Stratosphere airship distributed time-varying formation control method based on affine transformation

Abstract

The application discloses a stratosphere airship distributed time-varying formation control method based on affine transformation and belongs to the technical field of formation control, and comprises the following steps: 1, using a sensor to measure the motion state of the airship; 2, generating an expected formation and sending the expected formation to a leader in the cluster; 3, setting a communication structure for the airship cluster; 4, calculating the expected attitude of a follower airship; 5, setting an auxiliary design system for the follower airship to obtain a virtual control law saturation compensation quantity and an actuator saturation compensation value; 6, setting an adaptive law for the follower airship to obtain an adaptive estimation value; and 7, using a backstepping controller to calculate the control quantity of the expected formation and attitude of the follower airship according to the results in steps 3 to 5. The application can realize time-varying formation control of the stratosphere airship without global information and can also ensure that the state of the airship is within a limited range during the formation maneuvering process of the airship cluster.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of formation control, and in particular to a stratosphere airship distributed time-varying formation control method based on affine transformation. BACKGROUND

[0002] As one of the ideal platforms for near-space exploration, stratosphere airships have great application value. At the same time, stratosphere airship clusters have more advantages than single airships in reconnaissance, observation, communication relay and regional coverage. The above tasks usually require stratosphere airship clusters to perform formation cruising and maneuvering in complex stratosphere environments, which means that the airship formation needs to have sufficient flexibility. Distributed formation control, as the core technology of airship formation application, has received extensive attention in recent years. However, how to improve the flexibility of the formation of the airship system has been rarely studied.

[0003] In recent years, formation maneuvering control has become an effective method to improve the flexibility of formation maneuvering. In order to realize formation maneuvering control, in the early stage, three formation control algorithms are proposed by imposing constant constraints on relative displacement, distance and orientation. Considering that the above described constraints of formation are not universally applicable to all maneuvers, the displacement-based method only allows translational maneuvering, the distance-based method also allows rotational maneuvering, and the orientation-based method can further realize scaling maneuvering. It is worth mentioning that the above methods still have irreplaceable role in some specific scenarios, such as the agent using the distance-based method does not need to calibrate the coordinate system in advance, and can measure the required signals through local sensors, which is suitable for environments without positioning signals. However, their inflexibility still limits the ability to complete complex tasks. In the field of stratosphere airship cluster control, there are still few achievements related to improving the flexibility of formation, and how to improve the flexibility of stratosphere airship formation is still urgently needed to be studied.

[0004] Another problem that cannot be ignored in the formation control of stratosphere airship clusters is error constraints. During formation maneuvering, certain position and attitude errors must be maintained to simultaneously perform observation or communication tasks. Error constraints include position error constraints related to coverage areas, attitude error constraints related to target observation, and velocity and angular velocity error constraints related to structural strength. Exceeding error limits can cause communication interruption, failure to observe a predetermined area, platform structure damage or other unforeseen consequences. Therefore, during formation maneuvering, the state error of the cluster system must be controlled within an acceptable range, and based on this, the present application proposes a stratosphere airship distributed time-varying formation control method based on affine transformation. SUMMARY

[0005] The purpose of the present application is to provide an affine transformation-based stratosphere airship distributed time-varying formation control method, based on affine transformation theory, a stratosphere airship formation maneuver control method is designed, which can realize the time-varying formation control of stratosphere airship without global information, at the same time, based on barrier Lyapunov theory, the state restriction problem of airship is converted into saturation error problem, and through the introduction of auxiliary design system method, the state of airship is ensured within the limit range in the process of realizing the formation maneuver of airship cluster.

[0006] To achieve the above purpose, the present application provides an affine transformation-based stratosphere airship distributed time-varying formation control method, comprising the following steps:

[0007] S1, using a sensor to measure the motion state of the airship;

[0008] S2, generating a desired formation and sending the desired formation to the leader in the cluster;

[0009] S3, after the leader obtains the desired formation, setting a communication structure for the airship cluster;

[0010] S4, after the communication structure setting is completed, calculating the desired attitude of the follower airship;

[0011] S5, after obtaining the desired attitude of each follower airship, setting an auxiliary design system for the follower airship, obtaining a virtual control law saturation compensation and an actuator saturation compensation value;

[0012] S6, setting an adaptive law for the follower airship to obtain an adaptive estimation value;

[0013] S7, using a backstepping controller to calculate the control amount of the desired formation and attitude of the follower airship according to the results in S3 to S5.

[0014] Preferably, the motion state of the airship in S1 includes position, velocity, attitude angle and attitude angle velocity, and the data is transmitted to the backstepping controller.

[0015] Preferably, the process of generating a desired formation in S2 is as follows:

[0016] S21, setting an initial nominal configuration r, the initial nominal configuration is represented as:

[0017] r=[r1,...,r N ];

[0018] ν l ={1,...,N l ];

[0019] v f ={N l +1,...,N};

[0020] where N denotes the number of airships, N l denotes the number of leader airships, v l denotes the set of leader airships, v f denotes the set of follower airships;

[0021] S22, using affine transformation on the initial nominal configuration to obtain the desired formation p * (t), the process is as follows:

[0022]

[0023]

[0024] where I N ∈R N×N denotes the identity matrix, denotes the maneuver matrix characterizing the rotation, scaling, shearing of the formation, b(t)R 3×1 denotes the maneuver matrix characterizing the translation of the formation, denotes the desired position of the i-th airship, 1 N denotes the N-order identity matrix;

[0025] S23, decomposing the desired formation to obtain:

[0026]

[0027] where denotes the desired formation of the leader airships, denotes the formation of the follower airships;

[0028] S24, transmitting the desired formation of the leaders to the leaders to obtain the actual formation of the leaders p l :

[0029]

[0030] Preferably, the process of setting the communication structure in S3 is as follows:

[0031] S31, setting a topological matrix

[0032] S32, using the topological matrix in S31 to specify the communication structure within the airship cluster, denoted as:

[0033]

[0034] where ω ij denotes the corresponding topological gain between airship i and airship j;

[0035] If denotes that there is no communication between airship i and airship j, and denotes that airship i and airship j are neighbors of each other;

[0036] S33, installing a communication structure for all airships before flight.

[0037] Preferably, the process of calculating the desired attitude of the follower airship in S4 is as follows:

[0038] S41, deploying a desired attitude generator on each follower airship, and using the desired attitude generator to obtain the flight attitude of each follower airship at this time respectively;

[0039] S42, calculating the follower block according to the topology matrix in S3, and the calculation process is as follows:

[0040]

[0041] wherein denotes the matrix after the topology matrix is multiplied by a three-order matrix, and denotes the follower block, and I3 denotes a three-order unit matrix;

[0042] S43, calculating the desired attitude of the follower airship, and the calculation process is as follows:

[0043]

[0044] wherein denotes the desired attitude of the i-th follower airship, φ * , θ * and ψ * denote the flight attitude of the follower airship, denotes the desired position of the i-th follower airship, z pj denotes the distributed position error of each neighbor of the follower airship, ω k,j denotes the corresponding topology gain between airship k and airship j, p j denotes the desired position of the j-th airship, j∈N i , p k denotes the desired position of the k-th airship, k∈N j .

[0045] Preferably, the process of obtaining the virtual control law saturation compensation and the actuator saturation compensation value in S5 is as follows:

[0046] S51, respectively arranging a first-order auxiliary design system and a second-order auxiliary design system on each follower airship;

[0047] S52, calculating the current virtual control law of the follower airship, and the calculation process is as follows:

[0048]

[0049] The saturation error of the virtual control law is calculated according to the virtual control law as Wherein:

[0050]

[0051] Wherein represents the inverse of the conversion matrix of the angular velocity of the airship from the body axis system to the ground axis system, α i = diag{α i1 ,α i2 ,α i3 ,α i4 ,α i5 ,α i6} represents the control law parameters to be selected, α ij > 0, j = 1, 2, …, 6, ω ij represents the corresponding topological gain between airship i and airship j, z 1i represents the first-order distributed error, ξ ξi represents the virtual control law saturation compensation quantity of the first-order auxiliary design system output, represents the derivative of the position of airship j;

[0052] S53, input the virtual control law and the first-order distributed error into the first-order auxiliary design system, and obtain the virtual control law saturation compensation quantity by the formula as follows:

[0053]

[0054] Wherein all represent the backstepping controller parameters to be designed, b ξj represents the elements of the first-order distributed error limit b ξ , z 1ij represents the elements of the first-order distributed error, z 1i = [z 1i1 ,...,z 1i6 ], represents the derivative of , and the intermediate variable output is the virtual control law saturation compensation quantity;

[0055] S54, input the actuator saturation value and the second-order distributed error into the second-order auxiliary design system to obtain the actuator saturation compensation value, and the calculation process is as follows:

[0056]

[0057] Wherein all represent the backstepping controller parameters to be designed, saturation error of the control law, z 2ij is the second order distributed error z 2i of the element z 2i = [z 2i1 ,...,z 2i6 ], is the derivative of z , the intermediate variable of the output is the actuator saturation compensation value;

[0058] S55, input the virtual control law saturation compensation amount and the actuator saturation compensation value into the backstepping controller.

[0059] Preferably, the dynamics model of the stratosphere airship is used, and the six-degree-of-freedom dynamics model is as follows:

[0060]

[0061] where ζ i = [x i , y i , z i , φ i , θ i , ψ i ] T represents the three-dimensional coordinates and attitude angles of the stratosphere airship, represents the projection of the airship's velocity in the body axis system and the projection of the airship's angular velocity in the body axis system, f1(ζ i ) represents the coordinate conversion matrix for converting the airship's state quantity in the body axis system to the ground axis system, represents the aerodynamic force and moment received by the airship, B represents the inverse of the mass and inertia matrix of the airship, τ' i = [τ'1, τ'2, τ'3, τ'4, τ'5, τ'6] T , represents the control quantity of the airship i, δ i = [δ u , δ v , δ w , δ p , δ q , δ r ] represents the unknown uncertainty composed of unknown external disturbances and unmodeled dynamics in the airship model, i ∈ N.

[0062] Preferably, the process of obtaining the adaptive estimation value in S6 is as follows:

[0063] S61, arrange an adaptive law on each follower airship;

[0064] S62, input the second order distributed error of the follower airship into the adaptive law to obtain the adaptive estimation value, and the process is as follows:

[0065]

[0066] wherein represents an adaptive estimation value, γ i,j >0, γ i0 >0 represents a controller parameter to be designed, is derivative, I j represents a diagonal matrix, I1=diag{1,0,0,0,0,0}, I2=diag{0,1,0,0,0,0}, …, I6=diag{0,0,0,0,0,6}, represents a backstepping controller parameter to be designed.

[0067] Preferably, the process of calculating the control amount of the desired formation and attitude of the follower airship in S7 is as follows:

[0068] S71, input the current motion state of the follower airship, the desired attitude, the virtual control law saturation compensation amount, the actuator saturation compensation value and the adaptive law estimation value into the backstepping controller;

[0069] S72, use the backstepping controller to calculate the attitude control amount τ i of the follower airship, the process is as follows:

[0070]

[0071] wherein β i =diag{β i1 ,...,β i6}, β ij >0 represents a controller parameter to be designed;

[0072] S73, obtain the time-varying desired formation of the follower airship according to the attitude control amount of the follower airship;

[0073] S74, obtain the distributed time-varying formation of the stratosphere airship according to the desired formation of the leader airship and the time-varying desired formation of the follower airship.

[0074] Therefore, the stratosphere airship distributed time-varying formation control method based on affine transformation with the above structure has the following advantages:

[0075] 1. Based on the affine transformation theory, the formation maneuvering control method of the stratosphere airship is designed, which can realize the time-varying formation control of the stratosphere airship without global information, and improves the formation flexibility;

[0076] 2. Based on barrier Lyapunov theory, the state restriction problem of the airship is converted into a saturation error problem, and the method of introducing an auxiliary design system is used to solve the problem, so as to ensure that the state of the airship is within the limit range during the formation maneuver of the airship cluster;

[0077] 3. Global information does not need to be transmitted to each airship, so that the requirement for communication bandwidth is reduced;

[0078] 4. The auxiliary design system is used to process the saturation problem, so that the actuator saturation problem is improved;

[0079] 5. The adaptive law is used to estimate unknown disturbances in the environment and uncertain terms in the model, and the estimated value is transmitted to the backstepping sliding mode controller, so that the airship can still track the expected trajectory under the influence of external disturbances.

[0080] The technical solutions of the embodiments of the present application will be further described in detail below with reference to the drawings and the embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0081] Figure 1 An execution process diagram of the stratospheric airship distributed time-varying formation control method based on affine transformation of the present application;

[0082] Figure 2 A flowchart of the stratospheric airship distributed time-varying formation control method based on affine transformation of the present application. DETAILED DESCRIPTION

[0083] EMBODIMENT

[0084] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0085] Therefore, the detailed description of the embodiments of the present application provided below in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without making creative efforts fall within the scope of protection of the present application.

[0086] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0087] In the description of the present application, it should be noted that the terms "upper", "lower", "inner", "outer" and the like indicate the orientation or positional relationship shown in the drawings, or the orientation or positional relationship commonly used when the product of the present application is used, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0088] In the description of the present application, it should be noted that unless otherwise explicitly specified and limited, the terms "set", "install", "connect" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0089] Some embodiments of the present application will be described in detail below with reference to the accompanying drawings. The following examples and features in the examples can be combined with each other without conflict.

[0090] As shown in Figure 1 and Figure 2 , the present application is a stratosphere airship distributed time-varying formation control method based on affine transformation, comprising the following steps:

[0091] S1, using a sensor to measure the motion state of the airship, including position, velocity, attitude angle and attitude angular velocity, and transmitting the data to a backstepping controller;

[0092] S2, generating a desired formation, and sending the desired formation to the leader in the cluster;

[0093] S21, setting an initial nominal configuration r, the initial nominal configuration is represented as:

[0094] r=[r1,...,r N ];

[0095] ν l ={1,...,N l};

[0096] v f ={N l +1,...,N};

[0097] Where N represents the number of airships, N l represents the number of leader airships, v l represents the set of leader airships, and v f represents the set of follower airships.

[0098] S22, using affine transformation on initial nominal configuration to get desired formation p * (t), as follows:

[0099]

[0100]

[0101] where I N ∈R N×N denotes identity matrix, denotes maneuver matrix representing formation rotation, scaling, shearing, b(t) R 3×1 denotes maneuver matrix representing formation translation, denotes desired position of i-th airship, 1 N denotes N-order identity matrix;

[0102] S23, decomposition of desired formation can get:

[0103]

[0104] where denotes desired formation of leader airship, denotes formation of follower airship;

[0105] S24, transmission of desired formation of leader to leader to get actual formation of leader p l :

[0106]

[0107] S3, after leader gets desired formation, set communication structure for airship cluster;

[0108] S31, set a topological matrix

[0109] S32, use topological matrix in S31 to specify communication structure of airship cluster, denoted as:

[0110]

[0111] where ω ij denotes corresponding topological gain between airship i and airship j;

[0112] if denotes that airship i and airship j have no communication, if denotes that airship i and airship j are neighbors;

[0113] S33, install communication structure for all airships before flight.

[0114] S4, after the communication structure setting is completed, the desired attitude of the follower airship is calculated;

[0115] S41, a desired attitude generator is deployed on each follower airship, and the flight attitude of each follower airship at this time is obtained using the desired attitude generator;

[0116] S42, the follower block is calculated according to the topology matrix in S3, and the calculation process is as follows:

[0117]

[0118] wherein represents the matrix after the topology matrix is multiplied by the third-order matrix, and represents the follower block, and I3 represents a third-order unit matrix;

[0119] S43, the desired attitude of the follower airship is calculated, and the calculation process is as follows:

[0120]

[0121]

[0122] wherein represents the desired attitude of the i-th follower airship, and * , θ * and * represent the flight attitude of the follower airship, represents the desired position of the i-th follower airship, and pj represents the distributed position error of each neighbor of the follower airship, k,j represents the corresponding topology gain between airship k and airship j, and j represents the desired position of the j-th airship, j∈N i represents the neighbor of the i-th airship, k represents the desired position of the k-th airship, k∈N j represents the neighbor of the j-th airship.

[0123] S5, after the desired attitude of each follower airship is obtained, an auxiliary design system is set for the follower airship, and a virtual control law saturation compensation quantity and an actuator saturation compensation value are obtained;

[0124] S51, a first-order auxiliary design system and a second-order auxiliary design system are respectively arranged on each follower airship;

[0125] S52, the current virtual control law of the follower airship is calculated, and the calculation process is as follows:

[0126]

[0127] The saturation error of the virtual control law is calculated according to the virtual control law as Wherein:

[0128]

[0129] Wherein represents the inverse of the conversion matrix of the angular velocity of the airship from the body axis system to the ground axis system, a i = diag{a i1 , a i2 , a i3 , a i4 , a i5 , a i6} represents the control law parameters to be selected, a ij > 0, j = 1, 2, …, 6, ω ij represents the corresponding topological gain between airship i and airship j, z 1i represents the first-order distributed error, represents the virtual control law saturation compensation of the first-order auxiliary design system output, represents the derivative of the position of airship j;

[0130] S53, input the virtual control law and the first-order distributed error into the first-order auxiliary design system, and obtain the virtual control law saturation compensation through the formula as follows:

[0131]

[0132] Wherein all represent the backstepping controller parameters to be designed, b ξj represents the elements of the first-order distributed error limit b ξ , z 1ij represents the elements of the first-order distributed error, z 1i = [z 1i1 ,..., z 1i6 ], represents the derivative of , the intermediate variable of the output is the virtual control law saturation compensation;

[0133] S54, input the actuator saturation value and the second-order distributed error into the second-order auxiliary design system to obtain the actuator saturation compensation value, and the calculation process is as follows:

[0134]

[0135] Wherein all represent the backstepping controller parameters to be designed, represents the saturation error of the control law, z 2ij is the second-order distributed error z 2i is the element z 2i =[z 2i1 ,...,z 2i6 ], is the derivative of z , the intermediate variable of output is the actuator saturation compensation value;

[0136] S55, input the virtual control law saturation compensation and the actuator saturation compensation value into the backstepping controller.

[0137] S6, set the adaptive law for the follower airship to obtain the adaptive estimation value;

[0138] S61, arrange the adaptive law on each follower airship;

[0139] S62, input the second-order distributed error of the follower airship into the adaptive law to obtain the adaptive estimation value, the process is as follows:

[0140]

[0141] wherein represents the adaptive estimation value, γ i,j >0, γ i0 >0 represents the controller parameter to be designed, is the derivative of z , I j represents a diagonal matrix, I1=diag{1,0,0,0,0,0}, I2=diag{0,1,0,0,0,0}, …, I6=diag{0,0,0,0,0,6}, represents the backstepping controller parameter to be designed.

[0142] S7, use the backstepping controller to calculate the control amount of the desired formation and attitude of the follower airship according to the results in S3 to S5;

[0143] S71, input the current motion state, desired attitude, virtual control law saturation compensation, actuator saturation compensation value and adaptive law estimation value of the follower airship into the backstepping controller;

[0144] S72, use the backstepping controller to calculate the attitude control amount τ i of the follower airship, the process is as follows:

[0145]

[0146] wherein β i =diag{β i1 ,...,βi6}, β ij > 0 represents the controller parameters to be designed;

[0147] S73, the follower airship tracking time-varying desired formation can be obtained according to the attitude control amount of the follower airship;

[0148] S74, the stratosphere airship distributed time-varying formation is obtained according to the desired formation of the leader airship and the desired formation of the follower airship tracking time-varying.

[0149] The present application uses the dynamics model of the stratosphere airship, and the six-degree-of-freedom dynamics model is as follows:

[0150]

[0151] Wherein ζ i = [x i , y i , z i , φ i , θ i , ψ i ] T represents the three-dimensional coordinates and attitude angles of the stratosphere airship, represents the projection of the velocity of the airship in the body axis system and the projection of the angular velocity of the airship in the body axis system, f1(ζ i ) represents the coordinate conversion matrix for converting the state quantity of the airship in the body axis system to the ground axis system, represents the aerodynamic force and aerodynamic moment received by the airship, B represents the inverse of the mass and inertia matrix of the airship, τ' i = [τ'1, τ'2, τ'3, τ'4, τ'5, τ'6] T , represents the control amount of the airship i, δ i = [δ u , δ v , δ w , δ p , δ q , δ r ] represents the unknown uncertainty composed of unknown external disturbance and unmodeled dynamics in the airship model, i ∈ N.

[0152] The principle of the method is that the sensor measures the motion state of the airship and transmits the position, speed, attitude angle and attitude angular velocity to the control system, and the airship will communicate with each neighbor according to the pre-set topological structure to obtain the distributed error and position information of the neighbor. The whole control system is composed of a first-order auxiliary design system, a second-order auxiliary design system, an adaptive law and a backstepping controller. After the airship obtains the sensor and neighbor information, the expected attitude of the airship is first calculated according to the neighbor information, then the first-order distributed error is calculated according to the expected attitude and the position of the airship, then the first-order auxiliary design system outputs the virtual control law saturation compensation value according to the virtual control law and the first-order distributed error and inputs it to the backstepping controller, the second-order auxiliary design system calculates the actuator saturation compensation value according to the actuator saturation value and the second-order distributed error and inputs it to the backstepping controller, the adaptive law calculates the estimation value of the uncertain term according to the second-order distributed error and outputs it to the backstepping controller, and finally the backstepping controller calculates the control value and transmits it to the actuator to control the airship to form the formation.

[0153] Therefore, the present application is a kind of based on affine transformation's stratosphere airship distributed time-varying formation control method, based on affine transformation theory, the formation maneuver control method of stratosphere airship is designed, the time-varying formation control of stratosphere airship can be realized without global information, improve the formation flexibility, simultaneously based on obstacle Lyapunov theory, the state restriction problem of airship is converted into saturation error problem, and the method of introducing auxiliary design system is solved, in the process of realizing the formation maneuver of airship cluster, it is ensured that the state of airship is within the limit range, without transmitting global information to each airship, the requirement of communication bandwidth is reduced, and the saturation problem is improved by using auxiliary design system to process the saturation problem, finally the adaptive law is used to estimate the unknown disturbance of environment and the uncertain term in model, and the estimation value is transmitted to the backstepping sliding mode controller, so that the airship can still track the expected trajectory under the influence of external disturbance.

[0154] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application but not to limit them, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A stratospheric airship distributed time-varying formation control method based on affine transformation, characterized in that, The method comprises the following steps: S1, measuring the motion state of the airship using a sensor; S2, generating a desired formation and sending the desired formation to the leader airship in the cluster; S3, after the leader airship obtains the desired formation, setting a communication structure for the airship cluster; S4, after the communication structure is set, calculating the desired attitude of the follower airship; S5, after the desired attitude of each follower airship is obtained, setting an auxiliary design system for the follower airship to obtain a virtual control law saturation compensation and an actuator saturation compensation value; S6, setting an adaptive law for the follower airship to obtain an adaptive estimation value; S7, using a backstepping controller to calculate the control amount of the desired formation and attitude of the follower airship according to the results in S3 to S5.

2. The stratospheric airship distributed time-varying formation control method based on affine transformation of claim 1, wherein: The motion state of the airship in S1 includes position, velocity, attitude angle and attitude angular velocity, and the data is transmitted to the backstepping controller.

3. The stratospheric airship distributed time-varying formation control method based on affine transformation of claim 2, wherein, In S2, the process of generating the desired formation is as follows: S21, set an initial nominal configuration r, and the initial nominal configuration is represented as: r＝[r1,...,r N ]； v l = {1,...,N l}; v f = {N l +1,...,N} where N represents the number of airships, N l represents the number of leader airships, v l represents the set of leader airships, v f represents the set of follower airships; S22, using affine transformation on the initial nominal configuration to obtain the desired formation p * (t), as follows: where I N ∈ R N×N denotes the identity matrix, denotes a maneuver matrix characterizing formation rotation, scaling, shearing, b(t) R 3×1 denotes a maneuver matrix characterizing formation translation, denotes the desired position of the i-th airship, 1 N denotes the N-order identity matrix; S23, decompose the desired formation to obtain: wherein represents the desired formation of the lead airship, represents the formation of the follower airship; S24, transmitting the desired formation of the pilot to the pilot to obtain the actual formation of the pilot p l :

4. The stratospheric airship distributed time-varying formation control method based on affine transformation of claim 3, wherein, In S3, the process of setting the communication structure is as follows: S31, setting a topology matrix S32, use the topological matrix in S31 to specify the communication structure inside the airship cluster, which is represented as: where ω ij denotes the respective topological gain between airship i and airship j; if denotes that there is no communication between airship i and airship j, if denotes that airship i and airship j are neighbors of each other; S33, install the communication structure for all airships before flight.

5. The stratospheric airship distributed time-varying formation control method based on affine transformation of claim 4, wherein, In S4, the process of calculating the desired attitude of the follower airship is as follows: S41, deploy a desired attitude generator on each follower airship to obtain the flight attitude of each follower airship at this time respectively using the desired attitude generator; S42, calculate the follower block according to the topological matrix in S3, and the calculation process is as follows: wherein denotes the matrix after multiplication of the topology matrix by a third order matrix, and denotes the follower block, I3denotes a third order identity matrix; S43, calculate the desired attitude of the follower airship, and the calculation process is as follows: where denotes the desired attitude of the i-th follower airship, φ * , θ * , and ψ * denote the flight attitude of the follower airship, denotes the desired position of the i-th follower airship, z pj denotes the distributed position error of each neighbor of the follower airship, ω k,j denotes the corresponding topological gain between airship k and airship j, p j denotes the desired position of the j-th airship, j e N i , p k denotes the desired position of the k-th airship, k e N j .

6. The stratospheric airship distributed time-varying formation control method based on affine transformation of claim 5, wherein, In S5, the process of obtaining the virtual control law saturation compensation and the actuator saturation compensation value is as follows: S51, respectively arrange a first-order auxiliary design system and a second-order auxiliary design system on each follower airship; S52, calculate the current virtual control law of the follower airship, and the calculation process is as follows: The saturation error of the virtual control law is calculated according to the virtual control law as wherein: where denotes the inverse of the transformation matrix that transforms the angular velocity of the airship from the body axis system to the earth axis system, a i = diag{a i1 , a i2 , a i3 , a i4 , a i5 , a i6} denotes the control law parameters to be selected, a ij > 0, j = 1, 2,..., 6, ω ij denotes the corresponding topological gain between airship i and airship j, z 1i denotes the first order distributed error, ξ ξi denotes the virtual control law saturation compensation quantity of the first order auxiliary design system output, denotes the derivative of the position of airship j; S53, input the virtual control law and the first-order distributed error into the first-order auxiliary design system to obtain the virtual control law saturation compensation through the formula, and the formula is as follows: in Both represent the backstepping controller parameters to be designed, b ξj represents the first-order distributed error limit b ξ The element b ξ =[b ξ1 ,...,b ξ6 ] T , z 1ij Represents the elements of the first-order distributed error, z 1i =[z 1i1 ,...,z 1i6 ], express The derivative of the output intermediate variable is the saturation compensation of the virtual control law; S54, input the actuator saturation value and the second-order distributed error into the second-order auxiliary design system to obtain the actuator saturation compensation value, and the calculation process is as follows: wherein both represent the backstepping controller parameters to be designed, represents the saturation error of the control law, z 2ij is the element z 2i of the second order distributed error z 2i = [z 2i1 ,..., z 2i6 ], is the derivative of the output intermediate variable is the actuator saturation compensation value; S55, input the virtual control law saturation compensation and the actuator saturation compensation value into the backstepping controller.

7. The stratospheric airship distributed time-varying formation control method based on affine transformation of claim 6, wherein, The dynamic model of the stratospheric airship is used, and the six-degree-of-freedom dynamic model is as follows: where ζ i = [x i , y i , z i , φ i , θ i , ψ i ] T denotes the three-dimensional coordinates and attitude angles of the stratospheric airship, denotes the projection of the airship's velocity in the body axis system and the projection of the airship's angular velocity in the body axis system, f1(ζ i ) denotes the coordinate transformation matrix from the body axis system to the ground axis system, denotes the aerodynamic force and moment acting on the airship, B denotes the inverse of the airship mass and inertia matrix, τ' i = [τ'1, τ'2, τ'3, τ'4, τ'5, τ'6] T , denotes the control inputs of the airship i, δ i = [δ u , δ v , δ w , δ p , δ q , δ r ] denotes the unknown uncertainty in the airship model consisting of unknown external disturbances and unmodeled dynamics, i ∈ N.

8. The stratospheric airship distributed time-varying formation control method based on affine transformation of claim 7, wherein, In S6, the process of obtaining the adaptive estimation value is as follows: S61, arrange an adaptive law on each follower airship; S62, input the second-order distributed error of the follower airship into the adaptive law to obtain the adaptive estimation value, and the process is as follows: wherein denotes an adaptive estimate, γ i,j > 0, γ i0 > 0 denotes a controller parameter to be designed, is derivative of I j denotes a diagonal matrix, denotes a backstepping controller parameter to be designed.

9. The stratospheric airship distributed time-varying formation control method based on affine transformation of claim 8, wherein, In S7, the process of calculating the control amount of the desired formation and attitude of the follower airship is as follows: S71, input the current motion state, desired attitude, virtual control law saturation compensation, actuator saturation compensation value and adaptive law estimation value of the follower airship into the backstepping controller; S72, calculate the attitude control amount τ of the follower airship using the backstepping controller i The process is as follows: where β i = diag{β i1 ,...,β i6}, β ij > 0 represents the controller parameters to be designed; S73, obtain the time-varying desired formation that the follower airship tracks according to the attitude control amount of the follower airship; S74, obtaining a stratospheric airship distributed time-varying formation according to the expected formation of the pilot airship and the time-varying expected formation tracked by the follower airship.

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