UAV formation obstacle avoidance method based on disturbed fluid, which can optimize the IFDS method parameters online in an analytical form, has good real-time performance and interpretability, and is easy to implement in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 This is an overall flow chart of the multi-UAV formation obstacle avoidance method based on disturbed fluid of the present invention;

[0092] Figure 2 is a UAV formation route map in an embodiment of the present invention; wherein, Figure 2 (a) It is a three-dimensional route; Figure 2 (b) is the projection of the route on the horizontal plane; Figure 2 (c) The projection of the route on the plumb plane;

[0093] Figure 3 This is a partial enlarged view of the route of the UAV formation in the embodiment of the present invention; wherein, Figure 3 (a) The route from 1s to 96s; Figure 3 (b) The route from 97s to 192s; Figure 3 (c) The route from 193s to 288s;

[0094] Figure 4 is a graph showing the closest distance between each UAV and the surface of an environmental obstacle in an embodiment of the present invention;

[0095] Figure 5 is a tracking error curve diagram of each UAV formation in an embodiment of the present invention;

[0096] Figure 6 is a graph of the distance between drones in an embodiment of the present invention;

[0097] Figure 7 is a speed curve diagram of a drone in an embodiment of the present invention;

[0098] Figure 8 is a graph showing the rate of change of the heading angle and climb angle of the UAV in an embodiment of the present invention;

[0099] Figure 9 This is a graph showing an overload curve of a drone according to an embodiment of the present invention;

[0100] Figure 10 is a FIFDS parameter curve diagram in an embodiment of the present invention;

[0101] Figure 11 is a performance index comparison curve diagram of different methods in the embodiment of the present invention;

[0102] Figure 12 It is a needle graph comparing the single-step calculation time consumption of different methods in the embodiment of the present invention. DETAILED DESCRIPTION

[0103] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0104] A multi-UAV formation obstacle avoidance method based on disturbed fluid, the overall process is as follows Figure 1 As shown, the specific steps include:

[0105] Step 1: N u The drones are divided into 1 pilot and N u -1 follower, numbered 1, 2, ..., N u , and determine the desired formation configuration;

[0106] In this embodiment, N is selected u =4; Multiple drones form a formation based on the pilot-follower method, and the pilot is manually designated based on the actual situation. The pilot drone is U1, and the other follower drones are U j ,j=2,...,N u .

[0107] Assume the formation coordinate system is O F x F y F z F , its origin is fixed to the center of mass of the pilot, which is in the inertial frame O at time t. I x I y I z I The position in O F x F y F z F The angle relative to the inertial system, that is, the formation heading angle χ F and climb angle γF In the present invention, it is assumed that the communication between the formation members can be realized through a two-way fully connected topology structure, that is, each aircraft can exchange information with each other.

[0108] set up and They are the i-th UAV (i=1,2,...,N u ) in the inertial and formation coordinate systems; where, represents the expected relative distance between the i-th UAV and the leader, which determines the formation configuration. and The conversion relationship between them can be expressed as:

[0109]

[0110] in, is the coordinate transformation matrix from the inertial system to the formation coordinate system, and its expression is:

[0111]

[0112] Since the navigator may perform maneuvers during flight, is time-varying. Therefore, even if remain unchanged, that is Expected relative distance in inertial frame It is still time-varying, and this should be taken into account and compensated for when designing formation-keeping methods.

[0113] Step 2: Acquire current airspace comprehensive information during the multi-UAV formation collision avoidance flight mission;

[0114] The comprehensive information specifically includes: the position and ground speed vector of each UAV in the formation, the position, shape and size of each environmental obstacle, the relative motion information between the UAV and the intruder, and the formation collision avoidance performance index.

[0115] The mathematical description of the comprehensive information is as follows:

[0116] When planning the route, it is usually assumed that the flight control system can ensure the stability of the UAV’s own attitude and speed, and the UAV can be regarded as a three-degree-of-freedom point mass. For the i-th UAV in the formation (i=1,2, ... ,N u ), its kinematic model in the inertial system can be expressed as:

[0117]

[0118] Among them, p i =[xi ,y i ,z i ] T is the three-dimensional position vector of the UAV in the inertial system; V i , χ i and γ i are the ground speed amplitude, track deviation angle and track inclination of the UAV respectively; as the control input, and are the overloads of the UAV along the three axes of the track system, where g is the acceleration due to gravity.

[0119] Assuming that all UAVs are homogeneous, the kinematic constraints imposed on each UAV can be uniformly expressed as follows:

[0120] as well as

[0121] Low-altitude environments may contain both static obstacles such as terrain and dynamic obstacles such as intruders. Dynamic obstacles can usually be approximated as spheres. In this invention, all obstacles are enclosed by standard convex polyhedrons such as spheres, hemispheres, cylinders, and cuboids. After being enclosed by convex polyhedrons, the obstacles can be uniformly represented in the inertial system as:

[0122]

[0123] Among them, a, b, c and d, e, f are all constants, which determine the size and shape of the obstacle respectively; p o =[x o ,y o ,z o ] T Represents the coordinates of the obstacle center in the inertial system; Γ(x, y, z) = 1 represents the obstacle surface.

[0124] To prevent collisions between formation members and the chain reaction caused by collision avoidance maneuvers, each drone is assigned a different priority. Low-priority drones treat high-priority drones as spherical obstacles, with a radius equal to the drone's minimum safe distance. The lower the drone number, the higher its priority.

[0125] In the present invention, for each UAV, the mass center of other high-priority UAVs in the formation and the closest point of the UAV to each environmental obstacle surface are uniformly regarded as virtual intruders. Assume that the position vector and ground speed vector of the i-th UAV and the j-th intruder are p respectively. i , v i and Their heading angle and climb angle are χ i , γ i and The distance and speed of the jth intruder relative to the ith drone are r ij and It should be noted that And R ij =||r ij ||, where ||·|| represents the modulus of the vector; the above motion variables can be obtained by onboard sensors and data links.

[0126] In order to describe relative motion, a relative coordinate system O is established. r x r y r z r , whose origin O r With p i Coincidence, O r x r Axis v i In the projection direction of the horizontal plane, O r z r Axis vertical to O r x r Pointing up, O r y r The axis is determined by the right-hand rule; O r x r and and r ij The angles between the horizontal projections of and v i , r ij With horizontal plane O r x r y r The angles between them are γ i ,

[0127] O r x r y r z r It can be obtained in another way: translate the origin of the inertial system to p i , and then rotate around the z axis by an angle χ i Therefore, there is a conversion relationship and in For r ij The angle between it and the x-axis of the inertial frame.

[0128] Assume that the detection range of the airborne sensor is R s , then when R ij >R sWhen the drone is in flight, it cannot detect the intruder.

[0129] Typically, the desired formation flight effect is for the UAVs in the formation to closely track their desired positions, and the planned routes should be collision-free and as short as possible. Furthermore, considering route feasibility, the planned routes should be smooth and require minimal overload.

[0130] Therefore, in order to quantitatively evaluate the collision avoidance performance of UAV formations, the present invention considers the following five indicators: formation tracking error index J f , collision avoidance index J c , route length index J l , route smoothness index J s , overload index J is required o .

[0131] Among the above indicators, J c Reflects flight safety, and other indicators jointly reflect the collision avoidance cost during formation flight. For the i-th UAV, the comprehensive performance index at time t can be expressed as:

[0132] J i (t) = λ f J fi (t)+λ c J ci (t)+λ l J li (t)+λ s J si (t)+λ o J oi (t) (5)

[0133] Among them, λ f ,λ c ,λ l ,λ s and λ o are the corresponding weights respectively. On the basis of ensuring that the magnitudes of weighted sub-indicators are at the same level, their specific values ​​can be further adjusted according to task requirements. i The smaller (t) is, the better the performance is.

[0134] Formation tracking error index J fi (t) reflects the formation maintaining performance, and its expression is:

[0135]

[0136] Among them, d(p i (t)) is the formation tracking error of the i-th UAV.

[0137] Collision avoidance index J ci(t) reflects the performance of the UAV in avoiding collisions with other formation members and environmental obstacles, and its expression is:

[0138]

[0139] Among them, N o is the number of environmental obstacles, L k (p i ) is the shortest distance from the i-th UAV to the k-th obstacle surface. When the UAV is outside the obstacle, L k (p i )>0, otherwise L k (p i )≤0. d min is the minimum safe distance. When the minimum distance between the UAV and each intruder is no greater than d min It is considered that a collision occurs.

[0140] It should be noted that for the sake of brevity, the contents in the variable brackets are omitted in the above formula. Similar situations also exist in the following text, which will not be repeated here.

[0141] Route length index J li (t) is closely related to the fuel consumption of the drone and is defined as:

[0142] J li (t)=||p i (t)-p i (t-ΔT)||+||p i (t)-p g (t)|| (8)

[0143] Among them, ΔT is the planning step size, p g (t) is the target point position at time t. When the target point is fixed, p g (t) is a constant value p g .||p i (t)-p g (t)|| reflects a rough estimate of the remaining route length.

[0144] Route smoothness index J si (t) and overload index J oi (t) is closely related to the feasibility of the route, and its expressions are:

[0145]

[0146]

[0147] For all UAVs in the formation, the total performance index can be expressed as:

[0148]

[0149] Step 3: At the current sampling moment, determine whether the formation collision avoidance flight mission is completed. If so, the algorithm ends; otherwise, proceed to step 4.

[0150] The mission is completed when the navigator reaches the target point with R d The neighborhood of radius is called R d is the target point distance threshold.

[0151] Step 4: Calculate the expected speed of each UAV without considering collision avoidance, that is, the confluence flow velocity;

[0152] The IFDS algorithm draws parallels between the natural phenomenon of water avoiding rocks and the collision avoidance route planning problem: rocks in a river can be considered obstacles for drones to avoid; straight streams can be considered confluences, with the confluence streamlines forming the initial route in an obstacle-free environment; and streams flowing around rocks can be considered a disturbed flow field, with the streamlines forming the planned route in an obstacle-free environment. The key to the IFDS algorithm lies in determining the flow velocity in the disturbed flow field.

[0153] Although the IFDS algorithm is highly effective for collision avoidance routing for single UAVs, it cannot be directly applied to formation flying. When there are no obstacles or threats in the airspace, the convergent flow velocity can directly guide the UAV from any starting point to the vicinity of the target point at a constant velocity amplitude. An intuitive approach to extending the IFDS algorithm to formation flying is to treat the desired position of the UAVs in the formation as the target point and generate the convergent flow. However, this approach cannot guarantee the desired formation maintenance performance for two reasons. First, in the IFDS algorithm, the convergent flow velocity is singular at the target point. Therefore, the convergent flow can only drive the UAV to the vicinity of the target point and cannot ensure that the UAV remains stable at the target point. For single-aircraft routing, planning is considered complete when the UAV reaches the specified neighborhood of the target point. However, formation flying requires the follower to stabilize at the desired position, so the IFDS algorithm cannot meet the formation maintenance requirements. Second, although the convergent flow direction always points to the target point, the IFDS algorithm does not consider adjusting the convergent flow velocity, that is, the UAV's desired velocity amplitude. Therefore, directly using the IFDS algorithm cannot achieve speed consistency among aircraft in the formation.

[0154] In order to solve the above problems and extend IFDS to formation collision avoidance flight, the convergence should be improved according to the formation maintenance requirements while maintaining its compatibility with the collision avoidance method. From the perspective of fluid methods, formation flight can be regarded as a group of fluids maintaining continuous flow. In single-aircraft route planning, the convergence is a straight straight line, and the convergence in multi-aircraft formation route planning can be compared to a cluster of parallel straight straight lines. This is because the intersection of streamlines can easily cause mutual collisions within the UAV formation. In addition, in order to guide the follower to converge accurately to the corresponding desired position, the singularity at the target point should be eliminated and the amplitude of the convergence flow velocity should be adaptively adjusted. Based on the above ideas, the formation maintenance problem can be converted into a problem of the follower tracking the desired point on the corresponding parallel streamline. The parallel streamline tracking (PST) method proposed in the present invention is as follows:

[0155] The reference flow lines are planned by the navigator.

[0156] In the IFDS algorithm, a confluence is defined as a straight line flowing from the surrounding area of ​​the target point to the target point at a constant speed. Assume that the navigator is flying at a cruising speed V1, and the positions of the navigator and the target point are p1 = [x1, y1, z1] T and p g =[x g ,y g ,z g ] T The confluence velocity u(p1) is the velocity from p1 to p g The vector can be expressed as:

[0157]

[0158] Considering collision avoidance and kinematic constraints, the planned speed v1 of the navigator can be obtained by correcting u(p1).

[0159] For the i-th UAV (i=2,...,N u ), whose corresponding streamline is parallel to v1 and passes through the desired position of the UAV The expression of this streamline is:

[0160]

[0161] Among them, l i is any point on the streamline, Δl is the linear parameter, indicating that the point is relative to distance.

[0162] Assumptions is a vector orthogonal to v1, where For p i In the streamline iTo achieve formation maintenance, the desired velocity of the follower can be divided into three parts: streamline convergence term, desired point tracking term, and leader motion compensation term. direction, which drives the follower to converge to the corresponding parallel streamline; the desired point tracking term is parallel to v1, and its function is to guide the follower to track the desired position on the parallel streamline; the leader motion compensation term is recorded as v c , can drive the follower to accompany the navigator. In addition, due to the navigator's maneuvering behavior, the expected relative position of the follower in the inertial system is time-varying, v c This will also be compensated to reduce the formation tracking error at this time. The desired speed u(p i ) can be expressed as:

[0163]

[0164] Among them, k1 and k2 are constant positive numbers. is the expected formation change rate. is a vector parallel to v1. Therefore, Orthogonal to d l (p i ), the UAV formation tracking error can also be expressed as

[0165] Assuming that the navigator plans one step ahead to obtain χ1(t+ΔT) and γ1(t+ΔT), it can be calculated according to formula (2): Then get Its expression is:

[0166]

[0167] Considering the allowable range of the UAV speed amplitude, u(p i ) is constrained as follows:

[0168]

[0169] In summary, the combined effect of the streamline convergence term and the desired point tracking term can drive the follower to converge to the parallel streamline and track the desired point, while Compensate for changes in the desired formation in the inertial frame caused by the leader's motion.

[0170] It should be noted that in low-altitude environments, in order to avoid collisions, the navigator may need to perform evasive maneuvers frequently. Compensating for the impact of this can effectively reduce the formation tracking error and improve the quality of formation flight.

[0171] Theorem 1: Parallel streamline tracking can ensure formation maintenance.

[0172] Prove that d(p i ) can be expressed as:

[0173]

[0174] because Orthogonal to d l (p i ),have:

[0175]

[0176] Therefore, the original problem can be decoupled into two sub-problems. Based on Lyapunov stability theory, in order to achieve the formation maintaining d(p i )→0, that is and d l (p i )→0, we can define the Lyapunov function:

[0177]

[0178] V L1 and V L2 The derivative of can be expressed as:

[0179]

[0180] When k1>0 and k2>0, and Therefore, we can get and d l (p i )→0, and then we get d(p i )→0, that is, parallel streamline tracking can ensure that the formation is maintained. Proof completed.

[0181] Step 5: Predict the collision risk of each drone based on the current flight status of each drone and the intruder;

[0182] It is of great significance to predict the collision risk and analyze how to perform appropriate evasive maneuvers during formation flying. As the theoretical basis for collision prediction in this invention, the closest approach point (CPA) represents two points on the route of the UAV and the intruder aircraft. When the two arrive at these two points at the same time, the relative distance between them reaches the minimum. The larger the CPA distance, the smaller the collision risk. If the CPA distance is not greater than the minimum safe distance d of the UAV, the collision risk will be reduced. min , a collision will occur.

[0183] To ensure flight safety, a safety margin should be considered during collision prediction to guide the drone to take timely action. In this invention, the restricted area for drones is defined as the area with p i Center, safety warning distance ds is a sphere with a radius of s >d min When there is an intruder in the forbidden zone, it is considered a potential collision. Due to the need to maintain the formation, the d corresponding to environmental obstacles and other formation members s should be different, that is, there are different and in It should be noted that due to the inclusion of a safety margin, the event of a collision can be considered a true subset of the occurrence of a potential collision, that is, when a potential collision occurs, a collision does not necessarily occur.

[0184] The dynamic collision zone is a time-varying subset of the mission airspace, its extent changing dynamically based on airspace situational information. If an intruder aircraft is currently located within the dynamic collision zone, a potential collision will occur under certain conditions. Based on the CPA distance, this invention proposes three three-dimensional dynamic collision zone models, laying the foundation for UAVs to perform appropriate evasive maneuvers.

[0185] When the intruder is in the no-maneuver collision zone, if the UAV does not perform an evasive maneuver, a potential collision will occur. The boundary condition of the no-maneuver collision zone is that the potential collision will occur when the relative distance between the UAV and the intruder reaches the minimum, that is, the CPA distance is equal to the safety warning distance d s The no-maneuver collision zone starts at the no-entry zone, and its boundary is tangent to the no-entry zone and along the relative velocity Therefore, the shape of the region is similar to a cylindrical pipe.

[0186] For the convenience of description, the current time is recorded as zero, and the prediction time interval is recorded as Δt, then r ij (0) = r ij Assume that the UAV and the intruder are both flying at a constant speed, and the relative distance between them is r ij (Δt) can be calculated by the following formula:

[0187]

[0188] According to the boundary conditions, when r ij (Δt) reaches its minimum value d s When there is r ij '(Δt)=0. In addition, due to r ij (Δt)≥d s >0, r ij ′(Δt)=0 is equivalent to Therefore, for r ij The derivative of (Δt) can be transformed into Taking the derivative, we have:

[0189]

[0190] in:

[0191]

[0192]

[0193] In engineering practice, when the relative speed If is small enough, the two objects can be regarded as approximately stationary relative to each other; that is, if make Where V th is the speed threshold. In the present invention, V th Set to 0.1V i .

[0194] r ij There is the following relationship between H:

[0195] (1) When H≥0, let Then when r ij When (Δt) is minimum, we have According to r ij (Δt)=d s , the relative distance to the boundary is

[0196] (2) When H<0, It always holds true, that is, the relative distance is the smallest at zero, so the relative distance to the boundary is r ij =d s .

[0197] In summary, in traversing and After that, the complete boundary value of the no-maneuver collision zone can be obtained according to the following formula:

[0198]

[0199] Generally speaking, collision avoidance maneuvers in three-dimensional space can be divided into climbing or descending in the vertical plane, horizontal turning, and various combinations of the two. Assume that the horizontal and vertical accelerations of the i-th UAV during the collision avoidance maneuver are and Its positive direction is respectively r y r and O r z r The positive direction of is the same. Therefore, and in is the average normal overload of the UAV, μ i is the speed roll angle, when the drone rolls to the right, μ i >0.

[0200] In the present invention, in order to balance flight safety and computational burden, five typical maneuvers are considered: horizontal left turn, climb and turn left, vertical climb, climb and turn right, horizontal right turn, namely μ i The values ​​of

[0201] When the UAV performs an evasive maneuver, the relative distance r ij (Δt) can be expressed as:

[0202]

[0203] When the intruder is in the maximum maneuver collision zone, if the UAV takes a certain maneuver from zero time to the maximum average overload If the vehicle maneuvers, a potential collision will occur. Similar to the no-maneuver collision zone, the boundary condition of the maximum maneuver collision zone can be expressed as:

[0204]

[0205] in, Can be expanded to:

[0206]

[0207] For the unknown quantity r ij and Δt, whose numerical solution can be obtained by iterative method.

[0208] Traversal and Then the complete maximum collision zone boundary value can be obtained.

[0209] Unavoidable areas can be divided into one-way unavoidable areas and completely unavoidable areas. is the intersection of the no-maneuver collision zone and a maximum maneuver collision zone, where the subscript s∈S represents a specific maneuver direction, and S is the set of optional maneuver directions defined in step five.

[0210] When the intruder is in a one-way non-avoidable zone If the UAV can only perform evasive maneuvers along direction s, a potential collision will occur. is the intersection of all one-way unavoidable regions, which can be recorded as When the intruder When the intruder is outside the zone, the drone can maneuver to avoid a potential collision. However, when the intruder is within this zone and moving toward the drone, no matter what maneuvers the drone can perform, a potential collision cannot be avoided. Therefore, the non-avoidable zone represents the boundary within which a drone can avoid a potential collision under certain conditions.

[0211] In summary, by predicting the CPA distance under different conditions, the three-dimensional dynamic collision zone contains both distance safety information and time safety information, and can dynamically change according to changes in relative speed. Compared with traditional collision zones based on fixed distance or time thresholds, it is more reasonable and can provide a strong basis for appropriate evasive maneuvers.

[0212] Although the computational burden of calculating the complete three-dimensional dynamic collision zone boundary is large, it is relatively easy to determine whether the intruder is in the corresponding collision zone and obtain the corresponding security information. ij Not greater than corresponding to a set and The region boundary value r ij , the intruder is within the collision zone; otherwise, the intruder is outside the collision zone. Therefore, collision prediction based on the three-dimensional dynamic collision zone can be achieved with a smaller computational burden.

[0213] Step 6: Based on the predicted collision risk of each UAV, calculate the appropriate avoidance maneuver criteria for each UAV;

[0214] Based on the three-dimensional dynamic collision zone model, this paper will discuss how drones can perform appropriate evasive maneuvers in the sense of CPA distance. An evasive maneuver consists of two parts: the maneuver amplitude and the maneuver direction. To reasonably balance flight safety and collision avoidance costs, an intuitive approach is to make the maneuver amplitude positively correlated with the collision risk. For example, when a collision is imminent, the drone should perform a large emergency evasive maneuver; when the collision risk is low, the drone's maneuver amplitude should be relatively gentle. In addition, to improve the efficiency of evasive maneuvers and indirectly reduce the required maneuver amplitude, the maneuver direction should be able to minimize the collision risk. If the evasive maneuver does not match the collision risk, the drone may fail to avoid the collision or unnecessarily disrupt the formation, that is, it is impossible to balance flight safety and collision avoidance costs. Therefore, it is necessary to quantitatively assess the collision risk, which can be achieved by utilizing the safety information in the three-dimensional dynamic collision zone.

[0215] Each dynamic collision zone mentioned above corresponds to a specific pair of drones and intruders. For each drone, the security information corresponding to one drone-intruder pair and all drone-intruder pairs are called local security information and global security information, respectively. Taking the i-th drone as an example, assume that there are If there is an intruder, the key safety information for evaluating the collision risk is the escape distance, which is defined in the present invention as the relative speed of the intruder. The distance in the direction relative to the boundary of the no-escape zone. The escape distance can be divided into the local one-way escape distance Local complete escape distance Global one-way escape distance and the global complete escape distance in and The arrival of the jth intruder aircraft is and The remaining distance. In summary, we can get:

[0216]

[0217] Since the UAV should avoid collision with any intruder, the global escape distance should be the minimum of the local escape distances, that is:

[0218]

[0219] It should be noted that when When , the escape distance does not exist. In addition, when the intruder is located or When the escape distance is less than 0.

[0220] when When the UAV maintains its current speed, potential collisions will not occur, so the collision risk is low. Therefore, the maneuver range should be small, and the requirements for the maneuver direction are relatively loose, which can be selected as a fixed direction, such as climbing upwards.

[0221] when When , the relationship between the global collision risk and the escape distance is derived as follows:

[0222] Theorem 2 Global complete escape distance It is positively correlated with the minimum CPA distance among all drone-intruder pairs and negatively correlated with the global collision risk.

[0223] Proof: For the UAV and the jth intruder, according to the definition of the completely unavoidable zone, the radius of the forbidden zone, i.e., the safety warning distance, can be adjusted to achieve arbitrary expansion or contraction of the completely unavoidable zone. Therefore, the intruder must be on the boundary of a virtual completely unavoidable zone, and its corresponding virtual safety warning distance is d s +Δd, that is, the CPA distance is d s +Δd. Obviously, the local complete escape distance is positively correlated with Δd; therefore, The larger the value is, the greater the CPA distance between the UAV and the jth intruder is, and the smaller the collision risk is. Similarly, considering all intruders, the global minimum CPA distance and global collision risk can be obtained from the global complete escape distance representation.

[0224] Theorem 3: To minimize the global collision risk, UAV U iShould follow the direction Maneuverability is defined as:

[0225]

[0226] Proof: Similar to Theorem 2, for the i-th UAV and the j-th intruder, the local one-way escape distance is The larger is , the larger is the local CPA distance after the UAV maneuvers along the direction s. Therefore, for a pair of UAV-intruder, the optimal maneuvering direction in the sense of CPA is Considering the situation of multiple intruders, the global one-way escape distance is positively correlated with the global CPA distance when the UAV maneuvers along direction s. Therefore, from the perspective of minimizing the global collision risk, is the optimal maneuvering direction.

[0227] Based on the above theorem, the following moderate avoidance maneuver criteria can be extracted: To achieve moderate avoidance maneuver, for UAV U i , the maneuver range should be Negatively correlated, the maneuvering direction should be

[0228] Step 7: Optimize the IFDS parameters of each UAV based on the appropriate avoidance maneuver criteria of each UAV;

[0229] The quality of the planned route and the IFDS algorithm parameter ρ i and θ i The selection of is closely related to , which respectively determine the magnitude and direction of the UAV’s evasive maneuver. For example, ρ i The larger the value, the earlier the evasive maneuver begins and the greater the magnitude. Therefore, to produce the desired evasive maneuver, the IFDS parameters should be optimized. To rationally balance flight safety and collision avoidance costs during formation collision avoidance, the present invention optimizes the IFDS parameters analytically based on the moderate evasive maneuver criterion.

[0230] Since the collision risk can be determined by the global complete escape distance Quantitative characterization. The magnitude of the evasive maneuver depends on ρ i , the latter should be To convert ρ i Limited to the allowed range [ρ min ,ρ max ], in the calculation After that, it needs to be limited to [e cmin ,e cmax ] inside. Then ρ i It can be expressed as:

[0231]

[0232] In the present invention, when When , the maneuvering direction is selected as climbing upward, that is, θ i =0.5π. When When , the optimal maneuvering direction can be obtained by calculating as described in step 6 In the track system O k x k y k z k Under optimal overload It can be expressed as:

[0233]

[0234] in, and Corresponding.

[0235] θ i Can be discretized into N θ sampling values, each sampling value corresponds to a planned overload n i In the present invention, let N θ =5,θ i ∈{0,0.25π,0.5π,0.75π,π}.

[0236] and n i The angle ζ between them can be expressed as:

[0237]

[0238] when When the optimal directivity coefficient θ i Corresponding to the direction The closest n i In summary, θ i It can be expressed as:

[0239]

[0240] Currently, no research has explored how to analytically select the appropriate IFDS parameters. Because it directly utilizes refined moderate avoidance maneuver information, MEMS is far more intuitive than parameter optimization methods such as RHC and machine learning. It also does not require extensive iterations or training, enabling efficient real-time optimization of IFDS parameters.

[0241] Step 8: Calculate the turbulent flow velocity of each UAV by combining the converging flow velocity of each UAV and the IFDS parameters;

[0242] In the IFDS algorithm, when there are obstacles in the environment, the confluence u(p i) will be disturbed by it. The difference between the leader and follower in route planning lies in the way the convergence is generated, while the mechanism for generating disturbance is the same for each aircraft. It should be noted that existing literature has demonstrated that the interference of obstacles does not affect the convergence, or the stability of the formation.

[0243] For UAV i (i=1,2,...,N u ), the impact of all obstacles including environmental obstacles and high-priority UAVs on their expected speed can be expressed by the perturbation matrix Quantitative representation, there are:

[0244]

[0245] Among them, N o is the number of obstacles; ω k (p i ) represents the weight coefficient of the kth obstacle, whose value depends mainly on the distance between the UAV and the obstacle surface. Generally speaking, the greater the distance, the smaller the weight coefficient, that is, the smaller the impact of the obstacle on the flow field.

[0246] ω k (p i ) is:

[0247]

[0248] Among them, Γ j (p i ) represents the jth obstacle. Assume Then the normalized weight coefficient is:

[0249]

[0250] Assumptions is the radial normal vector of the k-th obstacle surface. k (p i )'s tangent plane S t In , define the following two orthogonal tangent vectors:

[0251]

[0252]

[0253] With p i is the origin, t k,1 (p i ), t k,2 (p i ) and n k (p i) establish coordinate systems O′x′y′z′ for x′, y′, and z′ axes respectively. In O′x′y′z′, the tangent plane S t Any unit vector on can be expressed as:

[0254]

[0255] in, t k ′(p i ) and the x′ axis is called the direction coefficient.

[0256] Assume t k ′(p i ) in the inertial frame S I Indicated as t k (p i ), the latter can be obtained by the following coordinate transformation:

[0257]

[0258] in, From coordinate system O′x′y′z′ to O I x I y I z I The transformation matrix.

[0259] In summary, the perturbation matrix of the kth obstacle is defined as:

[0260]

[0261] Where I is the 3×3 dimensional unit matrix, which is called the attraction matrix; the second and third terms on the right side of Equation (43) are called the repulsion matrix and the tangent matrix, respectively; is the reaction coefficient, which determines the shape of the disturbance streamline. The larger it is, the earlier and greater the magnitude of the evasive maneuver.

[0262] In order to facilitate parameter optimization, the reaction coefficient and direction coefficient of each obstacle are usually taken to be the same value, that is, k=1,...,N o Considering the case of obstacle motion, use the sum perturbation matrix Corrected confluence velocity The following disturbed flow field velocity can be obtained

[0263]

[0264] in, is the weighted sum of obstacle velocities, and its expression is:

[0265]

[0266] in, is the moving speed of the kth obstacle.

[0267] Step 9: kinematically constrain the flow velocity of the disturbed flow field and calculate the planned overload and planned speed of each UAV;

[0268] Considering the requirements of route flyability, it is necessary to kinematically constrain the flow velocity of the spoiler flow field, i.e., the desired speed of the UAV, and use the constrained overload as the control input n i , and then get the feasible actual planning speed v of each UAV i For i=1,...,N u , assuming and is the pre-planned motion variable without considering the kinematic constraints, and its expression is:

[0269]

[0270] right Limit the speed to the allowable range [V min ,V max ]. Assuming the planning step is ΔT, the motion variable V at the current moment is i , χ i , γ i The expected rate of change can be expressed as:

[0271]

[0272] First, the maximum turning rate and maximum climbing angular rate of the UAV are respectively and The limiting process can be expressed as:

[0273]

[0274] Then, the expected required overload is limited according to the available overload range. and Substituting back into the UAV kinematic model, that is, formula (3), the expected required overload can be calculated Limit it to get a practical control input in:

[0275]

[0276] n i Substituting it back into formula (3) as the control input, we can calculate the practical planning result and Therefore, the actual planned speed v after kinematic constraints is i It can be expressed as:

[0277]

[0278] Step 10: Calculate the next desired waypoint for each drone using its planned speed.

[0279] The next expected waypoint of drone i is denoted as p i,next , whose expression is:

[0280] p i,next =p i +v i ·ΔT (52)

[0281] Step 11: Return to step 2 to plan the UAV formation collision avoidance flight route for the next sampling moment.

[0282] Example

[0283] The three-dimensional formation route planned in this embodiment is as follows Figure 2 As shown in the figure, at the initial moment, the drones are loosely distributed and do not form the desired formation. As time goes by, the multiple drones are able to form and maintain the desired formation and can smoothly bypass obstacles like a cluster of fluid until they finally reach the target point. Due to moderate avoidance maneuvers, the drones can better maintain the continuity of the formation under the interference of obstacles. It should be noted that in order to clearly show the route, Figure 2 In (c), some obstacles are made transparent.

[0284] In order to more clearly show the formation maintenance during the flight, the UAV formation is partially enlarged as shown below: Figure 3 As shown in the figure, the circles represent the positions of the drones at the corresponding moment, and the lines connecting them represent the geometric relationships between the drones. The entire formation flight process lasted 288 seconds and was divided into three phases for detailed presentation. Clearly, the drones are capable of flying in formation. The formation can be deformed by nearby obstacles, but it quickly converges to the preset formation after passing through the obstacle area.

[0285] The closest distance between each drone and the surface of the environmental obstacle is as follows: Figure 4 As shown in Figure 2, the obstacles include static obstacles and moving obstacles. During the entire formation flight process, the above closest distances are all greater than the minimum safe distance, that is, no aircraft collides with environmental obstacles.

[0286] Figure 5The figure shows the formation tracking error. When the formation flies over a dense obstacle area, the tracking error fluctuates around zero due to the UAVs' evasive maneuvers. After passing the obstacle area, the tracking error quickly converges to 0. This shows that the proposed method can effectively balance formation maintenance and collision avoidance.

[0287] Figure 6 The figure shows the relative distance between each pair of drones. It can be seen that the distance between drones converges to the expected value, and the minimum distance between drones is greater than the minimum safe distance, which means that the planned route is collision-free.

[0288] Figure 7 The speed of each drone is shown, including ground speed amplitude, track deviation angle, and track inclination. As can be seen, these variables fluctuate due to the collision avoidance maneuver, but they all meet the drone kinematic constraints. When the drone formation is not disturbed by obstacles, the speeds of each drone are accurately consistent.

[0289] The change rate of the UAV's track deflection angle and track inclination angle is as follows: Figure 8 The dotted lines in the figure indicate the allowable range of the corresponding variables. It can be seen that throughout the formation flight process, the angle change rate of the UAVs can meet the kinematic constraints.

[0290] Figure 9 The following table shows the control input of each UAV, i.e. the control input along the track system O k x k y k z k Overloads on the three axes. The dashed lines represent the upper and lower bounds of the corresponding overloads. It can be seen that the actual overloads are strictly constrained within the allowable range, and the changes in overloads are relatively smooth.

[0291] The FIFDS parameters during formation flying are as follows: Figure 10 As shown in Figure 2, the algorithm parameters can be adaptively adjusted online according to the collision risk, thereby achieving moderate avoidance maneuvers and improving the quality of the planned route.

[0292] In order to verify the effectiveness of FIFDS and MEMS respectively, this paper selects two groups of methods for comparison: the first group of comparison methods combines the formation keeping method proposed in recent years with the IFDS method based on moderate avoidance maneuvering strategy, the former including the converging flow speed adjustment strategy (OFSAS) and the initial reference speed (ORV). The second group of comparison methods combines FIFDS with the traditional RHC method, the latter is used to calculate ρ i and θ i Online optimization was performed. The RHC solver selected was the classic particle swarm optimization (PSO) algorithm. To ensure a fair comparison, all other relevant settings of the compared methods were identical to those of the method proposed in this paper, including planning step size, kinematic constraints, etc.

[0293] The comparison of the formation collision avoidance performance indicators and average single-step calculation time of different methods are as follows: Figure 11 and Figure 12 As shown, it should be noted that when the rolling time domain N = 1 in the comparison method, the performance index reaches positive infinity due to collision avoidance failure, and the simulation ends prematurely. Under the same collision avoidance method conditions, the performance index of the proposed method is better than that of the first group of comparison methods, indicating that FIFDS has certain advantages over existing methods in formation maintenance. As the rolling time domain increases, the performance index of the second group of comparison methods gradually decreases, but is still inferior to the proposed method, thus demonstrating the effectiveness of MEMS. From the FIFDS-RHC method with N = 5 to the proposed method, the average single-step calculation time is 0.4712s, 0.2842s, 0.0931s, 0.0126s, 0.0120s, and 0.0086s, respectively. It can be seen that due to the use of MEMS, the single-step calculation time of the proposed method and the first group of comparison methods is much shorter than that of the second group of comparison methods. In addition, compared with OFSAS and ORV, FIFDS has a slight advantage in computational efficiency due to its simpler form.

[0294] In summary, the proposed method can drive drones to perform appropriate evasive maneuvers in real time during formation flight, balancing flight safety and collision avoidance costs. In terms of both formation collision avoidance performance and computational efficiency, the proposed method significantly outperforms traditional methods.

Claims

1. A multi-UAV formation obstacle avoidance method based on disturbed fluid, characterized in that: The specific steps include: Step 1: N u The UAVs are divided into leaders and followers, numbered in sequence, and then the desired formation configuration is set; The pilot is designated manually based on the actual situation; Step 2: Acquire current airspace comprehensive information during the multi-UAV formation collision avoidance flight mission; Step 3: At the current sampling moment, determine whether the formation collision avoidance flight mission is completed. If so, the algorithm ends; otherwise, proceed to step 4. The mission is completed when the navigator reaches the target point with R d In the neighborhood of radius R d is the target point distance threshold; Step 4: For the i-th UAV, calculate the expected speed of the UAV without considering collision avoidance, that is, the confluence flow velocity; Step 5: For the i-th UAV, predict the collision risk of the UAV based on the current flight status of the UAV and the intruder; i=1,...,N u ;The minimum safe distance of the drone is d min ; Step 6: Based on the predicted collision risk of the i-th UAV, calculate the appropriate avoidance maneuver criterion for the UAV; The escape distance can be divided into local one-way escape distance Local complete escape distance Global one-way escape distance and the global complete escape distance in and The jth intruder aircraft arrives at the one-way non-avoidable zone and completely unavoidable areas The remaining distance; The criterion for moderate evasive maneuver is the global complete escape distance and global one-way escape distance Since the UAV should avoid collision with any intruder, the global one-way / complete escape distance should be the minimum of the local one-way / complete escape distances, that is: Among them, the local complete escape distance The calculation formula is: Step 7: Based on the appropriate avoidance maneuver criterion of the i-th UAV, optimize the IFDS parameters of the UAV; IFDS parameters include: reaction coefficient ρ i and the directional coefficient θ i ; ρ i It can be expressed as: θ i It can be expressed as: Directivity coefficient θ i Can be discretized into N θ sampling values, each sampling value corresponds to a planned overload n i , optimal overload and planning overload i The angle ζ between them is expressed as: Step 8: Combine the confluence velocity and IFDS parameters of the i-th UAV to calculate the disturbance velocity of the UAV, that is, the expected velocity of the UAV considering collision avoidance; The reaction coefficient and direction coefficient of each obstacle are taken to be the same value, that is, Considering the case of obstacle motion, use the sum perturbation matrix Corrected confluence velocity The following disturbed flow field velocity can be obtained in, is the weighted sum of obstacle velocities; u(p i ) is the convergent flow velocity of the i-th UAV; Step 9: Perform kinematic constraints on the flow velocity of the disturbed flow field, and obtain the constrained overload as the control input to plan the overload n i , and then get the feasible actual planning speed v of the UAV i ; Step 10: Use the planned speed v of the i-th UAV i Get the next desired waypoint corresponding to the UAV; The next expected waypoint of drone i is denoted as p i,next , whose expression is: p i,next =p i +v i ·ΔT (7) p i is the position of the i-th UAV; Step 11: Return to step 2 to plan the UAV formation collision avoidance flight route for the next sampling moment.

2. The multi-UAV formation obstacle avoidance method based on disturbed fluid according to claim 1, characterized in that: The airspace comprehensive information in step 2 includes: the position and ground speed vector of each UAV in the formation, the position, shape and size of each environmental obstacle, the relative motion information between the UAV and the intruder aircraft, and the formation collision avoidance performance index; The relative motion information includes: the distance r between the jth intruder and the ith drone ij and speed and the relative direction angle and relative elevation angle The formation collision avoidance performance indicators include: formation tracking error indicator, collision avoidance indicator, route length indicator, route smoothness indicator, and required overload indicator.

3. The multi-UAV formation obstacle avoidance method based on disturbed fluid according to claim 2, characterized in that: In step 4, the reference streamline is planned by the navigator; The navigator's cruising speed is V1 and its position is p1 = [x1, y1, z1] T , the position of the target point is p g =[x g ,y g ,z g ] T ; The confluence velocity u(p1) is the velocity from the pilot position p1 to the target point position p g The vector is expressed as: After correcting the confluence velocity u(p1), the planned velocity v1 of the navigator is obtained; For the i-th follower drone, i=2,...,N u , whose corresponding streamline is parallel to the planned velocity v1 and passes through the desired position of the UAV The expression is: Among them, l i is any point on the streamline of the i-th UAV, Δl is the straight line parameter, indicating that the point l i Relative to the desired position distance; The desired speed required for the follower to maintain the formation is the convergence flow velocity u(p i ) is expressed as: Among them, k1 and k2 are constant positive numbers. is the expected formation change rate, is a vector parallel to v1, is a vector orthogonal to v1, For p i The projection on the corresponding streamline, v c It is the navigator motion compensation item.

4. The multi-UAV formation obstacle avoidance method based on disturbed fluid according to claim 3, characterized in that: The step 5 specifically includes the following three three-dimensional dynamic collision zone models: 1) When the intruder is in the no-maneuver collision zone, if the UAV does not perform an evasive maneuver, a potential collision will occur; the boundary condition of the no-maneuver collision zone is that the potential collision will occur when the relative distance between the UAV and the intruder reaches the minimum, that is, the CPA distance is equal to the safety warning distance d s ; According to the relative motion information, and After that, the complete boundary value of the no-maneuver collision zone can be obtained according to the following formula: in: and V i are the ground speed amplitudes of the intruder and drone respectively, and γ i are the climb angles of the intruder and drone respectively, is the angle between the projection of the intruder ground speed vector on the horizontal plane and the x-axis of the relative system; 2) When the intruder is in the maximum maneuver collision zone, if the UAV takes a certain maneuver from zero to the maximum average overload maneuver, a potential collision will occur; n nmax is the maximum average normal overload of the UAV, n ymax and n zmax are the maximum overload components of the UAV along the y-axis and z-axis of the track system respectively; Assume that the horizontal and vertical accelerations of the i-th UAV during collision avoidance maneuvers are and Its positive direction is respectively r y r and O r z r The positive direction of is the same; therefore, and in is the average normal overload of the UAV, μ i is the speed roll angle, when the drone rolls to the right, μ i >0; For the following five typical maneuvers: horizontal left turn, climb and turn left, vertical climb, climb and turn right, horizontal right turn; speed roll angle μ i The values ​​of Similar to the non-maneuverable collision zone, the boundary condition of the maximum maneuverable collision zone can be expressed as: in, Can be expanded to: Obtain the unknown quantity r by iterative method ij and numerical solutions of Δt; Traversal and Then the complete maximum collision zone boundary value can be obtained; 3) The non-avoidable zone can be divided into a one-way non-avoidable zone and a completely non-avoidable zone, which represents the dividing line where the drone can avoid potential collisions under certain conditions; One-way unavoidable zone is the intersection of the no-maneuver collision zone and the maximum maneuver collision zone, where the subscript s∈S represents the maneuver direction, and S is the set of optional maneuver directions; Completely unavoidable area is the intersection of all one-way unavoidable areas; When the intruder is in a one-way non-avoidable zone When , if the UAV can only perform evasive maneuvers along direction s, a potential collision will occur; When the intruder is in a completely unavoidable area When the intruder is outside the area, the UAV can avoid potential collision by maneuvering; when the intruder is in the area and moving towards the UAV, no matter what possible maneuvers the UAV takes, it cannot avoid the occurrence of potential collision.

5. The multi-UAV formation obstacle avoidance method based on disturbed fluid according to claim 4, characterized in that: The step nine is specifically as follows: First, the pre-planned motion variables V that have not yet considered kinematic constraints are i p , and V i p Limit the speed to the allowable range [V min ,V max ]Inside; Assuming the planning step size is ΔT, calculate the motion variable V at the current moment i , χ i , γ i the expected rate of change; Then, the maximum turning rate and maximum climbing angular rate of the UAV are respectively and Perform clipping; According to the available overload range, the expected required overload is limited to obtain the constrained and Substituting back into the UAV kinematic model, the expected overload can be calculated Limit it to get a practical control input in: Actual planned speed v i Expressed as:

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