A distributed formation control method for multiple UAVs based on relative information

Abstract

The present invention discloses a distributed formation control method for a swarm of multiple unmanned aerial vehicles (UAVs) based on relative information. The method comprises the following steps: providing a controller in each UAV, excluding the pilot UAV; forming a formation of different UAVs using a topological diagram so that any UAV in the swarm can connect to the pilot UAV via at least one link; and, excluding the pilot UAV, using the controller to track the UAVs connected to their links, thereby enabling formation tracking of the pilot UAV by the swarm. The distributed formation control method for a swarm of multiple UAVs based on relative information disclosed by the present invention utilizes active measurement to control the UAV formation in complex electromagnetic environments or those with communication interference, thereby improving the formation control performance of the multi-UAV system in complex electromagnetic environments.

Description

Technical Field

[0001] The present invention relates to a distributed formation control method for a group of multiple unmanned aerial vehicles (UAVs) based on relative information, and belongs to the field of guidance control. Background Art

[0002] Rotor UAV control problems usually rely on communication to achieve formation control. If the drone is attacked by external forces or is in an electromagnetic interference environment, the control effect of the drone formation will be severely affected.

[0003] Therefore, it is necessary to study a method to realize UAV formation control under non-communication conditions. Summary of the Invention

[0004] To overcome the above problems, the inventors conducted in-depth research and designed a distributed formation control method for multiple UAV groups based on relative information, which includes the following steps:

[0005] S1. Set up a controller in each drone except the pilot drone.

[0006] S2. Use a topology map to form a formation of different drones so that any drone in the cluster can connect to the pilot drone through at least one link;

[0007] S3. Except for the pilot UAV, the remaining UAVs track the UAVs connected to their links through the controller, thereby realizing formation tracking of the pilot UAV by the cluster.

[0008] In a preferred embodiment, in S1, the controller includes thrust control and torque control. The thrust control part can be expressed as:

[0009] T i =m i ‖u ci ‖

[0010]

[0011]

[0012] Among them, T i represents the thrust required by the i-th UAV, g is the acceleration due to gravity, m i is the mass of the i-th UAV, R i is the rotation matrix of the i-th UAV, R ci is the control rotation matrix of the i-th UAV, u ci represents the control input of the i-th UAV, u i represents the thrust control quantity of the i-th UAV, Q is a positive definite matrix, K is the feedback gain matrix; β is a positive constant, is the adaptive coupling gain, ξ i represents the consistency error vector, Denotes the estimated value of consistency error, B[0 3×3 ,3×3] T .

[0013] In a preferred embodiment, the thrust required by the i-th UAV is T i Based on the kinematic and dynamic model design of the UAV, the kinematic and dynamic model of the i-th UAV is expressed as

[0014]

[0015]

[0016] Among them, is the position of the i-th UAV, and is the speed of the i-th UAV, g is the acceleration of gravity, m i is the mass of the i-th UAV, T i is the applied thrust of the i-th UAV, R i is the rotation matrix of the i-th UAV, is the angular velocity of the i-th UAV, is the inertia matrix of the i-th UAV, is the control torque of the i-th UAV, R ci is the control rotation matrix of the i-th UAV.

[0017] In a preferred embodiment, in thrust control, the thrust control amount u of the i-th UAV is i Expressed as:

[0018]

[0019] Where g is the acceleration due to gravity, m i is the mass of the i-th UAV, T i is the applied thrust of the i-th UAV, R i is the rotation matrix of the i-th UAV, R ci is the control rotation matrix of the i-th UAV, u ci represents the control input of the i-th UAV.

[0020] In a preferred embodiment, the consistency error vector ξ is estimated by using the relative state measurement information of the UAV through the state observer. i , and obtain the consistency error estimate Using consistent error estimates Design the controller to avoid using absolute state information of neighboring drones.

[0021] In a preferred embodiment, the state observer is expressed as:

[0022]

[0023] Where E=B[(CB) T CB] -1 (CB) T , G=I+EC, F is the feedback gain matrix and satisfies F(CI)=0, A, B, C are constant matrices, I represents the unit matrix, o i is the intermediate quantity of the process, I m represents an m*m unit matrix, j represents different drones, N represents the total number of drones in the drone cluster, a ij represents the adjacency state of UAV i and UAV j, δ ij represents the expected deviation between the i-th UAV and the j-th UAV, and the expected deviation includes position deviation and velocity deviation.

[0024] In a preferred embodiment, u is differentiated by a high-order synovial differentiator. ci and its derivatives to estimate the control angular velocity ω ci and ω ci Derivative, and then obtain the control torque τ of the controller i .

[0025] In a preferred embodiment, u is differentiated by a high-order synovial differentiator. ci The process of estimating and its derivative form can be expressed as:

[0026]

[0027]

[0028]

[0029] Where subscript k = x, y, z, represents different directions, i.e. u = u x ,u y ,u z ] T ; For u ci estimated value of; For estimated value of; For The estimated value of ; λ0, λ1, λ2 are positive constants.

[0030] In a preferred embodiment, in S1, the torque control part can be expressed as:

[0031]

[0032] η i =ω ei +k ε ε i ;

[0033]

[0034] Among them, τ i represents the control torque of the i-th UAV, k ε and k η is a positive constant, η i 、 is an intermediate variable;

[0035] ω i is the angular velocity vector of the i-th UAV, J i is the inertia matrix of the i-th UAV; ω ei is the error angular velocity of the i-th UAV, R ei is the error rotation matrix of the i-th UAV, I3 is the three-dimensional unit matrix, tr () represents the trace of the matrix, ω ci is the control angular velocity of the i-th UAV.

[0036] In a preferred embodiment, the control angular velocity and its derivative in the attitude control part are estimated, and the estimation result is used as the aircraft attitude control parameter at the next moment.

[0037] The beneficial effects of the present invention include:

[0038] (1) The present invention realizes the UAV formation control effect based on active measurement, relies on relative information measurement and estimation of system state quantity based on observer, and realizes the formation control effect based on adaptive distributed controller;

[0039] (2) In complex electromagnetic environments or environments with communication interference, UAV formation control is performed through active measurement, which improves the formation control performance of multi-UAV systems in complex electromagnetic environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A schematic flow chart of a method for controlling a distributed formation of multiple UAVs based on relative information according to a preferred embodiment of the present invention is shown;

[0041] Figure 2 The formation intention of 9 drones in Example 1 is shown;

[0042] Figure 3 The three-dimensional tracking evolution diagram of the formation in Example 1 is shown;

[0043] Figure 4 The figure shows the position error change diagram of the four drones in Example 1. DETAILED DESCRIPTION

[0044] The present invention will be described in further detail below with reference to the accompanying drawings and examples, through which the features and advantages of the present invention will become more clearly understood.

[0045] The word "exemplary" is used exclusively herein to mean "serving as an example, example, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise indicated.

[0046] According to the present invention, a distributed formation control method for a multi-UAV group based on relative information is provided, comprising the following steps:

[0047] S1. Set up a controller in each drone except the pilot drone.

[0048] S2. Use a topology map to form a formation of different drones so that any drone in the cluster can connect to the pilot drone through at least one link;

[0049] S3. Except for the pilot UAV, the remaining UAVs track the UAVs connected to their links through the controller, thereby realizing formation tracking of the pilot UAV by the cluster.

[0050] According to the present invention, in S1, the controller includes thrust control and torque control.

[0051] Furthermore, the thrust control produces a control effect on the position of the UAV. Furthermore, the thrust control can be expressed as:

[0052] T i =m i ‖u ci ‖

[0053]

[0054]

[0055] Among them, u i represents the thrust control quantity of the i-th UAV, Q is a positive definite matrix, K is the feedback gain matrix; β is a positive constant and satisfies Input upper bound for pilot drone control, is the adaptive coupling gain, and its initial value And its derivative satisfies where ξ i represents the consistency error vector, Represents the consistency error estimate.

[0056] According to a preferred embodiment of the present invention, the thrust control is performed using an adaptive controller, and the output of the adaptive controller is u i .

[0057] In the present invention, by setting a consistency error estimation value in thrust control, direct use of the absolute state quantity measured by the UAV is avoided, thereby improving control accuracy.

[0058] In a preferred embodiment, in the thrust control part, the inverse matrix of the positive definite matrix Q satisfies:

[0059] Q -1 A T +AQ -1 +Q -1 -2BB T <0

[0060] The feedback gain matrix K satisfies: K = B T Q.

[0061] In a preferred embodiment, the thrust required by the i-th UAV is T i and the required torque τ i The kinematic and dynamic models of the UAV are designed and expressed as follows:

[0062]

[0063]

[0064] Among them, is the position of the i-th UAV, and is the speed of the i-th UAV, g is the acceleration of gravity, m i is the mass of the i-th UAV, T i is the applied thrust of the i-th UAV, R i is the rotation matrix of the i-th UAV, is the angular velocity of the i-th UAV, is the inertia matrix of the i-th UAV, is the control torque of the i-th UAV, R ci is the control rotation matrix of the i-th UAV.

[0065] Further preferably, according to the above kinematic and dynamic models, the thrust control amount u of the i-th UAV is i Expressed as:

[0066]

[0067] Where g is the acceleration due to gravity, m i is the mass of the i-th UAV, T i is the thrust required by the i-th UAV, R i is the rotation matrix of the i-th UAV, R ci is the control rotation matrix of the i-th UAV, u ci represents the control input of the i-th UAV.

[0068] Furthermore, the required thrust can be expressed by T i =m i ‖u ci ‖ obtain, where The control rotation matrix can be expressed as follows

[0069]

[0070] Among them, u cxi 、u cyi 、u czi are the components of the control input of the i-th UAV on the x, y, and z axes respectively;

[0071] In order to simplify the expression, the position dynamics system state is expressed in the following form:

[0072]

[0073] Among them, x i =[p i ,v i ] T Represents the system state, y i represents the position dynamics output of the i-th UAV, C is a constant matrix, is the position of the i-th UAV, and is the speed of the i-th UAV, A and B are constant matrices.

[0074] In a preferred embodiment, the consistency error estimate in the controller is obtained through the state observer to obtain the estimated deviation between the current position of the drone and the expected position. The estimated deviation is used as the deviation, combined with the current position of the drone, to obtain the expected position of the drone at the next moment.

[0075] The thrust control proposed in the present invention can achieve the desired position output of the aircraft. Specifically, it can be proved by the following theoretical derivation:

[0076] In order to achieve posture tracking, the rotation matrix needs to converge to R ci And the angular velocity error ω ei satisfy The error rotation matrix and error angular velocity are defined as follows

[0077]

[0078]

[0079] Therefore R i =R ci Can be made by R ei =I3 represents, R ei The derivative of represent.

[0080] Definition 1: and Satisfies the following equation

[0081] tr(x × M)=-x T (MM T )

[0082] (x × M+M T x × ) ∨ =(tr(M)I3-M)x

[0083] According to Definition 1, we can get

[0084]

[0085] in

[0086] Definition 2: For a rotation matrix R, the following relationship exists

[0087]

[0088] tr(I3-R)=2(1-cosθ)

[0089] Based on Definition 2, we can know that if ε i =0, which means R ei =I3 or θ ei =π (which is what we don’t expect). By the equation tr(I3-R)=

[0090] 2(1-cosθ), we can use θei =π is converted to tr(I3-R ei )=4. Therefore, when And tr(I3-R ei )≠4, posture tracking is achieved.

[0091] Based on the attitude dynamics of the rotorcraft, we can get the following error attitude dynamics expression:

[0092]

[0093] According to the above analysis, the system control target can be obtained as follows:

[0094]

[0095] That is, if the controller meets the current conditions, it can achieve posture tracking control.

[0096] Based on the designed adaptive control rate, the consistency error derivative can be written as follows:

[0097]

[0098] Notice Therefore, the Written in the following form

[0099]

[0100] in

[0101] Consider the following Lyapunov equation

[0102]

[0103] in S is a positive definite matrix, and α1 and α2 are positive constants. Definition -X=-S(GA-FC)-(GA-FC) T S<0. When GA-FC is stable, it is easy to know that matrices D and S exist. is non-negative, so is non-decreasing. Therefore, we can get V p The derivative form of is as follows

[0104]

[0105] in Notice that there is

[0106]

[0107]

[0108] because We can get

[0109]

[0110]

[0111] Define W(QA+A T Q+Q-2QBB T Q, since the P matrix satisfies the conditions, it can be deduced that W>0. Therefore, we can get the following formula

[0112]

[0113] Other And there is

[0114]

[0115] make Choose α2 ≥ γλ max (S / λ min (X, α1≥α3+(α2+γ)α0, so

[0116]

[0117] Let α3 satisfy α3≥max{d i}λ max (QBB T Q / λ min (Q)λ0), we can get

[0118]

[0119] That is

[0120]

[0121] Therefore, by defining Can be written as

[0122]

[0123] Therefore, we know that V p (t、 are bounded, which means that ψ and are all bounded. Since u N is bounded, meaning is also bounded, so it is obvious that is bounded. So V pNon-increasing and positive. We can infer The limit is finite. Integrating the above formula gives the following formula

[0124]

[0125] Therefore, it can be known Finite. Since ψ and is bounded, so it can be deduced that The derivative of is also bounded. This means is uniformly continuous. According to Barbara's definition, when t→∞, Therefore, we know that ψ→0, Hence consistency tracking is achieved.

[0126] Further preferably, the state observer is expressed as:

[0127]

[0128] Where E=B[(CB) T CB] -1 (CB) T , G=I+EC, F is the feedback gain matrix and satisfies F(CI)=0, I represents the unit matrix, o i It is an intermediate quantity in the process and has no physical meaning. m represents an m*m unit matrix, j represents different drones, N represents the total number of drones in the drone cluster, a ij represents the adjacency state of UAV i and UAV j, δ ij represents the expected deviation between the i-th UAV and the j-th UAV, and the expected deviation includes position deviation and velocity deviation.

[0129] Furthermore, the expected deviation between the i-th UAV and the j-th UAV can be expressed as:

[0130] δ ij =δ i -δ j

[0131] Among them, δ i represents the expectation of the i-th drone, δ j represents the expectation of the j-th UAV, is the expected position of the i-th UAV, is the expected speed of the i-th UAV, δ j Same thing.

[0132] The state observer proposed in the present invention has extremely high stability, which can be proved by the following theoretical derivation:

[0133] Definition of the estimated error of the consistency error So we can get the estimation error dynamics

[0134]

[0135] Note that (EC+I)B=0 and F(CI)=0. If δ v = 0, we have

[0136]

[0137] The estimation error dynamics can thus be transformed into

[0138]

[0139] Consider a candidate Lyapunov function It is easy to prove that when GA-FC is stable, e i It gradually converges to 0, that is, the observer can obtain the observation results stably.

[0140] In a preferred embodiment, u is differentiated by a high-order synovial differentiator. ci and its derivatives to estimate the control angular velocity ω ci and ω ci Derivative, and then obtain the control torque τ of the controller i .

[0141] In a preferred embodiment, the thrust controller output u is estimated by a high-order sliding film differentiator i The process of its derivatives can be expressed as:

[0142]

[0143]

[0144]

[0145] Where subscript k = x, y, z, represents different directions, i.e. u = u x ,u y ,u z ] T ; For u ci estimated value of; For estimated value of; For The estimated value of ; λ0, λ1, λ2 are positive constants.

[0146] In a preferred embodiment, in S1, the torque control can be expressed as:

[0147]

[0148] η i =ω ei +k ε ε i ;

[0149]

[0150] Among them, τ i represents the control torque of the i-th UAV, k ε and k η is a positive constant, η i represents the error vector, is the intermediate variable; ω i is the angular velocity vector of the i-th UAV, J i is the inertia matrix of the i-th UAV; ω ei is the error angular velocity of the i-th UAV, R ei is the error rotation matrix of the i-th UAV, I3 is the three-dimensional unit matrix, I3∈R 3×3 , tr(represents the trace of the matrix, ω ci is the control angular velocity of the i-th UAV.

[0151] Furthermore, according to η i =ω ei +k ε ε i , we can get

[0152]

[0153] Furthermore, the following expression can be obtained:

[0154]

[0155] Furthermore, according to the control torque, we can get The expression:

[0156]

[0157] In a preferred embodiment, the error rotation matrix R of the i-th UAV is ei It can be expressed as

[0158]

[0159] The error angular velocity ω of the i-th UAV ei It can be expressed as:

[0160]

[0161] in, is the angular velocity of the i-th UAV, is the inertia matrix of the i-th UAV, is the control torque of the i-th UAV.

[0162] The torque control proposed in the present invention can effectively achieve autonomous attitude control of the aircraft. Specifically, it can be proved by the following theoretical derivation:

[0163] Design the following Lyapunov function

[0164]

[0165] Taking the derivative of the above Lyapunov function, we can get

[0166]

[0167] According to Definition 2, we can get the following inequality

[0168]

[0169] Therefore, it is possible to Simplify and get

[0170]

[0171] where ι i =min{k ε ,2k η / λ(J i )}. Therefore,

[0172]

[0173] This means that there and Therefore, it can be inferred that Since η i =ω ei +k ε ε i , so we can get In addition, from the above formula we can get

[0174]

[0175] Therefore, it is easy to obtain tr(I3-R ei ≠4). Prove that the proposed posture dynamics form is obtained if the initial rotation matrix satisfies tr(I3-R ei(0) )∈[0,4), the proposed applied force formula can achieve and And tr(I3-R ei )≠4.

[0176] According to a preferred embodiment of the present invention, the control angular velocity and its derivative in the torque control are calculated, and the calculation results are used as the aircraft attitude control parameters at the next moment.

[0177] Further preferably, the control angular velocity and its derivative are expressed as:

[0178]

[0179]

[0180] Among them, the control rotation matrix R ci Expressed as:

[0181]

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188] Among them, R i1 、R i2 、R i3 , σ i 、φ i 、 Θ i , Π, Λ i is the intermediate parameter.

[0189] According to the present invention, in S2, a directed graph is used to construct the topological structure of the UAV formation, such as Figure 2 As shown, it is used to indicate whether there is a path for obtaining information between drones.

[0190] A directed graph is a commonly used form in graph theory. The specific process of constructing a directed graph is a conventional technical means in this field and will not be described in detail in the present invention.

[0191] In the present invention, represents a directed graph, where and are the node set and edge set respectively. Edge (i, j)∈ε means that node i is a neighbor of node j, that is, node j can obtain information from node i. Represents the neighbor set of node i. If there is an ordered edge (i k ,i k+1 ),k=1,…,p-1, then we believe that node i1 has p The direct path of The adjacency matrix It has the following characteristics: (1) a ii =0; (2) If (j,i)∈ε then a ij >0; (3) otherwise a ij = 0. Laplace matrix There are the following definitions, l ij =-a ij ,i≠j, definition As the neighbor set of node i.

[0192] In S3, the drone's own position and speed, the relative position and speed between the drone and the adjacent drones obtained through measurement, and the drone's own attitude information are input into the drone's controller, and the controller outputs the required thrust and torque of the drone at the next moment. Each drone tracks other drones and adjusts their flight attitude based on the thrust and torque, thereby achieving formation tracking of the leading drone.

[0193] Example

[0194] Example 1

[0195] In the simulation experiment, 9 drones were used to form a cluster for formation control. The tracking trajectory of the leader was designed as follows

[0196]

[0197] where p x0 , p y0 With p z0 They are the initial position of the navigator, set at the origin of the coordinate system.

[0198] The formation control is performed by the following steps:

[0199] S1. Except for the pilot drone, each of the remaining drones is equipped with a controller.

[0200] S2. Design a directed topology graph so that a directed spanning tree exists, that is, any UAV in the cluster can connect to the pilot UAV through at least one link;

[0201] S3. Except for the pilot UAV, the remaining UAVs track the UAVs connected to their links through the controller, thereby realizing formation tracking of the pilot UAV by the cluster.

[0202] In S1, the controller includes thrust control and torque control. The thrust control can be expressed as

[0203]

[0204] in,

[0205] The estimated output of the consistency error in the controller is obtained through the state observer, and the current consistency error of the drone is obtained. The estimated value is used as the actual value, combined with the current position of the drone, to obtain the required thrust of the drone at the next moment.

[0206] The state observer is expressed as:

[0207]

[0208] in,

[0209] Since the control torque design process uses the control angular velocity and its derivative, the control angular velocity and its derivative need to be controlled by the thrust controller u i And its derivative is obtained. Because its expression is complex and difficult to obtain, it is estimated based on the high-order synovial differentiator i The estimation process of its derivatives can be expressed as:

[0210]

[0211]

[0212]

[0213] In S1, the torque control can be expressed as:

[0214]

[0215] η i =ω ei +k ε ε i ;

[0216]

[0217] Among them, k η =2,k ε =2.

[0218] The control angular velocity and its derivative in torque control are calculated, and the calculation results are used as the aircraft attitude control parameters at the next moment.

[0219] In S2, a directed graph is used to construct a UAV formation, and the result is as follows: Figure 2shown.

[0220] The final tracking effect is as follows Figure 3 As shown in the figure, it can be seen that the cluster can effectively and stably track the flight trajectory of the pilot aircraft.

[0221] Figure 4 The figure shows the formation tracking error curve of four drones in the cluster. As can be seen from the figure, when tracking starts, the drones will have a small tracking error, but the maximum error is less than 0.7 meters. After 5 seconds, the drones in the cluster can accurately track the pilot aircraft.

[0222] In the description of the present invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front," and "rear" and the like, indicating positions or locations, are based on the operating state of the present invention and are intended solely to facilitate and simplify the description of the present invention. They are not intended to indicate or imply that the devices or components referred to must have, be constructed, or operate in a specific orientation, and therefore should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0223] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention in specific contexts.

[0224] The present invention has been described above with reference to preferred embodiments, but these embodiments are merely exemplary and serve only as illustrations. On this basis, various replacements and improvements can be made to the present invention, all of which fall within the scope of protection of the present invention.

Claims

1. A distributed formation control method for multiple UAVs based on relative information, characterized in that: The following steps are involved: S1. Set up a controller in each drone except the pilot drone. S2. Use a topology map to form a formation of different drones so that any drone in the cluster can connect to the pilot drone through at least one link; S3. Except for the pilot drone, the remaining drones track the drones connected to their links through the controller, thereby achieving formation tracking of the pilot drone by the cluster; In S1, the controller includes thrust control and torque control, and the thrust control is expressed as: T i =m i ‖u ci ‖ Among them, T i represents the thrust required by the i-th UAV, g is the acceleration due to gravity, m i is the mass of the i-th UAV, R i is the rotation matrix of the i-th UAV, R ci is the control rotation matrix of the i-th UAV, u ci represents the control input of the i-th UAV, u i represents the thrust control quantity of the i-th UAV, Q is a positive definite matrix, K is the feedback gain matrix; β is a positive constant, is the adaptive coupling gain, ξ i represents the consistency error vector, Denotes the estimated value of consistency error, B=[0 3×3 ,I 3×3 ] T ; Among them, the consistency error estimate is obtained by using the relative state measurement information of the UAV through the state observer This avoids the use of absolute status information of adjacent drones. The state observer is expressed as: Where E = -B[(CB) T CB] -1 (CB) T , G=I+EC, F is the feedback gain matrix and satisfies F(CI)=0, A, B, C are constant matrices, I represents the unit matrix, o i is the intermediate quantity of the process, I m represents an m*m unit matrix, j represents different drones, N represents the total number of drones in the drone cluster, a ij represents the adjacency state of UAV i and UAV j, δ ij represents the expected deviation between the i-th UAV and the j-th UAV, which includes position deviation and velocity deviation, y i Represents the position dynamics output of the i-th UAV, y j represents the j-th UAV position dynamics output; In S1, the torque control is expressed as: or i =ω ei +k ε e i ; Among them, τ i represents the control torque of the i-th UAV, k ε and k η is a positive constant, η i 、 is an intermediate variable; ω i is the angular velocity vector of the i-th UAV, J i is the inertia matrix of the i-th UAV; ω ei is the error angular velocity of the i-th UAV, R ei is the error rotation matrix of the i-th UAV, I3 is the three-dimensional unit matrix, tr() represents the trace of the matrix, ω ci is the control angular velocity of the i-th UAV.

2. The method for controlling a multi-UAV swarm distributed formation based on relative information according to claim 1, characterized in that: The thrust T required by the i-th UAV i Based on the kinematic and dynamic model design of the UAV, the kinematic and dynamic model of the i-th UAV is expressed as Among them, is the position of the i-th UAV, and is the speed of the i-th UAV, g is the acceleration of gravity, m i is the mass of the i-th UAV, T i is the applied thrust of the i-th UAV, R i is the rotation matrix of the i-th UAV, is the angular velocity of the i-th UAV, is the inertia matrix of the i-th UAV, is the control torque of the i-th UAV, R ci is the control rotation matrix of the i-th UAV.

3. The method for controlling a multi-UAV swarm distributed formation based on relative information according to claim 1, characterized in that: Through the high-order synovial differentiator, u ci and its derivatives to estimate the control angular velocity ω ci and ω ci Derivative, and then obtain the control torque τ of the controller i .

4. The method for controlling a multi-UAV swarm distributed formation based on relative information according to claim 3, characterized in that: Through the high-order synovial differentiator, u ci The process of estimating its derivative form is expressed as: Wherein, subscript k = x, y, z, represents different directions, i.e. u = [u x ,u y ,u z ] T ; For u ci estimated value of; For estimated value of; For The estimated value of ; λ0, λ1, λ2 are positive constants.

5. The method for controlling a multi-UAV swarm distributed formation based on relative information according to claim 1, characterized in that: The control angular velocity and its derivative in torque control are estimated, and the estimation results are used as the aircraft attitude control parameters at the next moment.

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