Cooperative formation control method for heterogeneous unmanned cluster

Abstract

The invention provides a cooperative formation control method for a heterogeneous unmanned cluster, and the method is applied to an air-land cooperative system of unmanned aerial vehicles and unmanned vehicles, and comprises the steps: building a heterogeneous unmanned cluster system model based on a discretized kinematic model of the unmanned aerial vehicles and the unmanned vehicles and considering the interference of the unmanned aerial vehicle cluster in the flight process; the method comprises the following steps: designing a hierarchical control framework, combining an extended state observer and a Kalman filter in an estimation layer to design an ESKF to estimate a system state and external interference, and designing a terminal cost function, a common state compatibility constraint, a terminal control input and a terminal area according to a control target of the heterogeneous unmanned cluster system in a decision layer. And the individual optimization problem of each unmanned aerial vehicle is synchronously solved by using a synchronous distributed MPC algorithm, and the control layer converts the control instruction obtained by the decision layer into the actual action of the heterogeneous unmanned cluster so as to update the individual state. According to the method, anti-interference cooperative control of trajectory tracking, formation keeping, real-time obstacle avoidance and communication keeping is realized.

Description

Technical Field

[0001] This application belongs to the field of unmanned aerial vehicle (UAV) control technology, and in particular relates to a cooperative formation control method for heterogeneous unmanned aerial vehicle (UAV) swarms. Background Technology

[0002] Distributed cooperative control of unmanned aerial vehicle (UAV) swarms has shown great application potential in civilian, industrial, agricultural, and urban construction fields. Its core idea is to drive collaborative operations through adjacent interactions and control strategy design. Formation control is currently receiving widespread attention in UAV swarm system research, typically aiming to enable swarms to simultaneously achieve complex task requirements such as trajectory tracking, formation maintenance, inter-UAV collision avoidance, and obstacle avoidance. To address communication delays and local information processing limitations in UAV swarms, researchers have proposed more complex distributed control strategies that consider both system dynamics and constraints, thereby enhancing the system's adaptability, flexibility, and robustness.

[0003] However, in practical applications of unmanned swarms, variable weather conditions, strong winds, electromagnetic noise in the natural environment, stray signals from other electronic devices, and active interference from hostile forces can severely impact the perception, communication, and navigation capabilities of unmanned swarms, leading to data transmission errors, sensor misjudgments, and navigation system deviations. Furthermore, unknown obstacles in complex terrain increase the difficulty of path planning and obstacle avoidance, while sensor noise levels are significantly higher in complex environments. Under resource constraints, achieving efficient task allocation, autonomous collaboration, and fault tolerance in complex physical environments has become a key research direction for unmanned swarms. While existing methods and technologies have achieved significant results in homogeneous unmanned swarm formation systems, heterogeneous unmanned swarms have received widespread attention in recent years due to the increasing complexity of collaborative tasks. However, current research still has limitations, and the collaborative operation of heterogeneous unmanned swarms in complex environments remains restricted. Summary of the Invention

[0004] In view of this, the purpose of this application is to provide a cooperative formation control method for heterogeneous unmanned swarms, based on an integrated estimation-decision-control architecture, which can realize anti-disturbance cooperative control with functions such as trajectory tracking, formation maintenance, real-time obstacle avoidance, and communication maintenance.

[0005] This application provides a cooperative formation control method for heterogeneous unmanned swarms, which is applied to an air-to-ground cooperative system of unmanned aerial vehicles and unmanned vehicles. The method includes: Based on the discretized kinematic models of UAVs and unmanned vehicles, and taking into account the interference encountered during the flight of UAV swarms, a heterogeneous unmanned swarm system model is constructed. A hierarchical control framework is designed. In the estimation layer, an extended state observer is combined with a Kalman filter to design an ESKF to estimate the system state and external disturbances. In the decision layer, the terminal cost function, common state compatibility constraints, terminal control input, and terminal region are designed according to the control objectives of the heterogeneous unmanned swarm system. The synchronous distributed MPC algorithm is used to solve the individual optimization problem of each UAV synchronously. The control layer transforms the control commands obtained from the decision layer into the actual actions of the heterogeneous unmanned swarm in order to update the individual states.

[0006] The beneficial effects of the cooperative formation control method for heterogeneous unmanned swarms provided in this application are as follows: Based on an integrated estimation-decision-control architecture, it achieves anti-disturbance cooperative control with functions such as trajectory tracking, formation maintenance, real-time obstacle avoidance, and communication maintenance. The estimation layer employs extended state Kalman filtering, enabling each agent in the unmanned swarm to estimate the system state and external disturbances in real time, effectively reducing the impact of uncertainty on formation control accuracy and enhancing the anti-disturbance capability of cooperative control. The decision layer proposes a synchronous distributed MPC algorithm, considering formation cost, tracking cost, and multiple constraints, achieving multi-functionality in cooperative control. By introducing compatibility constraints and assumed states, the terminal controller is designed to ensure the stability of the system's real-time solution. Attached Figure Description

[0007] Figure 1 A flowchart of the cooperative formation control method for heterogeneous unmanned swarms provided in an embodiment of this application is shown; Figure 2 This application provides a heterogeneous unmanned swarm formation trajectory diagram according to an embodiment of the present application. Figure 3 This application provides different perspectives for the trajectory diagrams of heterogeneous unmanned swarm formations from various viewpoints. Figure 4 This paper shows a graph illustrating the trend of formation tracking error values ​​of various agents in a heterogeneous unmanned swarm provided in an embodiment of this application. Figure 5 This paper shows a graph illustrating the changing trend of cost function values ​​for each agent in a heterogeneous unmanned swarm provided in an embodiment of this application. Figure 6 This illustrates an obstacle avoidance diagram of a heterogeneous unmanned swarm provided in an embodiment of this application; Figure 7 The diagram illustrates obstacle avoidance patterns of heterogeneous unmanned swarms from different perspectives, as provided in the embodiments of this application. Detailed Implementation

[0008] To make the objectives, technical solutions, and advantages of this technical solution clearer, the following detailed description, in conjunction with specific embodiments, further illustrates this technical solution. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this technical solution.

[0009] Example 1:

[0010] Please see as follows Figure 1 The flowchart illustrates a cooperative formation control method for heterogeneous unmanned swarms. Figure 1 As shown, the method includes; S1. Based on the discretized kinematic models of UAVs and unmanned vehicles, and taking into account the interference encountered during the flight of UAV swarms, a heterogeneous unmanned swarm system model is constructed.

[0011] The kinematic models of the discretized UAVs and unmanned vehicles are unified as follows: (1) In the formula, Represents intelligent agents (Drones or unmanned vehicles) in The state at any given moment, Represents intelligent agents exist The state at any given moment, This is a state matrix used to describe the agent. Unable to control the natural motion characteristics during input. This is the input matrix, used to describe how the control input affects the state changes. For intelligent agents The control input represents the desired speed command. Represents intelligent agents Measurable output, This is the output matrix, used to describe the correspondence between states and observable outputs; definition A collection of drones, A collection of driverless cars. The sampling period; when At that time, the discrete system matrix of the UAV is: ; The continuous state matrix is ​​represented as follows: The input matrix is ​​represented as , Represents a 3D zero-order matrix. Represents a 3D identity matrix. Represents the time constant in the velocity loop; when At that time, the discrete system matrix of the autonomous vehicle is: ; The continuous state matrix is ​​represented as follows: The input matrix is ​​represented as , Represents a 2D zero-order matrix. Represents a 2D identity matrix. Represents the time constant in the velocity loop. It is a 4-dimensional identity matrix; Considering the interference, uncertainties, and noise in actual drone swarm flight, interference and noise terms are introduced, resulting in the following heterogeneous drone swarm system model: (2) In the formula, This represents the disturbance distribution matrix, used to map unknown disturbances to the state space. Represents intelligent agents exist The state at time is Unknown nonlinear disturbances encountered at that time Process noise is used to describe the random uncertainty in state evolution. Represents intelligent agents exist Measurable output at any given time For measuring noise, it is used to describe random errors in the output measurement.

[0012] S2. Design a hierarchical control framework. In the estimation layer, combine the extended state observer with the Kalman filter to design an ESKF to estimate the system state and external disturbances. In the decision layer, design the terminal cost function, common state compatibility constraints, terminal control input and terminal region according to the control objectives of the heterogeneous unmanned swarm system. Use the synchronous distributed MPC algorithm to solve the individual optimization problem of each UAV synchronously. The control layer transforms the control commands obtained from the decision layer into the actual actions of the heterogeneous unmanned swarm in order to update the individual states.

[0013] In practical implementation, the Extended State Observer (ESKF) is designed by combining the extended state observer with the Kalman filter at the estimation layer to estimate the system state and external disturbances in the following way: The augmented state, composed of the state of the heterogeneous unmanned swarm system and external disturbances, is as follows: (3) In the formula, This represents the state transition matrix of the augmented system. , This is the state transition matrix of the original system. For interference For the original state Influence matrix To interfere with its own first-order difference model, where, , Represents the input matrix of the augmented system. , To control input For the original state The function, Represents the interference differential input matrix. The first-order difference of the disturbance is used to describe the rate of change of the disturbance. , Augmented output matrix, used to describe the original state and interference To measurement output The mapping, This is the output matrix of the original system; The following assumptions are made when setting up a heterogeneous unmanned cluster system: Assumption 1: Noise is bounded. The noise is uncorrelated and satisfies ; In the formula, This represents the mathematical expectation operator, used to calculate the statistical average of random variables. Given a positive semi-definite matrix, it is used to define the upper bound of the process noise. Given a positive semi-definite matrix, it is used to define the upper bound of the measurement noise; Assumption 2: The initial estimation error is bounded. (4) In the formula, For intelligent agents Original state Initial estimate, For intelligent agents interference The initial estimate, where, , Given a positive semi-definite matrix, it is used to limit the upper bound of the initial estimation error covariance; Assumption 3: Boundedness of interference energy: (5) In the formula, Indicates the first One interference component, Indicates the first The uniform bounded upper bound of the disturbance energy; An ESKF is designed by combining an extended state observer and a Kalman filter to obtain the updated values ​​of the augmented state as follows: (6) In the formula, The filter gain is expressed as follows: (7) In the formula, The covariance intersection term of the state prediction and measurement outputs. To predict the covariance of the output, These are adaptive parameters used to balance model uncertainty and measurement noise, specifically represented as follows: (8) In the formula, The trace of a matrix (the sum of its diagonal elements) is used to characterize the total energy of the matrix. This represents the covariance matrix related to the initial disturbance energy. Furthermore, the covariance update equation is expressed as follows: (9) In the formula, This represents the covariance reduction term introduced by measurement corrections, used when the uncertainty is known. , The noise covariance matrix is ​​represented as follows: (10) (11) In the formula, The original system process noise covariance, Indicates in Constant interference The diagonal covariance matrix is ​​represented as follows: (12) In the formula, For interference Dimensions This represents the diagonal matrix construction operator. Indicates in Time of the first The upper bound scalar of the energy of each disturbance component; In addition, the disturbance saturation constraint is as follows: (13) In the formula, Represents intelligent agents exist The disturbance estimate after saturation processing at time [time]. Represents intelligent agents exist The original disturbance estimate at time (obtained from ESKF). This represents a saturation function, used to limit the magnitude of a variable. Indicates the saturation threshold, which is... The maximum allowable value of the amplitude of the first interference component at any given time.

[0014] In practical implementation, the terminal cost function is designed as follows: (14) In the formula, Represents intelligent agents The finite-time cost function aims to minimize the cumulative cost over the next N (prediction time) steps, derived from the stage cost function. and terminal costs constitute; The stage cost function is expressed as follows: (15) In the formula, the first term To track the error term, Represents intelligent agents Compared with reference trajectory The relative state, This is the weight matrix, used to penalize tracking bias; the second term... To input the difference item, Represents intelligent agents With reference input Control input difference, This is the weight matrix, used to limit abrupt changes in the control input and ensure smooth control. The third term... For formation constraints, Represents intelligent agents with neighbors The relative output, This is a weight matrix used to force the cluster to maintain a preset formation. To predict the step size; And, the terminal cost term is represented as follows: (16) In the formula, Indicates the terminal time Secondary penalty for relative states This is the terminal weight matrix; Among them, based on Time information prediction Time-based intelligent agent relative reference The state deviations are as follows: (17) In the formula, For the desired offset, It is used to achieve tracking and maintain formation; predict Time-based intelligent agent with neighbors The output deviation is as follows: (18) In the formula, For the desired spacing, ; predict Time-based intelligent agent relative reference The input deviations are as follows: (19) In practical implementation, the common state compatibility constraint is designed as follows: Since the current UAV is unaware of the actual control inputs and states of other UAVs when using a synchronous control strategy, the following assumption is made regarding the control inputs: (20) In the formula, For model predictive control at The optimal control input sequence obtained at each time step. This is the terminal control input, and the gain is controlled by the terminal. Obtained from the terminal status, ; The following hypothetical predictions about the future state at the current moment are derived: ;(twenty one) In the formula, For model predictive control at The optimal state prediction sequence obtained at time t. The terminal's assumed state is recursively derived from the previous optimal state and the terminal's control input, as shown below: ;(twenty two) In the formula, The system state space matrix; To eliminate the impact of the assumed state replacing the actual state on system stability, the following common state compatibility constraint is introduced: ;(twenty three) in, This is a positive definite weight matrix, used to reflect the degree of importance given to different output components. For intelligent agents The output prediction bias, To constrain the boundary, the specific representation is as follows: ;(twenty four) In the formula, the coefficients Represents all neighbors The weights sum, Used to represent the number of neighbors and the coupling strength The influence of the constraint boundary, coefficient This represents the weighted sum of the assumed output biases among neighbors. , Intelligent agents used for reflection with neighbors The difference in the hypothetical output, coefficient Indicates reference state Convergence speed and the negative constant related to N in the prediction time domain, Used to guarantee It is a positive real number; in, (25) In the formula, For the specified convergence rate parameters, For intelligent agents with neighbors The hypothetical output prediction, For intelligent agents with neighbors The relative deviation between the expected outputs.

[0015] In practical implementation, the terminal control input is designed as follows: (26) In the formula, Represents intelligent agents The reference state prediction value; Terminal set is defined as: (27) In the formula, The radius of the terminal set defines the maximum tolerable range of state deviation from the reference target. definition And transform the constraints of the terminal set into the form of linear matrix inequalities (LMI); When N≤1, the terminal set satisfies the following constraints: (1) In order to limit the deviation of state components (such as position) from not exceeding the physical upper limit With reference upper limit The difference is such that the design location constraints are as follows: (28) In the formula, The selection matrix is ​​used to extract specific components (such as position) from the state vector. (2) In order to limit the amplitude of the control input from not exceeding the physical limit of the actuator. With reference input upper limit The difference is as follows: The input constraints are designed as follows: (29) In the formula, The selection matrix is ​​used to extract specific components (such as thrust) from the control vector. (3) In order to limit the impact of positional disturbances on the system and ensure that the disturbance intensity does not exceed At that time, the system remains stable, and the design disturbance constraints are as follows: (30) In the formula, The perturbation distribution matrix is... This represents the upper limit of the disturbance amplitude; in, (31) In the formula, To ensure minimum safe distance, individual constraints are applied. The minimum value is obtained as follows: intelligent agent The minimum safe distance from neighboring drones is as follows: (32) In the formula, The drone's own safety radius (or collision radius); intelligent agent The maximum safe distance from neighboring drones is as follows: (33) In the formula, This represents the maximum distance limit for communication / cooperation. intelligent agent The minimum safe distance from static obstacles is as follows: (34) In the formula, The location of the static obstacle. Represents intelligent agents exist Reference position at any moment The safe radius of the obstacle; (4) The stability constraints are as follows: (35) in, ; ; Based on the above constraints (1)-(4), solve get To obtain the maximum terminal area.

[0016] In practical implementation, the synchronous distributed MPC algorithm is designed as follows: In the offline phase, for each drone, the neighbor set of that drone is determined, and simulation calculations are performed. The initial assumed state sequence under the step size is used to determine the terminal stability parameters by solving a linear matrix inequality optimization problem. and setting reference state trajectory Reference control input Expected relative position vector Expected relative output vector Weight matrix and parameters ; During the online phase, at the initial time k=0, we have Drone i sends the initial hypothetical state To drone j, and simultaneously receive the initial assumed state of drone j. At time k≤ First, the estimated state at the current moment is obtained by fusing sensor data using ESKF, which serves as the initial state for subsequent predictions. Then, the hypothetical state at the current moment is updated based on the state estimate and the hypothetical control input. Then drone i sends the updated hypothetical state. Send to drone j, and simultaneously receive the updated hypothetical state of drone j. ; In the iterative phase, based on the current estimated state, the neighbor assumption state, and various constraints, the individual optimization problem of the UAV is solved to obtain the optimal control input sequence in the prediction time domain. The first element of the optimal control sequence is applied to UAV i, and the time step is updated. .

[0017] In practice, the individual optimization problem for each drone is described by the following objective function: (36) The constraints of the objective function are as follows: (1) The system state return constraints are as follows: (37) (2) The constraints of the output equation are as follows: (38) (3) The state and input physical feasible region constraints are as follows: (39) (4) The minimum collision avoidance constraints between UAVs are as follows: (40) (5) The maximum distance constraints for communication / formation between UAVs are as follows: (41) (6) The collision avoidance constraints with static obstacles are as follows: (42) (7) The relative positional coordination constraints between UAVs are as follows: (43) The common state compatibility constraints are as follows: (44) (9) The initial state constraints are as follows: (45) (10) The stability constraints of the terminal set are as follows: (46) (11) The collision avoidance constraints with obstacles / targets are as follows: (47) In the formula, Indicates limitation by intelligent agent The state trajectory, Indicates moving obstacles / targets Position function, Indicates moving obstacles / targets velocity function, Indicates moving obstacles / targets The safe radius.

[0018] Example 2: Simulation Verification For heterogeneous unmanned swarms, the integrated estimation-decision-control strategy proposed in this application can meet the complex task requirements such as trajectory tracking, formation maintenance, and obstacle avoidance. To illustrate the superiority and effectiveness of the proposed method, detailed simulations are performed in this embodiment.

[0019] Consider two drone swarms and one unmanned vehicle swarm, where , , Each cluster has a leader, and the cluster members satisfy the model described in formula (2), where Sampling time The covariance matrices of process noise and measurement noise are respectively The matrix is ​​set as follows: Convergence speed parameters The state constraints are satisfied. Input constraints satisfy , The drone's safe radius is set to... The safe radius of the autonomous vehicle is set to 1m, the maximum communication radius is set to 50m, and the prediction time domain of the model prediction algorithm is set to... The cost function weight matrices are respectively , , .

[0020] The communication topology and the neighbor relationship topology between UAVs are as follows: The communication topology between heterogeneous unmanned clusters is a directed graph. Description, in which For a set of nodes, Represents an edge set. For directed graphs Let the adjacency matrix be denoted by . If and only if hour, ,otherwise, .

[0021] To better describe formation performance, formation tracking error and formation maintenance error are defined as follows: (48) The initial states of each agent in the unmanned cluster are set as follows: (49) (50) The reference trajectory is designed as follows: (51) (52) (53) By solving the LMI optimization problem, we can obtain Taking drone 1 and unmanned vehicle 3 as examples, the specific values ​​are as follows: (54) (55) (56) (57) (58) (59) Based on the above data, the individual optimization problem of the UAV is solved to ensure the stability of the algorithm.

[0022] Simulation results are as follows Figure 2-7 As shown. Figure 2The image shows the trajectory of a heterogeneous unmanned swarm formation. Figure 3 The diagram shows the trajectories of a heterogeneous unmanned swarm formation from different perspectives. Unmanned aerial vehicles (UAVs) are represented by circles, unmanned vehicles by squares, the desired trajectory by dashed lines, and the swarm trajectory by solid lines.

[0023] Figure 4 The figure shows the trend of formation tracking error values ​​of each agent in a heterogeneous unmanned swarm. In a complex environment, each agent changes from a straight line to the desired formation. The initial error value is large, but the error value gradually decreases over time under the presence of interference and noise.

[0024] Figure 5 The figure shows the trend of cost function values ​​of each agent in the heterogeneous unmanned cluster. It can be seen that JΣ(K) decreases monotonically and tends to zero, indicating that the system is asymptotically stable.

[0025] Figure 6 The image shows an obstacle avoidance diagram for a heterogeneous unmanned swarm. Figure 7 The image shows obstacle avoidance diagrams of heterogeneous unmanned swarms from different perspectives. Figure 6 and Figure 7 It demonstrates that each agent can autonomously avoid obstacles starting from its initial position and can restore its original formation to continue tracking the reference trajectory.

[0026] The simulation experiments demonstrated that the unmanned swarm can track trajectories in real time, maintain formation, and perform complex tasks such as collision avoidance in complex environments.

[0027] The above content is only a preferred embodiment of the present invention. For those skilled in the art, many changes can be made in the specific implementation and application scope based on the ideas of the present invention. As long as these changes do not depart from the concept of the present invention, they all fall within the protection scope of the present invention.

Claims

1. A cooperative formation control method for heterogeneous unmanned swarms, characterized in that, The method is applied to an air-to-ground cooperative system of unmanned aerial vehicles and unmanned vehicles, and the method includes: Based on the discretized kinematic models of UAVs and unmanned vehicles, and taking into account the interference encountered during the flight of UAV swarms, a heterogeneous unmanned swarm system model is constructed. A hierarchical control framework is designed. In the estimation layer, an extended state observer is combined with a Kalman filter to design an ESKF to estimate the system state and external disturbances. In the decision layer, the terminal cost function, common state compatibility constraints, terminal control input, and terminal region are designed according to the control objectives of the heterogeneous unmanned swarm system. The synchronous distributed MPC algorithm is used to solve the individual optimization problem of each UAV synchronously. The control layer transforms the control commands obtained from the decision layer into the actual actions of the heterogeneous unmanned swarm in order to update the individual states.

2. The method as described in claim 1, characterized in that, The unified kinematic models of the discretized UAVs and unmanned vehicles are as follows: ； In the formula, Represents intelligent agents (Drones or unmanned vehicles) in The state at any given moment, Represents intelligent agents exist The state at any given moment, This is a state matrix used to describe the agent. Unable to control the natural motion characteristics during input. This is the input matrix, used to describe how the control input affects the state changes. For intelligent agents The control input represents the desired speed command. Represents intelligent agents Measurable output, This is the output matrix, used to describe the correspondence between states and observable outputs; definition A collection of drones, A collection of driverless cars. The sampling period; when At that time, the discrete system matrix of the UAV is: , ; The continuous state matrix is ​​represented as follows: The input matrix is ​​represented as , Represents a 3D zero-order matrix. Represents a 3D identity matrix. Represents the time constant in the velocity loop; when At that time, the discrete system matrix of the autonomous vehicle is: ; The continuous state matrix is ​​represented as follows: The input matrix is ​​represented as Represents a 2D zero-order matrix. Represents a 2D identity matrix. Represents the time constant in the velocity loop. It is a 4-dimensional identity matrix; Considering the interference, uncertainties, and noise in actual drone swarm flight, interference and noise terms are introduced, resulting in the following heterogeneous drone swarm system model: ； In the formula, This represents the disturbance distribution matrix, used to map unknown disturbances to the state space. Represents intelligent agents exist The state at time is Unknown nonlinear disturbances encountered at that time Process noise is used to describe the random uncertainty in state evolution. Represents intelligent agents exist Measurable output at any given time For measuring noise, it is used to describe random errors in the output measurement.

3. The method as described in claim 1, characterized in that, The method of combining an extended state observer with a Kalman filter at the estimation layer to design an ESKF for estimating system state and external disturbances includes: The augmented state, composed of the state of the heterogeneous unmanned swarm system and external disturbances, is as follows: ； In the formula, This represents the state transition matrix of the augmented system. , This is the state transition matrix of the original system. For interference For the original state Influence matrix To interfere with its own first-order difference model, where, , Represents the input matrix of the augmented system. , To control input For the original state The function, Represents the interference differential input matrix. , The first-order difference of the disturbance is used to describe the rate of change of the disturbance. , Augmented output matrix, used to describe the original state and interference To measurement output The mapping, , This is the output matrix of the original system; The following assumptions are made when setting up a heterogeneous unmanned cluster system: Assumption 1: Noise is bounded. The noise is uncorrelated and satisfies ; In the formula, This represents the mathematical expectation operator, used to calculate the statistical average of random variables. Given a positive semi-definite matrix, it is used to define the upper bound of the process noise. Given a positive semi-definite matrix, it is used to define the upper bound of the measurement noise; Assumption 2: The initial estimation error is bounded. ； In the formula, For intelligent agents Original state Initial estimate, For intelligent agents interference The initial estimate, where, , Given a positive semi-definite matrix, it is used to limit the upper bound of the initial estimation error covariance; Assumption 3: Boundedness of interference energy: ； In the formula, Indicates the first One interference component, Indicates the first The uniform bounded upper bound of the disturbance energy; An ESKF is designed by combining an extended state observer and a Kalman filter to obtain the updated values ​​of the augmented state as follows: ； In the formula, The filter gain is expressed as follows: ； In the formula, The covariance intersection term of the state prediction and measurement outputs. To predict the covariance of the output, These are adaptive parameters used to balance model uncertainty and measurement noise, specifically represented as follows: ； In the formula, The trace of a matrix (the sum of its diagonal elements) is used to characterize the total energy of the matrix. This represents the covariance matrix related to the initial disturbance energy. Furthermore, the covariance update equation is expressed as follows: ； In the formula, This represents the covariance reduction term introduced by measurement corrections, used when the uncertainty is known. , The noise covariance matrix is ​​represented as follows: ； ； In the formula, The original system process noise covariance, Indicates in Constant interference The diagonal covariance matrix is ​​represented as follows: ； In the formula, For interference Dimensions This represents the diagonal matrix construction operator. Indicates in Time of the first The upper bound scalar of the energy of each disturbance component; In addition, the disturbance saturation constraint is as follows: ； In the formula, Represents intelligent agents exist The disturbance estimate after saturation processing at time [time]. Represents intelligent agents exist The original disturbance estimate at time (obtained from ESKF). This represents a saturation function, used to limit the magnitude of a variable. Indicates the saturation threshold, which is... The maximum allowable value of the amplitude of the first interference component at any given time.

4. The method as described in claim 1, characterized in that, The terminal cost function is designed as follows: ； In the formula, Represents intelligent agents The finite-time cost function aims to minimize the cumulative cost over the next N (prediction time) steps, derived from the stage cost function. and terminal costs constitute; The stage cost function is expressed as follows: ； In the formula, the first term To track the error term, Represents intelligent agents Compared with reference trajectory The relative state, This is the weight matrix, used to penalize tracking bias; the second term... To input the difference item, Represents intelligent agents With reference input Control input difference, This is the weight matrix, used to limit abrupt changes in the control input and ensure smooth control. The third term... For formation constraints, Represents intelligent agents with neighbors The relative output, This is a weight matrix used to force the cluster to maintain a preset formation. To predict the step size; And, the terminal cost term is represented as follows: ； In the formula, Indicates the terminal time Secondary penalty for relative states This is the terminal weight matrix; Among them, based on Time information prediction Time-based intelligent agent relative reference The state deviations are as follows: ； In the formula, For the desired offset, It is used to achieve tracking and maintain formation; predict Time-based intelligent agent with neighbors The output deviation is as follows: ； In the formula, For the desired spacing, ; predict Time-based intelligent agent relative reference The input deviations are as follows: 。 5. The method as described in claim 1, characterized in that, The common state compatibility constraint design is as follows: Since the current UAV is unaware of the actual control inputs and states of other UAVs when using a synchronous control strategy, the following assumption is made regarding the control inputs: ； In the formula, For model predictive control at The optimal control input sequence obtained at each time step. This is the terminal control input, and the gain is controlled by the terminal. Obtained from the terminal status, ; The following hypothetical predictions about the future state at the current moment are derived: ； In the formula, For model predictive control at The optimal state prediction sequence obtained at time t. The terminal's assumed state is recursively derived from the previous optimal state and the terminal's control input, as shown below: ； In the formula, The system state space matrix; To eliminate the impact of the assumed state replacing the actual state on system stability, the following common state compatibility constraint is introduced: ； in, This is a positive definite weight matrix, used to reflect the degree of importance given to different output components. For intelligent agents The output prediction bias, To constrain the boundary, the specific representation is as follows: ； In the formula, the coefficients Represents all neighbors The weights sum, Used to represent the number of neighbors and the coupling strength The influence of the constraint boundary, coefficient This represents the weighted sum of the assumed output biases among neighbors. , Intelligent agents used for reflection with neighbors The difference in the hypothetical output, coefficient Indicates reference state Convergence speed and the negative constant related to N in the prediction time domain, Used to guarantee It is a positive real number; in, ; In the formula, For the specified convergence rate parameters, For intelligent agents with neighbors The hypothetical output prediction, For intelligent agents with neighbors The relative deviation between the expected outputs.

6. The method as described in claim 1, characterized in that, The terminal control input design is as follows: ； In the formula, Represents intelligent agents The reference state prediction value; Terminal set is defined as: ； In the formula, The radius of the terminal set defines the maximum tolerable range of state deviation from the reference target. definition And transform the constraints of the terminal set into the form of linear matrix inequalities (LMI); When N≤1, the terminal set satisfies the following constraints: (1) In order to limit the deviation of state components (such as position) from not exceeding the physical upper limit With reference upper limit The difference is such that the design location constraints are as follows: ； In the formula, The selection matrix is ​​used to extract specific components (such as position) from the state vector. (2) In order to limit the amplitude of the control input from not exceeding the physical limit of the actuator. With reference input upper limit The difference is as follows: The input constraints are designed as follows: ； In the formula, The selection matrix is ​​used to extract specific components (such as thrust) from the control vector. (3) In order to limit the impact of positional disturbances on the system and ensure that the disturbance intensity does not exceed At that time, the system remains stable, and the design disturbance constraints are as follows: ； In the formula, The perturbation distribution matrix is... This represents the upper limit of the disturbance amplitude; in, ; In the formula, To achieve the minimum safe distance, it consists of three sub-constraints. The minimum value is obtained as follows: intelligent agent The minimum safe distance from neighboring drones is as follows: ； In the formula, The drone's own safety radius (or collision radius); intelligent agent The maximum safe distance from neighboring drones is as follows: ； In the formula, This represents the maximum distance limit for communication / cooperation. intelligent agent The minimum safe distance from static obstacles is as follows: ； In the formula, The location of the static obstacle. Represents intelligent agents exist Reference position at any moment The safe radius of the obstacle; (4) The stability constraints are as follows: ； in, ; ； Based on the above constraints (1)-(4), solve get To obtain the maximum terminal area.

7. The method as described in claim 1, characterized in that, The synchronous distributed MPC algorithm is designed as follows: In the offline phase, for each drone, the neighbor set of that drone is determined, and simulation calculations are performed. The initial assumed state sequence under the step size is used to determine the terminal stability parameters by solving a linear matrix inequality optimization problem. and setting reference state trajectory Reference control input Expected relative position vector Expected relative output vector Weight matrix and parameters ; During the online phase, at the initial time k=0, we have Drone i sends the initial hypothetical state To drone j, and simultaneously receive the initial assumed state of drone j. At time k≤ First, the estimated state at the current moment is obtained by fusing sensor data using ESKF, which serves as the initial state for subsequent predictions. Then, the hypothetical state at the current moment is updated based on the state estimate and the hypothetical control input. Then drone i sends the updated hypothetical state. Send to drone j, and simultaneously receive the updated hypothetical state of drone j. ; In the iterative phase, based on the current estimated state, the neighbor assumption state, and various constraints, the individual optimization problem of the UAV is solved to obtain the optimal control input sequence in the prediction time domain. The first element of the optimal control sequence is applied to UAV i, and the time step is updated. .

8. The method as described in claim 7, characterized in that, The individual optimization problem for each drone is described by the following objective function: ； The constraints of the objective function are as follows: (1) The system state return constraints are as follows: ； (2) The constraints of the output equation are as follows: ； (3) The state and input physical feasible region constraints are as follows: ； (4) The minimum collision avoidance constraints between UAVs are as follows: ； (5) The maximum distance constraints for communication / formation between UAVs are as follows: ； (6) The collision avoidance constraints with static obstacles are as follows: ； (7) The relative positional coordination constraints between UAVs are as follows: ； The common state compatibility constraints are as follows: ； (9) The initial state constraints are as follows: ； (10) The stability constraints of the terminal set are as follows: ； (11) The collision avoidance constraints with obstacles / targets are as follows: ； In the formula, Indicates limitation by intelligent agent The state trajectory, Indicates moving obstacles / targets Position function, Indicates moving obstacles / targets velocity function, Indicates moving obstacles / targets The safe radius.

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