A distributed cooperative formation control method for space parameterized formation flying

Abstract

The application discloses a kind of distributed cooperative formation control methods of space parameterization fly-around formation, comprising: determining cluster individual number, each individual dynamics model, target configuration parameter evolution model, each individual initial position and velocity, target configuration mathematical model and each individual target configuration parameter initial value;Based on target configuration mathematical model, determine each individual target position expression;Design cluster target configuration parameter cooperative control law, calculate each individual target configuration parameter under current time, into each individual target position expression, calculate each individual target position estimated value under current time;Design cluster motion control law, based on each individual dynamics model, each individual target position and each individual target position estimated value under current time, carry out cluster motion simulation.The application avoids the communication bandwidth pressure caused by establishing communication relationship with all individuals of cluster, adapts to the need of real-time change of target configuration.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of intelligent agent / unmanned aerial vehicle / spacecraft cluster motion control, and relates to a distributed cooperative formation control method for a space parameterized fly-around formation. BACKGROUND

[0002] In real cluster motion control of unmanned aerial vehicles, spacecrafts and the like, formation formation control is an important research aspect thereof, and has important application value in the fields of regional cooperative detection, cooperative transportation and the like. However, the traditional formation formation control algorithm depends on the pre-determination of the absolute or relative target position of each individual, and even the distributed control algorithm also depends on the accurate knowledge of the final configuration shape of each individual, and it is difficult to temporarily change the formation configuration shape. In real tasks, the pre-set formation configuration may not meet the needs of the target task (such as intersecting with environmental obstacles), and often needs to transmit new target configuration information to the cluster. However, the centralized target configuration updating strategy which depends on the communication with each individual of the cluster depends on a large communication bandwidth, and is easy to fail due to the interruption of the communication relationship with individual individuals. SUMMARY

[0003] The purpose of the present application is to solve the problems in the prior art, and to provide a distributed cooperative formation control method for a space parameterized fly-around formation, which overcomes the shortcomings of the prior art that the prior formation formation control research depends on the pre-accurate knowledge of the target configuration of each individual and is difficult to perform real-time configuration reconstruction.

[0004] To achieve the above purpose, the following technical scheme is adopted in the present application:

[0005] A distributed cooperative formation control method for a space parameterized fly-around formation, comprising the following steps:

[0006] Determine the number of cluster individuals, the dynamics model of each individual, the initial position and velocity of each individual, the target configuration mathematical model, the target configuration parameter evolution model and the initial value of the target configuration parameter of each individual;

[0007] Based on the target configuration mathematical model, determine the target position expression of each individual;

[0008] Design a cluster target configuration parameter cooperative control law, based on the target configuration parameter evolution model and the initial value of the target configuration parameter of each individual, calculate the target configuration parameter of each individual at the current time, and bring the target configuration parameter of each individual at the current time into the target position expression of each individual to calculate the target position estimation value of each individual at the current time;

[0009] Design a cluster motion control law, based on the dynamics model of each individual, the target position of each individual and the target position estimation value of each individual at the current time, and perform cluster motion simulation.

[0010] Further, the individual dynamic model is:

[0011]

[0012] wherein n is the number of individuals in the swarm, is the position vector of individual i at time t, is the velocity vector of individual i at time t, f(ξ i (t), ζ i (t)) is a function with value range R 3×1 is the open-loop dynamic function of individual, U i (t)∈R 3×1 is the control variable of individual i at time t.

[0013] Further, the target configuration mathematical model is:

[0014] c(θ; p1, p2,..., p n )

[0015] wherein θ∈R is the curve coordinate parameter, p1, p2,..., p n are shape parameters, and (p1, p2, p3) is the curve center coordinate, when p1, p2,..., p n are given, the target configuration curve can be uniquely determined, and when θ is given, a point on the target configuration curve can be uniquely determined.

[0016] Further, the target configuration mathematical model satisfies the following periodicity condition, so that the target configuration curve forms a closed curve:

[0017] c(θ+T; p1, p2,..., p n ) = c(θ; p1, p2,..., p n )

[0018] wherein T is a constant.

[0019] Further, the target configuration mathematical model satisfies the following shrinkage condition:

[0020]

[0021] that is, when all the target configuration curve shape parameters except p1, p2, and p3 are taken as 0, the target configuration curve degenerates into the curve center coordinate.

[0022] Further, the target configuration parameter evolution model is

[0023]

[0024] wherein p i(t) is the individual target configuration parameter at current time t, is the cluster target configuration parameter to be designed.

[0025] Further, the individual target position expression is:

[0026]

[0027] where θ is the curve coordinate parameter, p1, p2,..., p n is the shape parameter, is the estimated value of the individual i to each shape parameter of the target configuration curve at time t, which can be recorded as vector

[0028] Further, the initial value of the individual target configuration parameter is solved by the following optimization problem:

[0029]

[0030] In the case of (p1, p2, p3) being the curve center coordinates, take p i (0) as

[0031]

[0032] Further, the cluster target configuration parameter cooperative control law is:

[0033]

[0034] where c i >0 is the cooperative coefficient, g i is the restraint coefficient, a ij corresponds to the cluster communication network topology (if the individual i can obtain the information of the individual j, then a ij =1, otherwise a ij =0), g i corresponds to the leading / following role of each individual in the cluster (for the leader, g i >0, otherwise g i =0).

[0035] Further, the cluster motion control law is:

[0036]

[0037] where k p is the position feedback coefficient, k v is the speed feedback coefficient, is the inter-individual collision avoidance term, which is in the following form:

[0038]

[0039] wherein, denotes the gradient of the corresponding function at the current position of the individual i, V ij (t) is the collision avoidance potential between individuals i and j (i, j = 1, 2,..., n, i≠j) and has the form:

[0040]

[0041] wherein, c c is the inter-individual avoidance coefficient, D c is the inter-individual avoidance detection distance.

[0042] Compared with the prior art, the present application has the following beneficial effects:

[0043] The present application provides a distributed cooperative formation control method for a spatial parameterized fly-around formation, specifies a target configuration mathematical model, and then makes the cognition of each individual to the target configuration asymptotically consistent through a cluster target configuration parameter cooperative control law, without the need for all individuals in the cluster to know the accurate shape of the target configuration and determine their own target positions according to the target configuration. As long as part of the individuals (i.e. the leaders) know the target configuration parameters, the formation configuration parameters can be negotiated and agreed within the connected branch where the leaders are located, and converge to the designed target configuration parameters, thereby realizing the real distributed formation control. Therefore, if the target configuration of the cluster needs to be temporarily changed, the new target configuration parameters can be informed to the leaders, and each individual in the cluster can asymptotically converge to the target position determined by their own target configuration cognition, so that the cluster forms a fly-around configuration around the specified point in a distributed manner, meeting the need for no difference formation of the changed target configuration in actual tasks. The present application overcomes the shortcomings of the prior art formation control research, which relies on the pre-accurate cognition of each individual to the target configuration and is difficult to perform real-time configuration reconstruction, avoids the communication bandwidth pressure caused by the communication relationship with all individuals in the cluster, and adapts to the need for real-time change of the target configuration in actual tasks, and the new target configuration can still be accurately formed by only informing a small number of individuals in the cluster of the new target configuration parameters. BRIEF DESCRIPTION OF DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0045] Figure 1 The present application is a distributed cooperative formation control method for a spatial parameterized fly-around formation.

[0046] Figure 2 A cluster communication network topology diagram in Embodiment One of the present application.

[0047] Figure 3 A motion trajectory of each individual target position estimate value of the cluster in Embodiment One of the present application.

[0048] Figure 4 A cluster motion trajectory diagram in Embodiment One of the present application.

[0049] Figure 5 A cluster individual control quantity modulus value change diagram in Embodiment One of the present application.

[0050] Figure 6 A cluster individual position error modulus value change diagram in Embodiment One of the present application.

[0051] Figure 7 A cluster inter-individual minimum distance change diagram in Embodiment One of the present application.

[0052] Figure 8 A cluster communication network topology diagram in Embodiment Two of the present application.

[0053] Figure 9 A motion trajectory of each individual target position estimate value of the cluster in Embodiment Two of the present application.

[0054] Figure 10 A cluster motion trajectory diagram in Embodiment Two of the present application.

[0055] Figure 11 A cluster individual control quantity modulus value change diagram in Embodiment Two of the present application.

[0056] Figure 12 A cluster individual position error modulus value change diagram in Embodiment Two of the present application.

[0057] Figure 13 A cluster inter-individual minimum distance change diagram in Embodiment Two of the present application. DETAILED DESCRIPTION

[0058] Exemplary embodiments of the present application are described herein with reference to the accompanying drawings, which are meant to be exemplary and not limiting. Therefore, it should be recognized that many modifications and variations of the exemplary embodiments described herein can be made without departing from the scope and spirit of the application. Also, for the purpose of clarity and the brevity of description, the description of well-known functions and constructions are omitted herein.

[0059] Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0060] It should be noted that the terminal involved in the embodiments of the present application can include, but is not limited to, a mobile phone, a personal digital assistant (PDA), a wireless handheld device, a tablet computer, a personal computer (PC), an MP3 player, an MP4 player, a wearable device (for example, smart glasses, a smart watch, a smart bracelet, etc.), a smart home device, and the like.

[0061] In addition, the term "and / or" in this paper is only to describe the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / " in this paper generally represents that the front and rear associated objects are in an "or" relationship.

[0062] The present application will be described in further detail below with reference to the accompanying drawings:

[0063] Referring to Figure 1 The present application provides a distributed cooperative formation control method for a spatial parameterized formation, comprising the following steps:

[0064] S1: determining the number of cluster individuals, the individual dynamics model, the initial position and velocity of each individual, the target configuration mathematical model, the target configuration parameter evolution model, and the initial value of the target configuration parameter of each individual.

[0065] In order to be compatible with different clusters such as spacecrafts and unmanned aerial vehicles, and at the same time be compatible with accurate, approximately accurate or linearized dynamics models, the individual dynamics model can be uniformly described as the following second-order system:

[0066]

[0067] Wherein, n is the number of cluster individuals, is the position vector of individual i at time t, is the velocity vector of individual i at time t, f(ξ i (t), ζ i (t)) is a function with a value range of R 3×1 is the open-loop dynamics function of the individual, U i (t) is a control variable of individual i at time t. 3×1

[0068] ​The initial position vector of individual i is denoted as ξ i The initial velocity vector of individual i is denoted as ζ i (0).

[0069] The mathematical model of the target configuration is given in the form of c(θ; p1, p2,..., p n ), where θ ∈ R is the curve coordinate parameter, and p1, p2,..., p n are shape parameters, where (p1, p2, p3) is the curve center coordinate. When p1, p2,..., p n are given, the target configuration curve can be uniquely determined. Further, when θ is given, a point on the target configuration curve can be uniquely determined.

[0070] The mathematical model of the target configuration satisfies the following periodicity condition (T is a certain constant):

[0071] c(θ + T; p1, p2,..., p n ) = c(θ; p1, p2,..., p n ) (2)

[0072] So that the target configuration curve forms a closed curve, and further, the swarm can realize the fly-around of the specified point at the target configuration. And the mathematical model of the target configuration satisfies the following shrinkage condition:

[0073]

[0074] That is, when all the shape parameters of the target configuration curve except p1, p2, p3 are taken as 0, the target configuration curve degenerates into the curve center coordinate (i.e., the line degenerates into the point).

[0075] The set of target configuration parameters P is taken as S = {p1, p2,..., p n} (i.e., all the shape parameters of the target configuration curve), or denoted as vector p = (p1, p2,..., p n ). If some parameters take certain values, these parameters constitute a set S', then the set of target configuration parameters is taken as P = S - S' (i.e., in the case where some shape parameters are given, remove these given shape parameters from the target configuration parameters). So that in the case where the structure of the target configuration curve equation is given, the specific values of a group of target configuration parameters can uniquely determine the target configuration curve.

[0076] The evolution model of the target configuration parameters is

[0077]

[0078] where, p i (t)Determine the target configuration parameters of each individual at the current time.

[0079] S2: Determine the target position of each individual based on the target configuration mathematical model.

[0080] In order to make the final position of the cluster along the curve coordinate parameter θ uniformly distributed, the target position of individual i at time t is taken as:

[0081]

[0082] where c(θ; p1, p2,..., p n ) is a curve equation, θ is a curve coordinate parameter, p1, p2,..., p n are shape parameters, is the estimated value of each shape parameter of the target configuration curve of individual i at time t, which can be denoted as a vector

[0083] S3: Design a cluster target configuration parameter cooperative control law, based on the target configuration mathematical model and the initial value of the target configuration parameter of each individual, calculate the target configuration parameter of each individual at the current time, and bring the target configuration parameter of each individual at the current time into the target configuration mathematical model to calculate the estimated value of the target position of each individual at the current time.

[0084] In principle, the initial value of the target configuration parameter of each individual can be arbitrarily set, and under the action of the control law, the final target configuration parameter can always converge to the expected target configuration parameter. However, in order to reduce the initial value of the control amount of individual i, a suitable p i (0) should be selected as much as possible to minimize the initial position error of individual i. Generally, p i (0) can be determined by solving the following optimization problem:

[0085]

[0086] In the case of (p1, p2, p3) as the center coordinates of the curve, p i (0) can be taken as

[0087]

[0088] Specifically, the cluster target configuration parameter cooperative control law can be designed in the form of the first-order consensus tracking algorithm as follows:

[0089]

[0090] where c i >0 is a cooperative coefficient, g i is a restraint coefficient. a ijcorresponding to the communication topology of the swarm (a ij = 1 if individual i has access to the information of individual j, otherwise a ij = 0), g i corresponding to the leader / follower role of each individual in the swarm (g i > 0 if individual i is a leader, i.e. has access to the desired target configuration parameter vector p, otherwise g i = 0). Each connected component of the communication topology of the swarm has at least one leader.

[0091] Based on the initial value problem of the differential equation consisting of the swarm target configuration parameter cooperative control law, the target configuration parameter evolution model shown in equation (4) and the initial value of the target configuration parameter of each individual p i (0), the following integral form of the target configuration parameter of each individual at the current time p i (t) can be obtained

[0092]

[0093] Substitute the obtained p i (t) into the expression of the target position of each individual shown in equation (5), and the estimated value of the target position of individual i at the current time is obtained.

[0094] S4: design the swarm motion control law, and perform swarm motion simulation based on the individual dynamics model, the target position of each individual and the estimated value of the target position of each individual at the current time.

[0095] Specifically, the swarm motion control law can be designed in the following form according to proportional-differential control:

[0096]

[0097] where k p is the position feedback coefficient, k v is the velocity feedback coefficient, is the collision avoidance term between individuals, which can be designed in the following form:

[0098]

[0099] where denotes the gradient of the corresponding function at the current position of individual i, V ij (t) is the collision avoidance potential between individual i and j (i, j = 1, 2,..., n, i≠j), which can be designed in the following form:

[0100]

[0101] where c c is the collision avoidance coefficient between individuals, and Dc To avoid detection distance between individuals.

[0102] Perform cluster motion simulation to determine if the cluster motion meets user requirements. If not, adjust the control law parameters (including c). i g i k p k v c c D c (This continues until the cluster movement meets the user's needs.)

[0103] Example 1: Formation of Elliptical Flight Formation of Spacecraft Cluster

[0104] S1: Determine the number of individuals n in the cluster, the dynamic model of each individual, the initial position and velocity of each individual, the mathematical model of the target configuration, the evolution model of the target configuration parameters, and the initial values ​​of the target configuration parameters for each individual.

[0105] Specifically, the number of individuals in the cluster is n = 10, and the dynamic model of each individual is expressed in the following form according to the CW equation:

[0106]

[0107] in, ω is the angular velocity of the reference spacecraft's orbit around the Earth (taken as 1.131 × 10⁻⁶ m at an orbital altitude of 400 m). -3 rad / s), U(t) is the control variable to be designed. The initial positions of each body are randomly distributed within the interval [-40m, 40m] × [-40m, 40m] × [-40m, 40m], and the initial velocity of each body is 0. Based on the mathematical model of the target configuration, the target configuration curve is taken as an ellipse as shown in the following equation:

[0108] c(θ)=ξ C +acosθ+bsinθ (13)

[0109] Where, ξ C Let a, b be the center vector, major axis vector, and minor axis vector of the ellipse, respectively, and ||a|| > ||b||, and a⊥b. Specifically, let ξ be taken here. C =(0,0,0), a=(20m,0,20m), b=(0,40m,0).

[0110] For the cluster target configuration parameters, since it can be seen from the configuration curve equation that the target configuration curve can be determined by 9 parameters (i.e., ξ). C The three components The three components of a x ,a y ,a z b has 3 components.x ,b y ,b z ) unique, thus set the target configuration parameter vector as

[0111] For each individual target configuration parameter initial value, in order to minimize the initial position error of individual i , reduce the initial control amplitude, a feasible solution is to take Ci (0) = ξ i (0), a i (0) = 0 3×1 , b i (0) = 0 3×1 , at this time , that is, the initial position error of individual i is 0. The corresponding individual i target configuration parameter estimation vector initial value

[0112] S2: Determine the individual target position expression based on the target configuration curve equation.

[0113] In order to make the final position of the swarm uniformly distributed along the curve coordinate parameter θ, the target position of individual i at time t is taken as

[0114]

[0115] Wherein, are the estimation values of individual i for ξ C , a, b at time t, which can be collectively expressed as the individual i target configuration parameter estimation vector , which represents the cognition of individual i for the target configuration at time t.

[0116] S3: Design the swarm target configuration parameter cooperative control law. Specifically, for the p i (t) dynamics system shown in formula (4), the individual target configuration parameter cooperative control law in the following form can be designed:

[0117]

[0118] Wherein, the cooperative coefficient c i = 0.005s -2 , the restraint coefficient g i = 0.005s -2 (the leader) or g i = 0s -2 (the follower). The two-way communication relationship between individuals is established with a probability of , thereby forming a swarm communication network topology, as shown in Figure 2 , and a leader is randomly assigned to each connected branch (corresponding toFigure 2 The restraining coefficient of the middle triangle node is taken as 0.005s -2 The restraining coefficient of other individuals is taken as 0s -2 .

[0119] Based on the initial value problem of the differential equation composed of the above-mentioned cluster target configuration parameter cooperative control law, the target configuration parameter evolution model shown in formula (4), and the initial value p i (0) of each individual target configuration parameter, the following integral form of the current time of each individual target configuration parameter p i (t) formula can be obtained

[0120]

[0121] Substitute the obtained p i (t) into the individual target position expression shown in formula (5), and the target position estimation value of individual i at the current time is obtained.

[0122] In order to intuitively display the above-mentioned calculation results, the motion trajectory of the target position estimation value of each individual at each time can be drawn, as shown in Figure 3 The hollow circle point represents the initial value of the target position of each individual (coinciding with the initial position of each individual), and the pentagram represents the final value of the target position of each individual determined by the target configuration mathematical model and the target configuration parameter.

[0123] S4: Design the cluster motion control law. Specifically, it can be designed in the following form according to the proportional-differential control:

[0124]

[0125] Wherein, the position feedback coefficient k p = 10 -4 s -2 , the velocity feedback coefficient k v = 10 -2 s -1 . The inter-individual collision avoidance term is designed according to formula (10), wherein the inter-individual avoidance coefficient c c = 1m 4 / s 2 , and the inter-individual avoidance detection distance D c = 10m.

[0126] Based on the cluster individual dynamics model (12), the target position of each individual, the target position estimation value of each individual at the current time, and the designed cluster motion control law (16), the cluster motion simulation is carried out, the cluster motion time is taken as 40000s, and the simulation result shown in Figures 4 to 7 is obtained. In Figure 4The cluster motion trajectory diagram shows that the hollow circle represents the initial position of each individual in the cluster, the solid circle represents the final position of each individual in the cluster, the pentagram represents the final value of the target position of each individual in the cluster, the dashed line represents the target configuration curve, and the solid line represents the motion trajectory of each individual. In combination with Figure 5 and Figure 6 It can be found that the cluster can converge to the target configuration with a small control amplitude of the order of 10 -3 m / s 2 and a higher precision of 10 -7 m, and the individuals maintain a sufficient distance of 5.8637m, as shown in Figure 7 .

[0127] If the user's demand is not met, adjust the control law parameters (including c i , g i , k p , k v , c c , D c ) until the cluster motion meets the user's demand.

[0128] Embodiment Two: Formation of Lissajous Formation Configuration for Spacecraft Cluster

[0129] The method of this embodiment is the same as that of Embodiment One, except that:

[0130] In S1, the target configuration curve is taken as the Lissajous curve shown in the following equation:

[0131]

[0132] Wherein, ξ C , a=(a x , a y , a z ) T , b=(b x , b y , b z ) T are the center vector, the main half-axis vector, and the auxiliary half-axis vector of the Lissajous curve, respectively, n x , n y , n z are the angular frequency multiples (integer) in x, y, z and z directions, respectively, and a⊥b, ξ C +a is a point on the curve, and ξ C +b is not a point on the curve. Specifically, here, ξ C =(0, 0, 0), a=(20m, 20m, 20m), b=(-20m, 20m, 0), n x =1, n y =1, nz = 2.

[0133] The cluster target configuration parameters in S1 are expanded to the following 12 parameters: ξ C 3 components of 3 components of a x a y a z 3 components of b x b y b z 3 angular frequency multiples n x n y n z . The corresponding target configuration parameter vector is

[0134] Under the cluster communication network topology shown in Figure 8 , the simulation results of the cluster motion 40000s are shown in Figures 9 to 13 . It can be found that the cluster can converge to the target configuration with a small control quantity amplitude of the order of 10 -3 m / s 2 and a high precision of 10 -5 m, and the individuals maintain a sufficient distance of 4.3422m, as shown in Figure 13 .

[0135] The above is only the preferred embodiment of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A distributed cooperative formation control method for a spatially parameterized formation of flybys, characterized by, The method comprises the following steps: determining the number of individuals in the swarm, the individual dynamic model, the initial position and speed of each individual, the target configuration mathematical model, the target configuration parameter evolution model and the initial value of the target configuration parameter of each individual; determining the target position expression of each individual based on the target configuration mathematical model; designing a swarm target configuration parameter cooperative control law, calculating the target configuration parameter of each individual at the current time based on the target configuration parameter evolution model and the initial value of the target configuration parameter of each individual, and bringing the target configuration parameter of each individual at the current time into the target position expression of each individual to calculate the estimated value of the target position of each individual at the current time; designing a swarm motion control law, and performing swarm motion simulation based on the individual dynamic model, the target position of each individual and the estimated value of the target position of each individual at the current time; the target configuration parameter evolution model is wherein, is the current time, is the cluster target configuration parameter collaborative control law to be designed; the swarm target configuration parameter cooperative control law is wherein, is a synergy coefficient, is a containment coefficient, corresponds to the cluster communication network topology (if the individual has information available about the individual , then , otherwise ), corresponds to the individual's role as a leader / follower in the cluster (for a leader, , otherwise ).

2. The distributed cooperative formation control method of a spatially parameterized formation of spacecraft according to claim 1, wherein, the individual dynamic model is wherein, is the number of individuals in the swarm, is is the position vector of the individual at time is is the velocity vector of the individual at time is the control variable of the individual at time is the open-loop dynamics function of the individual, is is the control variable of the individual at time ​​​ 3. The distributed cooperative formation control method of a spatially parameterized formation of spacecraft according to claim 2, wherein, the target configuration mathematical model is wherein, is a shape parameter, and is a shape parameter, and is a curve center coordinate, and Given, the target configuration curve can be uniquely determined, and Given, a point on the target configuration curve can be uniquely determined.

4. The distributed cooperative formation control method of a spatially parameterized formation of spacecraft according to claim 3, wherein, the target configuration mathematical model satisfies the following periodicity condition, so that the target configuration curve forms a closed curve: wherein is a constant for a certain.

5. The distributed cooperative formation control method of a spatially parameterized formation of spacecraft according to claim 4, wherein, the target configuration mathematical model satisfies the following contraction condition: i.e. when all target configuration curve shape parameters other than are taken to be zero, the target configuration curve degenerates to the curve center coordinate.

6. The distributed cooperative formation control method of spatially parameterized formation flying according to claim 3, wherein, the target position expression of each individual is wherein, is a shape parameter, is a shape parameter, is a shape parameter, at a time instant, The estimate of each shape parameter of the target configuration curve can be denoted by the vector .

7. The method of claim 3, wherein, the initial value of the target configuration parameter of each individual is solved through the following optimization problem: In For the case of curvilinear center coordinates, the is taken as 。 8. The method of claim 2, wherein, the swarm motion control law is wherein, is a position feedback coefficient, is a velocity feedback coefficient, is an inter-agent collision avoidance term, which takes the form: wherein, represents the gradient of the respective function at the individual current position, is the collision avoidance potential between the individual and ( , ) is of the form: wherein, is an inter-individual evasion coefficient, is an inter-individual evasion detection distance.

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