A method for controlling air-ground heterogeneous cluster coordinated formations triggered by fixed-time events

Abstract

The present invention belongs to the field of aerospace technology, and relates to a method for controlling an air-ground heterogeneous cluster by fixed-time event triggering collaborative formation, comprising the following steps: establishing a second-order heterogeneous follower mathematical model for the air-ground heterogeneous cluster; designing a fixed-time extended state observer to observe and compensate for unknown speed and disturbance; designing a distributed fixed-time event triggering estimator based on an event-triggered communication strategy to estimate the information of the heterogeneous leader, so as to facilitate the tracking control of the heterogeneous followers; designing a fixed-time event triggering control protocol based on the fixed-time extended state observer and the distributed fixed-time event triggering estimator, so that the air-ground heterogeneous cluster can complete the desired formation within a fixed time; the fixed-time control method based on the event triggering strategy proposed by the present invention can save communication resources and control energy for the air-ground heterogeneous cluster, and can also ensure the collaborative formation control performance of the cluster.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and in particular relates to a method for controlling a coordinated formation triggered by a fixed-time event of an air-ground heterogeneous cluster. Background Art

[0002] The cooperative formation control technology of multi-agents is an important way to demonstrate group intelligent behavior at the motion level. The agents in the cluster adjust their positions and speeds in real time through local information interaction, and then obtain a specific task formation configuration, which further provides time and space convenience for actual cluster collaborative tasks (such as collaborative detection and positioning, collaborative target collaborative capture). At present, the research on multi-agent cooperative formation control technology is mainly focused on homogeneous cluster systems, such as multi-spacecraft clusters, multi-UAV clusters, and multi-ground robot systems. However, when a cluster composed of a single object faces complex multi-domain tasks, it is difficult to meet the above task requirements due to its weak collaborative ability and single intelligent emergence mode. For this reason, the cooperative control of heterogeneous clusters composed of UAVs and unmanned vehicles has begun to attract people's attention.

[0003] Drones and unmanned vehicles have completely different physical structures, and their kinematic and dynamic models are also completely different, which will bring certain difficulties and challenges to the subsequent design of collaborative formation controllers for the entire system; therefore, how to model air-ground heterogeneous systems with different degrees of freedom characteristics to facilitate subsequent controller design is the primary key issue; in addition, objects in the cluster use the communication network to continuously communicate with their neighbor sets to obtain the status of their neighbors, and use the obtained local state information to design their own controllers to control their own movements. When the cluster is too large, a large amount of continuous network communication will bring severe challenges to the communication bandwidth of the air-ground system. How to design an event-triggered communication strategy for each cluster object to intermittently transmit information and reduce the frequency of communication and transmission is also an issue that needs to be considered urgently; finally, the designed formation control signal requires the device actuator to continuously implement it to maintain the desired control performance. How to design an event-triggered actuator mechanism to intermittently update the control signal and thereby increase the service life of the actuator is also a problem that needs to be solved.

[0004] At present, there are few studies on formation control involving heterogeneous air-ground systems. Existing literature (Zhou Siquan, Dong Xiwang, Li Qingdong, et al., "UAV-UAV Heterogeneous Time-Varying Formation Control and Disturbance Suppression", Acta Aeronautica Sinica, 2020, 41(S1):72376) modeled the kinematics and dynamics of UAVs and UAVs respectively, and designed a distributed time-varying output formation controller with a hierarchical architecture, including a formation center estimation term based on consistency theory and a disturbance suppression compensation term based on the internal model principle. The dynamics and controllers of the UAV cluster and the UAV cluster were designed separately, and the event triggering strategy was not considered at all. References (Gu Zhenzhen, Wang Xugang, Wang Zhongyuan and Hua Siyu, "Fixed-time formation control of multiple missiles under event-triggered mechanism", Journal of Astronautics, 2023, 44(2): 266-281) focus on the fixed-time cooperative tracking control problem of the leader-follower formation structure, and in order to save communication bandwidth and missile-borne computing resources, a fixed-time formation control algorithm based on event-triggered mechanism under directed topology is proposed based on multi-agent consistency theory. However, this scenario only considers homogeneous missile systems, and does not further design an event-triggered actuator mechanism for the proposed fixed-time formation control algorithm. Similarly, the existing literature (G. Cui, H. Xu, X. Chen, and J. Yu, “Fixed-time distributed adaptive formation control for multiple QUAVs with full-state constraints ”IEEE Transactions on Aerospace and Electronic Systems, 2023.59(4), pp.4192-4206) designed a fixed-time distributed adaptive formation control algorithm for multi-rotor UAVs with full-state constraints under the event-triggered framework to ensure that the cluster can converge to the desired formation style. However, this study also only considered the homogeneous rotor UAV system as the research object, and only designed the event-triggered actuator strategy in each UAV control channel, without considering the communication trigger strategy of the cluster. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a fixed-time event-triggered collaborative formation control method for air-ground heterogeneous clusters, so as to fill the research deficiencies in the existing collaborative formation control research on unified modeling of air-ground heterogeneous multi-agent systems, fixed-time event-triggered communication estimation and fixed-time event-triggered control.

[0006] In order to achieve the purpose of the present invention, the present invention will be implemented by adopting the following technical solutions.

[0007] A method for controlling an air-ground heterogeneous cluster coordinated formation triggered by a fixed-time event, comprising the following steps:

[0008] S1. By defining the index subscripts and state dimension variables of the corresponding subsets of any heterogeneous intelligent agents in the heterogeneous cluster composed of the unmanned vehicle cluster and the unmanned aerial vehicle cluster, and bridging the state dimension variables of the unmanned vehicles and unmanned aerial vehicles in the heterogeneous cluster, a second-order air-ground heterogeneous follower dynamics model characterizing the characteristics of different degrees of freedom is established with the help of the state dimension variables of the corresponding subsets, and a second-order air-ground heterogeneous leader dynamics model of the heterogeneous leader is determined according to the index subscripts of the corresponding subsets;

[0009] S2: Considering the speed measurement is limited and affected by the unknown environmental disturbance, a fixed time dilation state observer is designed to observe and compensate for the unmeasurable speed of the heterogeneous follower itself and the disturbance suffered by the unknown environment;

[0010] S3: According to the distributed information transmission characteristics between heterogeneous followers and heterogeneous leaders, a distributed fixed-time event-triggered estimator is designed based on the event-triggered communication strategy, so that each heterogeneous follower can estimate the state and input of the heterogeneous leader to achieve collaborative tracking of the heterogeneous leader;

[0011] S4: Using the fixed-time extended state observer designed in step S2 and the distributed fixed-time event-triggered estimator designed in step S3, a fixed-time event-triggered collaborative formation control protocol is designed through an event-triggered actuator strategy to control each heterogeneous follower to complete the task of forming the desired formation within a fixed time;

[0012] The second-order space-ground heterogeneous follower dynamics model is described as:

[0013] ,

[0014] In the formula, , , ,and are the position, velocity, control input and unknown disturbance vector of the i-th heterogeneous follower agent; and is the matrix of heterogeneous follower system; and for the dynamics of position and velocity; is the index set of all heterogeneous followers; The dimension is A set of real vectors.

[0015] The second-order space-ground heterogeneous leader dynamics model is described as:

[0016] ,

[0017] In the formula, , ,and are the position, velocity and input vector of the leader respectively; and are the first-order derivatives of the leader’s position and velocity, respectively; the remaining variables are consistent with the above definitions.

[0018] The fixed-time dilated state observer is described as:

[0019]

[0020] In the formula, , and They are the observed dynamics of the heterogeneous follower on its own position, velocity and unknown disturbance variables; , and are their observed values ​​respectively; Expressed as position estimation error; parameter and Set to and ,in , ,and and ; The remaining variables are defined above.

[0021] The distributed fixed-time event-triggered estimator is described as:

[0022] ,

[0023] In the formula, , and are the i-th heterogeneous follower at the event triggering communication moment The estimated value broadcast to its set of neighbors; is the most recent triggering time of the ith heterogeneous follower, and ; , and They are position, velocity, and input local trigger estimation errors respectively; , and are the estimated values ​​of the most recent trigger received by the ith heterogeneous follower from its neighbor j, The most recent event triggering communication time for its neighbor j; , and . represents the connection weight between the i-th heterogeneous follower and its j-th neighbor, represents the connection weight between the ith heterogeneous follower and the leader; the remaining variables are defined above.

[0024] The event-triggered communication strategy is described as:

[0025] ,

[0026] In the formula, Represents dimension;

[0027] ,

[0028] , and . Event trigger function , and The definition is as follows:

[0029] ,

[0030] In the formula, .

[0031] The fixed time event-triggered collaborative formation control protocol and the event-triggered actuator strategy are designed as follows:

[0032] ,

[0033] In the formula, , , , , and . Defined as the measurement error of the i-th heterogeneous follower controller; is the triggering time of the i-th heterogeneous follower controller; , , , , , and ; The remaining variables are defined above. represents a continuous intermediate control signal and is designed as follows:

[0034] ,

[0035] In the formula, , , .

[0036] As a preferred embodiment of the present invention, the process of establishing the second-order space-ground heterogeneous follower dynamics model and the second-order space-ground heterogeneous leader dynamics model includes the following steps:

[0037] S21. Unmanned vehicle cluster consisting of M unmanned vehicles A drone swarm consisting of NM drones ;

[0038] S22. Definition As a heterogeneous cluster composed of unmanned vehicles and drones; any heterogeneous agent ,definition As the index subscript of the corresponding subset, that is, , and the corresponding subset The state dimension variable is defined as ,in ;

[0039] S23, bridge the state variable dimensions of the unmanned vehicles and drones in the heterogeneous cluster, and define the following state matching matrix for bridging;

[0040] ,

[0041] In the formula, and The dimensions are and The identity matrix of , and the symbols of other variables have been defined above.

[0042] S24, any two heterogeneous agents in a heterogeneous cluster For example, if , then ;if , then ;

[0043] S25. Using state dimension variables , construct a second-order space-ground heterogeneous follower dynamics model:

[0044] ,

[0045] In the formula, , , ,and are the position, velocity, control input and unknown disturbance vector of the i-th heterogeneous follower agent; and is the heterogeneous follower system matrix; the remaining variables are defined above.

[0046] S26. Assume that the index of the heterogeneous leader is 0, its state variable dimension is three-dimensional, and belongs to the subset , and its second-order space-ground heterogeneous leader dynamics model is described as:

[0047] ,

[0048] In the formula, , ,and are the position, velocity and input vector of the leader respectively; the rest of the variables are defined above.

[0049] As a preferred solution of the present invention, the design process of the fixed time extended state observer (FESO) is as follows:

[0050] Define , ,and For the observation values ​​of the heterogeneous follower agent on its own position, unmeasurable speed and unknown disturbance, the fixed-time dilated state observer is designed as follows:

[0051] ,

[0052] In the formula, It is expressed as the position estimation error. Parameters and Set to and ,in , ,and and are sufficiently small constants; in addition, the observation gain and Make the following two matrices Hurwitz respectively:

[0053] ,

[0054] definition and As the velocity observation error and disturbance error of the i-th heterogeneous follower, respectively, according to the dynamic model in S1 and the designed fixed time dilation observer, we can get:

[0055] ,

[0056] Preferably, step S3 is to design a distributed fixed-time event-triggered estimator (DF-ETE) to observe the information of the three-dimensional leader:

[0057] ,

[0058] In the formula, , and In the time period Internal leader status , and leader input An estimated value of; , and are the i-th heterogeneous follower at the event triggering communication moment The estimated value broadcast to its set of neighbors; is its most recent triggering moment, and ; , and are position, velocity, and input local trigger estimation errors respectively; , and are the estimated values ​​of the most recent trigger received by the ith heterogeneous follower from its neighbor j, The most recent event triggering communication time for its neighbor j; , and .

[0059] definition , and They are the trigger position estimation error, trigger velocity estimation error and trigger input estimation error respectively. Combining the dynamic model in S1, the error dynamics of the distributed fixed-time event trigger estimator are designed as follows:

[0060] ,

[0061] In the formula, , and In addition, the definition , and ; represents the connection weight between the i-th heterogeneous follower and its j-th neighbor, represents the connection weight between the ith heterogeneous follower and the leader; for the ith heterogeneous agent, its event triggering measurement error is:

[0062] ,

[0063] In the formula, ,Based on the above measurement errors, the event-triggered communication strategy is designed as:

[0064] ,

[0065] In the formula, Represents a dimension; and the event triggers a function , and The definition is as follows:

[0066] ,

[0067] In the formula, .

[0068] Furthermore, we need to prove that the proposed distributed fixed-time event-triggered estimator is fixed-time stable: First, we need to estimate the local input error Taking the derivative with respect to time, we get:

[0069] ,

[0070] Estimated error for local input Define the Lyapunov function:

[0071] ,

[0072] In the formula, For variables No. variables. Take the derivative of the above equation and substitute it into We can get:

[0073] ,

[0074] After a series of derivations, the above formula can be simplified to:

[0075] ,

[0076] In the formula, For the matrix The minimum eigenvalue of ; and It is also its minimum eigenvalue; and Variables Two nonlinear functions of ; ; ; is a diagonal matrix The largest element in; the remaining variables are defined and explained in the above steps. According to the fixed time stability theory, it can be known that the local input estimation error is stable. Similarly, using the above idea, it can also be proved that the local velocity estimation error and the local position estimation error They are all stable at fixed times.

[0077] Preferably, according to the above-mentioned fixed-time extended state observer (FESO) and distributed fixed-time event-triggered estimator (DF-ETE), a fixed-time event-triggered formation control protocol is designed:

[0078] Define the following tracking signal:

[0079] ,

[0080] The tracking signal defined above can be further defined as the following heterogeneous cluster cooperative formation tracking error:

[0081] ,

[0082] In the formula, and They are formation position tracking error and formation velocity tracking error respectively; and They are the expected time-varying offset of position and the expected time-varying offset of speed respectively. A virtual speed control signal is introduced into the speed channel as follows:

[0083] ,

[0084] In the formula, represents the virtual velocity tracking error. Then, taking the derivative with respect to time, the transformed error dynamics can be obtained as

[0085] ,

[0086] For the above error dynamics model, first define the following appropriate Lyapunov function

[0087] ,

[0088] let Take the derivative with respect to time and substitute it into the above formula We can further get:

[0089] ,

[0090] First, we design the following fixed-time control protocol, event-triggered actuator strategy (ETAM), and coefficient adaptation law:

[0091] ,

[0092] In the formula, ,and Represents a continuous intermediate control signal and will be given later; defines two continuous time-varying parameters and , and satisfy and ;when , we can get . Then it can be further transformed into:

[0093] ,

[0094] Rewrite the above formula as ,and and ; and bring it into the above In , we can further get:

[0095] ,

[0096] Design the following continuous intermediate control signal :

[0097] ,

[0098] In the formula, , ; Substituting it into the above formula, we can further obtain:

[0099] ,

[0100] From S2 and S3, we can know that the designed fixed-time extended state observer (FESO) and distributed fixed-time event-triggered estimator (DF-ETE) have converged in advance, so we have ; In addition, we have , which can be simplified into the above formula:

[0101] ,

[0102] According to the fixed-time stability theory, It can be stabilized within a fixed time; at the same time, it is the formation position tracking error Consider the following Lyapunov function:

[0103] ,

[0104] Derivative the above equation and substitute ,available:

[0105] ,

[0106] Similarly, according to the fixed-time stability theory, Get stable within a fixed time.

[0107] The present invention aims at the collaborative formation control problem of an air-to-ground heterogeneous multi-agent system composed of unmanned vehicles and unmanned aerial vehicles. Firstly, a fixed-time extended state observer is designed to observe and compensate for the unmeasurable speed and unknown external disturbances of the system. In order to save communication resources between clusters and facilitate subsequent control design, a fixed-time event-triggered estimator is then proposed for each heterogeneous follower to observe the leader's information in real time. Based on the fixed-time event-triggered actuator strategy, the designed event-triggered control protocol can not only enable the cluster to complete the formation task collaboratively, but also save the control resources of the system. The present invention has strong overall innovation, can provide theoretical guidance for the collaboration of unmanned systems in reality, and has certain engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 This is a block diagram of the main idea of ​​the present invention;

[0109] Figure 2 It is the main MATLAB / Simulink model algorithm simulation diagram of the present invention;

[0110] Figure 3 It is a directed information interaction topology diagram of the space-ground heterogeneous cluster and the leader in the present invention;

[0111] Figure 4 It is a schematic diagram of the trajectory of the three-dimensional cooperative formation of the air-ground heterogeneous multi-agent system in the simulation of the present invention;

[0112] Figure 5 It is a schematic diagram of the speed tracking error and position tracking error of the air-ground heterogeneous multi-agent system cooperative formation in the present invention;

[0113] Figure 6 is a schematic diagram of the communication triggering time of the distributed fixed time event triggered estimator (DF-ETE) designed for each heterogeneous follower in the present invention;

[0114] Figure 7 Schematic diagram of the estimated norm error of each heterogeneous follower to the position, velocity, and control input of the leader in the present invention;

[0115] Figure 8 It is a triggering time schematic diagram of a fixed time event triggering protocol designed for each heterogeneous follower in the present invention;

[0116] Fig. 9 It is a schematic diagram of the estimated curves of each axis of all unmanned vehicles in the present invention for their own unmeasurable speed and unknown disturbance;

[0117] Fig.10 It is a schematic diagram of the estimated curves of each axis of all drones for their own unmeasurable speed and unknown disturbances. DETAILED DESCRIPTION

[0118] In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

[0119] As an embodiment of the present invention, Figure 1 As shown, a method for controlling a coordinated formation of heterogeneous clusters triggered by fixed-time events includes the following steps:

[0120] Step 1: Establish the following second-order dynamics model of the air-ground heterogeneous multi-agent system:

[0121] ,

[0122] In the formula, , , ,and are the position, velocity, control input and unknown disturbance vector of the i-th heterogeneous follower agent; and is the matrix of heterogeneous follower system;

[0123] The three-dimensional leader dynamics model is established as:

[0124] ,

[0125] In the formula, , ,and are the position, velocity and input vector of the leader respectively.

[0126] Step 2: Based on the unique measurable position vector of heterogeneous followers , the following fixed-time extended state observer (FESO) is designed to account for the unmeasured speed variable and unknown disturbances Perform online observation and compensation; the fixed time expansion state observer is as follows:

[0127]

[0128] In the formula, , ,and Represent the position, velocity and unknown disturbance observation value of the heterogeneous follower agent itself; is the position estimation error; parameter and Set to and ,in , ,and and are sufficiently small constants; in addition, the observed gain and Make the following two matrices Hurwitz respectively:

[0129] ;

[0130] Step 3: Based on Figure 3 Given the information interaction topology, a distributed fixed-time event-triggered estimator (DF-ETE) is designed for each heterogeneous follower to estimate the information of the three-dimensional leader. The distributed fixed-time event-triggered estimator (DF-ETE) is as follows:

[0131] ,

[0132] In the formula, , and In the time period Internal leader status , and leader input An estimated value of , and are the i-th heterogeneous follower at the event triggering communication moment The estimated value broadcast to its set of neighbors; is the most recent triggering moment of the ith heterogeneous follower; , and They are position, velocity, and input local trigger estimation errors respectively; , and are the estimated values ​​of the most recent trigger received by the ith heterogeneous follower from its neighbor j, The most recent event triggering communication time for its neighbor j; , and The designed event-triggered communication strategy (ETCM) is:

[0133] ,

[0134] In the formula,

[0135] ;

[0136] ;

[0137] , and .

[0138] Step 4: Based on the observation and estimation algorithms designed in steps 2 and 3, a fixed-time event-triggered control protocol is designed for each heterogeneous follower:

[0139] ,

[0140] In the formula, , , , , and ; Defined as the measurement error of the i-th heterogeneous follower controller; is the triggering time of the i-th heterogeneous follower controller; , , , , , and ; represents a continuous intermediate control signal and is designed as follows:

[0141] ,

[0142] In the formula, , , .

[0143] Step 5: If Figures 2 to 10 As shown in the figure, in order to verify the effectiveness of the algorithm designed above, four unmanned vehicles (numbered 1, 2, 3, 4) and five drones (numbered 5, 6, 7, 8, 9) are selected to build a simulation model in Simulink for numerical simulation. The cluster information interaction topology is shown in the figure. Figure 3 As shown. Set the initial state of the three-dimensional leader to , the control input is The initial states of the remaining heterogeneous followers are , , , , , , , and (Units: m and m / s).

[0144] Furthermore, the parameters of the fixed-time extended state observer (FESO) in the second step are set as , , , , , , , and The parameters of the distributed fixed-time event-triggered estimator (DF-ETE) in the third step are set as , , and Its event-triggered communication parameters are Set the fixed time event trigger control protocol parameters in step 4 to , , , , , , , , and The final event-triggered actuator strategy (ETAM) parameters are and .

[0145] The preferred embodiments of the embodiments of the present application are described above with reference to the accompanying drawings, but the scope of rights of the embodiments of the present application is not limited thereby.

Claims

1. A method for controlling an air-ground heterogeneous cluster coordinated formation triggered by a fixed-time event, characterized in that: The steps include: S1. By defining the index subscripts and state dimension variables of the corresponding subsets of any heterogeneous intelligent agents in the heterogeneous cluster composed of the unmanned vehicle cluster and the unmanned aerial vehicle cluster, and bridging the state dimension variables of the unmanned vehicles and unmanned aerial vehicles in the heterogeneous cluster, a second-order air-ground heterogeneous follower dynamics model characterizing the characteristics of different degrees of freedom is established with the help of the state dimension variables of the corresponding subsets, and a second-order air-ground heterogeneous leader dynamics model of the heterogeneous leader is determined according to the index subscripts of the corresponding subsets; S2: Considering the speed measurement is limited and affected by the unknown environmental disturbance, a fixed time dilation state observer is designed to observe and compensate for the unmeasurable speed of the heterogeneous follower itself and the disturbance suffered by the unknown environment; S3: According to the distributed information transmission characteristics between heterogeneous followers and heterogeneous leaders, a distributed fixed-time event-triggered estimator is designed based on the event-triggered communication strategy, so that each heterogeneous follower can estimate the state and input of the heterogeneous leader to achieve collaborative tracking of the heterogeneous leader; S4: Using the fixed-time extended state observer designed in step S2 and the distributed fixed-time event-triggered estimator designed in step S3, a fixed-time event-triggered collaborative formation control protocol is designed through an event-triggered actuator strategy to control each heterogeneous follower to complete the task of forming the desired formation within a fixed time; The second-order space-ground heterogeneous follower dynamics model is described as: ； In the formula, , , ,and are the position, velocity, control input and unknown disturbance vector of the i-th heterogeneous follower agent; and is the matrix of heterogeneous follower system; and Position variables and speed variables The dynamics of The dimension is The set of real vectors of ; is the index set of all heterogeneous followers; The second-order space-ground heterogeneous leader dynamics model is described as: ； In the formula, and are position vectors and the velocity vector The dynamics of For Dimension The set of real vectors of ; , ,and are the position, velocity and input vector of the leader respectively; The fixed-time dilated state observer is described as: ； In the formula, is the estimated error of the position vector; , and are the observed variables of the i-th heterogeneous follower agent about its own position, velocity and unknown disturbance respectively; , and are the dynamics corresponding to position, velocity and disturbance respectively; the parameters and Set to and ,in , ,and and ; In addition, the design factor and Make the following two matrices Hurwitz respectively: ； The distributed fixed-time event-triggered estimator is described as: ； In the formula, , and are the estimated dynamic models of the position, velocity and input of the i-th heterogeneous follower to the leader, respectively; , and are the i-th heterogeneous follower at the event triggering communication moment The estimated value broadcast to its set of neighbors; is the most recent triggering time of the ith heterogeneous follower, and ; , and They are position, velocity, and input local trigger estimation errors respectively; , and are the estimated values ​​of the most recent trigger received by the ith heterogeneous follower from its neighbor j, The most recent event triggering communication time for its neighbor j; represents the connection weight between the i-th heterogeneous follower and its j-th neighbor, represents the connection weight between the ith heterogeneous follower and the leader; , , and ; The event-triggered communication strategy is described as: ； In the formula, represents a dimension; and ； ， ， ; , and They are the estimated errors of position, speed and input respectively; event trigger function , and The design is as follows: ； In the formula, ; The fixed time event-triggered collaborative formation control protocol and the event-triggered actuator strategy are designed as follows: ； In the formula, and are the virtual speed control signal and actual control signal of the i-th heterogeneous follower respectively; , , , , and ; Intermediate control signal At the triggering moment The value of is the triggering time of the i-th heterogeneous follower controller; The trigger time for its next event; is defined as the measurement error of the ith heterogeneous follower controller and is its j-th element; is an adaptive adjustable parameter, and its initial value is ,and for its dynamics; , , , , and ; Continuous intermediate control signal The design is as follows: ； In the formula, ; is the virtual speed tracking error; is the first-order derivative of the time-varying migration velocity; is the first-order derivative of the virtual speed control signal; is the state dimension matching matrix; , ; is an adjustable positive parameter; the definitions of the remaining variables are consistent with the above.

2. The method for controlling an air-ground heterogeneous cluster coordinated formation triggered by a fixed time event according to claim 1, characterized in that: The process of establishing the second-order space-ground heterogeneous follower dynamics model and the second-order space-ground heterogeneous leader dynamics model includes the following steps: S21. Unmanned vehicle cluster consisting of M unmanned vehicles A drone swarm consisting of NM drones ; S22. Definition As a heterogeneous cluster composed of unmanned vehicles and drones; any heterogeneous agent ,definition As the index subscript of the corresponding subset, that is, , and the corresponding subset The state dimension variable is defined as ,in ; S23, bridge the state variable dimensions of the unmanned vehicles and drones in the heterogeneous cluster, and define the following state matching matrix for bridging; ； In the formula, and The dimensions are and The identity matrix of and are the subscripts of the corresponding subsets mentioned above; S24, any two heterogeneous agents in a heterogeneous cluster For example, if , then ;if , then ; S25. Using state dimension variables , construct a second-order space-ground heterogeneous follower dynamics model: ； In the formula, , , ,and are the position, velocity, control input and unknown disturbance vector of the i-th heterogeneous follower agent; and is the matrix of heterogeneous follower system; S26. Assume that the index of the heterogeneous leader is 0, its state variable dimension is three-dimensional, and belongs to the subset , and its second-order space-ground heterogeneous leader dynamics model is described as: ； In the formula, , ,and are the position, velocity and input vector of the leader respectively.

3. The method for controlling an air-ground heterogeneous cluster coordinated formation triggered by a fixed time event according to claim 1, characterized in that: The fixed-time dilated state observer observes the unmeasurable speed and unknown disturbance of the heterogeneous followers: ； In the formula, , ,and Respectively represent the position, velocity and unknown disturbance observation value of the heterogeneous follower agent itself; is the position estimation error; parameter and Set to and ,in , ; At the same time, the observation gain of the designed observer and Make the following two matrices Hurwitz respectively: 。 4. The method for controlling an air-ground heterogeneous cluster coordinated formation triggered by a fixed time event according to claim 1, characterized in that: The heterogeneous followers estimate the state and input of the heterogeneous leader: definition , and In the time period Internal heterogeneous leader status , and input The estimated value of the distributed fixed-time event-triggered estimator is: ； In the formula, , and are the i-th heterogeneous follower at the event triggering communication moment The estimated value broadcast to its set of neighbors; is the most recent triggering time of the ith heterogeneous follower, and ; , and They are position, velocity, and input local trigger estimation errors respectively; , and are the estimated values ​​of the most recent trigger received by the ith heterogeneous follower from its neighbor j, The most recent event triggering communication time for its neighbor j; , and ; represents the connection weight between the i-th heterogeneous follower and its j-th neighbor, represents the connection weight between the ith heterogeneous follower and the leader; let , and They are respectively the trigger position estimation error, the trigger speed estimation error and the trigger input estimation error. Combined with step S1, the error dynamics model of the distributed fixed-time event trigger estimator is: ； In the formula, , and In addition, the definition , and ; For the i-th heterogeneous agent, the measurement error of its event triggering is: ； In the formula, ; Based on the above measurement error, the event-triggered communication strategy is: ； In the formula, Represents a dimension; and the event triggers a function , and The definition is as follows: ； In the formula, .

5. The method for controlling an air-ground heterogeneous cluster coordinated formation triggered by a fixed time event according to claim 1, characterized in that: The process of establishing the fixed time event-triggered collaborative formation control protocol and the event-triggered execution strategy includes the following steps: S51. Define tracking signal: ； In the formula, represents the connection weight between the ith heterogeneous follower and the leader; if ,but , which indicates that the ith heterogeneous follower can track the leader's true signal, otherwise it can only track its own estimated signal of the leader, that is, ; S52, the tracking error of the heterogeneous cluster cooperative formation is defined as: ； In the formula, and are the formation position tracking error and formation velocity tracking error of the i-th heterogeneous follower respectively; and are the expected time-varying offset of position and the expected time-varying offset of velocity respectively; S53. Derivative of the tracking error expression with respect to time is obtained: ; In the formula, and They are the dynamics of formation position tracking error and formation velocity tracking error, respectively; S54: In order to complete the task of forming the desired formation within a fixed time, a virtual speed control signal is introduced into the speed channel. : ； In the formula, represents the virtual speed tracking error; S55. The error dynamics model can be transformed into the following form: ； S56, in order to make the transformation form of the error dynamics model tend to be stable within a fixed time, the virtual speed control signal , Fixed time event trigger control protocol , and the event-triggered executor strategies are designed as follows: ； In the formula, , , , , and ; Defined as the measurement error of the i-th heterogeneous follower controller; is the triggering time of the i-th heterogeneous follower controller; , , , , , and ; represents a continuous intermediate control signal and is designed as follows: ； In the formula, , , .

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