An adaptive pre-defined time event triggered platoon tracking control method

Abstract

The application discloses a kind of self-adapting pre-defined time event trigger formation tracking control methods: step 1: establishing position subsystem, attitude subsystem, position loop error system and attitude loop error system to each unmanned aerial vehicle;Step 2: design position loop pre-defined time sliding mode surface, position loop controller and adaptive law;Step 3: in each unmanned aerial vehicle, the desired roll angle and desired pitch angle of position loop error system output are input to attitude loop error system, and the obtained attitude error is input to the attitude loop controller of corresponding unmanned aerial vehicle;Step 4: design attitude loop pre-defined time sliding mode surface, attitude loop controller and adaptive law, event trigger mechanism for each unmanned aerial vehicle;Step 5, each unmanned aerial vehicle flies according to the instruction of position loop controller and attitude loop controller.The application can enhance the robustness of controller;Make formation system convergence time upper limit can be set, reduce the communication burden of unmanned aerial vehicle in the process of formation.

Description

Technical Field

[0001] This invention belongs to the field of UAV formation control technology, specifically relating to an adaptive predefined time event triggered formation tracking control method. Background Technology

[0002] Due to the complex mountainous terrain, with numerous natural barriers and communication blind spots, single-aircraft reconnaissance missions are prone to omissions or low efficiency. However, rotorcraft UAV swarms, through multi-aircraft collaboration, can achieve multi-dimensional, multi-layered, three-dimensional reconnaissance coverage. Figure 1 As shown, this poses a demand for formation coordination control. However, the turbulent airflow in the mountains causes great interference to the formation and maintenance of the formation, and may even destroy the formation in severe cases. Reference [1] assumes that the nominal mass of the UAV and the upper limit of the disturbance are known, and thus designs a preset gain in the controller to cancel the disturbance. However, the actual mass of the UAV and the upper limit of the external disturbance in the mountain environment are difficult to obtain accurately, which makes it impossible for the controller to issue precise control commands, resulting in adverse effects on the reconnaissance process and results. In addition, since the reconnaissance mission is relatively urgent, the commander usually issues a mission time limit, which puts forward a high requirement for the rapid formation of the formation.

[0003] Therefore, it is essential to design a new formation tracking control method.

[0004] The following are the publicly available documents involved in this invention:

[0005] [1] Tan Weicong, Wu Qiwu, Zhu Li, et al. Adaptive fixed-time quadrotor event-triggered control [J]. Journal of Ordnance Equipment Engineering, 2025, 46 (04): 225-234. [2]Wang C, Lin Y. Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems[J]. Automatica, 2015, 54:16-24. [3]Muñoz-Vázquez AJ, Sánchez-Torres JD, Jiménez-Rodríguez E, et al. Predefined-time robust stabilization of robotic manipulators[J]. IEEE / ASME Transactions on mechatronics, 2019, 24(3): 1033-1040. [4]Xie S, Chen Q. Adaptive nonsingular predefined-time control forattitude stabilization of rigid spacecrafts[J]. IEEE Transactions on Circuitsand Systems II: Express Briefs, 2021, 69(1): 189-193. [5]Zuo Z. Nonsingular fixed-time consensus tracking for second-ordermulti-agent networks[J]. Automatica, 2015, 54: 305-309. [6] Li Qinglin. Research on trajectory tracking control of quadrotor UAV based on event triggering [D]. North University of China, 2024. [7] Hu Jinfan. Unmanned aerial vehicle (UAV) formation control based on virtual navigator [J]. Electronic Measurement Technology, 2023, 46(22):70-77. Summary of the Invention The purpose of this invention is to provide an adaptive predefined time event triggered formation tracking control method to solve the problems of existing technologies, such as difficulty in adapting to external time-varying wind disturbances, the inability to preset the convergence time of the formation system, and the heavy burden on airborne communication.

[0006] To achieve the above objectives, the present invention employs the following technical solution: An adaptive predefined time event triggered formation tracking control method includes the following steps: Step 1: Set the center of the quadcopter drone formation as the virtual navigator position, set the virtual navigator's trajectory as the path to be inspected, and assign the desired position of each other drone relative to the virtual navigator in the formation; establish a position subsystem, attitude subsystem, position loop error system and attitude loop error system for each drone in the formation. Step 2: The virtual navigator, following a preset motion trajectory, inputs its desired position information into the position loop error system of each UAV, and then inputs the obtained position error into the position loop controller of the corresponding UAV; design the predefined time sliding surface of the position loop, the position loop controller, and the adaptive law; Step 3: In each UAV, the desired roll angle, desired pitch angle, and total thrust output from the position loop error system are input into the attitude loop error system, and the obtained attitude error is input into the attitude loop controller of the corresponding UAV. Step 4: Design a predefined time sliding surface for the attitude loop, an attitude loop controller, and an adaptive law for each UAV, and design an event triggering mechanism; Step 5: Each drone flies according to the instructions of the position loop controller and attitude loop controller.

[0007] Compared with the prior art, the present invention has the following technical effects: The method of this invention introduces a neural network into the pose dual-loop control structure to estimate unknown model parameters in the system, replacing the traditional preset gain and thus enhancing the robustness of the controller. Simultaneously, the pose controller is designed based on predefined time stability theory, allowing the upper limit of the convergence time of the formation system to be directly set by the user, improving the planarability of mission time. Furthermore, a corresponding event triggering mechanism is constructed to reduce the communication burden on UAVs during formation. Attached Figure Description

[0008] Figure 1 Diagram illustrating the coverage reconnaissance mission; Figure 2 This is a schematic diagram of the coordinate system of a quadcopter UAV. Figure 3 This is a scenario diagram of a formation-coverage reconnaissance mission in an embodiment of the present invention; Figure 4 This is a diagram illustrating the formation tracking effect. Figure 5 For formation position tracking error; Figure 6 For formation speed tracking error; Figure 7 For formation attitude tracking error; Figure 8 For formation angular velocity tracking error; Figure 9 Total lift; Figure 10 For position loop adaptive parameters; Figure 11 These are the attitude loop adaptive parameters; Figure 12 This is the time interval for triggering the event. Detailed Implementation

[0009] This invention takes a quadcopter UAV as the research object and, based on the adaptive fixed-time event-triggered control framework in reference [1], further proposes an adaptive predefined time event-triggered formation tracking control method. This method introduces a neural network into the pose dual-loop control structure to estimate the unknown model parameters in the system, replacing the traditional preset gain, thereby enhancing the robustness of the controller; at the same time, the pose controller is designed based on the predefined time stability theory, so that the upper limit of the convergence time of the formation system can be directly set by the user, improving the planarability of the task time. In addition, a corresponding event triggering mechanism is constructed to reduce the communication burden of the UAV in the formation process. By constructing a suitable Lyapunov function, the predefined time stability and robust performance of the closed-loop system are theoretically analyzed, and numerical simulation verification is performed in the Matlab / Simulink environment.

[0010] I. Preliminary Knowledge (a) Lemma Lemma 1 [2] For any as well as The following inequality will always hold: (1) Lemma 2 [3] For the following systems: (2) in, It is a continuous function. The initial state of the system is defined as... If there exists a definition in Lyapunov functions on satisfy the following form: (3) in A positive number set by the user, the system at a predefined time. The interior converges to the origin.

[0011] Lemma 3 [4] For system (2), if there exists a definition in Lyapunov functions on satisfy the following form: (4) in , All of them are positive numbers that were artificially assigned. If the system is bounded, then the convergence time and region of convergence satisfy the following relationship: (5) in It is worth noting that... It is bounded.

[0012] Lemma 4 [5] For all positive numbers, ,and The following relationship can be obtained: (6).

[0013] (ii) Radial Basis Function Neural Network Among all neural networks, the Radial Basis Function Neural Network (RBFNN) is widely used due to its simple structure and ease of implementation. In UAV controller design, RBFNN is used to estimate unknown model parameters under uncertain wind disturbances, thanks to its excellent generalization ability and superior approximation performance.

[0014] The definition of a radial basis function neural network is: a neural network defined on a compact set... Unknown nonlinear function within It can be approximated using RBFNN:

[0015] in, The input vector representing the neural network. The weights representing the RBFNN are usually an unknown constant matrix used only for theoretical analysis. Represents the estimation error of the neural network. The vector representing the basis functions of the neural network. This represents the number of nodes in the neural network. Each component in It is usually a Gaussian function, specifically described as follows:

[0016] in Represents the center of the Gaussian function. This represents the width of the Gaussian function.

[0017] Furthermore, by approximating the unknown nonlinear function using radial basis functions, it can be expressed in the following form:

[0018] in, This represents a set of optimal neural network weights, whose function is to minimize the estimation error. Minimize. However, due to the optimal weights This is typically an unknown constant matrix, defined only for theoretical stability proofs and other analytical processes, and therefore cannot be directly applied to practical controller design. In practical applications, it is related to... The corresponding approximation error is given by express.

[0019] (III) Mathematical Model of Quadrotor When modeling a rotary-wing UAV, it is usually necessary to understand the physical characteristics of the object being modeled in order to determine the model parameters. This section takes a quadcopter UAV as an example to establish a mathematical model.

[0020] As a typical underactuated mechanical system, a quadcopter controls its attitude and position by adjusting the speed of its four motors to change thrust. When the quadcopter is stationary, the ground coordinate system and the body coordinate system coincide; however, when in motion, the attitude angles continuously change, which involves the transformation between the body coordinate system and the ground coordinate system. To accurately describe the quadcopter's flight position and attitude information, it is necessary to define both the ground coordinate system and the body coordinate system. Figure 2 As shown, Represents the roll, pitch, and yaw angles in a ground coordinate system. For the UAV ground coordinate system, Let be the body coordinate system. Based on existing research, the specific expression for the coordinate transformation matrix of the UAV in the Euler angle system is as follows:

[0021] Based on the rigid body assumption of the quadrotor and the premise that the origin, center of mass, and geometric center of the body coordinate system coincide, and neglecting the elastic deformation of the fuselage and control surfaces, a force analysis is performed on the quadrotor UAV, and its dynamic relationship is described by Newton's second law:

[0022] in, Indicates the mass of a quadcopter drone. Let be the net external force acting on the drone, which consists of three parts: the drone's own weight, the total lift generated by the rotor, and the wind disturbance force experienced during flight. The above equation can be further rewritten as follows:

[0023] in, It is a unit vector in the vertical direction. The total lift generated by the four rotors of the drone, This refers to the disturbance force (i.e., wind disturbance force) caused by airflow on the drone. It represents gravitational acceleration.

[0024] In summary, the dynamic model of the quadcopter UAV is as follows:

[0025] in, , , These represent the roll angle, pitch angle, and yaw angle of the drone, respectively. These represent the spatial positions of the drone in three directions; Represents the linear velocity of the drone in three directions; Represents gravitational acceleration; The vector representing the unknown external disturbance of the drone; Total lift; It represents virtual control variables in three directions.

[0026] II. Problem Description Control Objective: This paper proposes an adaptive predefined time-triggered formation control method to enable the quadrotor UAV to achieve formation control under conditions where parameter uncertainties and unknown disturbances exist in both the position and attitude loops. The tracking errors of each state variable converge, enabling rapid tracking of the virtual navigator's trajectory and completing the formation tracking task covering the reconnaissance trajectory.

[0027] The established model satisfies the following assumptions: Assumption 1: Drone mass It is a constant but unknown, moment of inertia. and derivative Both have an upper bound.

[0028] Assumption 2: External disturbances to the UAV's position loop and attitude loop both have upper bounds, but these are unknown.

[0029] Assumption 3: The drone always flies within the permissible attitude.

[0030] To reduce the complexity of controller design, a formation task numbered as follows is established. The quadcopter UAV's position and attitude dual closed-loop system [6] as follows: drones The location subsystem is modeled as follows: (7) in, Representative to Differentiate, Representing drones In respectively Spatial position in three directions; Representing drones exist Velocity in three directions; Representing drones The quality; Representing drones exist Control torque in three directions; Representing drones Unknown external disturbance vector. ,in g This is the acceleration due to gravity.

[0031] drones The attitude subsystem is modeled as follows: (8) in, Representative to Differentiate; Representing drones The posture; , , These represent the roll angle, pitch angle, and yaw angle of the drone, respectively. The rotation matrices are represented by the following formula (9); It is a drone Rotational angular velocity in the body coordinate system; It is the moment of inertia matrix, which is a diagonal matrix in which all elements on the diagonal are greater than 0; It is the input to the attitude loop; This represents the attitude disturbance moment, which has an upper bound but is unknown. Its corresponding It is a skew-symmetric matrix: (9) Assuming the center of this formation is a virtual navigator, and its position is... drones The deviation of the desired position in the formation from the center position is: Therefore, drones The position relative to the virtual navigator is The speed is acceleration is .

[0032] In summary, drones The position loop error system is modeled as follows: (10) in, They represent drones Compared to the position and speed errors of its virtual navigator; represent The second derivative; given the desired angle In this situation, the UAV can obtain control commands output by the position subsystem. i Desired attitude and total lift: (11) in, Representing drones i Total lift; , , Representing drones i The expected pitch angle, expected roll angle, and expected yaw angle; drones Expected posture These represent its first and second derivatives, respectively.

[0033] definition , can be obtained .

[0034] Combining formula (8), the UAV The attitude loop error system is modeled as follows: (12) III. Design of an Adaptive Predefined Time Event Triggered Controller (I) Position Subsystem Controller Design and Stability Analysis 1. Position Subsystem Controller Design Design position loop predefined time sliding surface: (13) in (14) in, It is a diagonal matrix in which all diagonal elements are greater than 0; This is a preset constant greater than 0; To ensure the continuity of the sliding surface, They respectively satisfy: (15) Combining formula (14), we get: (16) in, .

[0035] Differentiating with respect to the sliding surface, we get: (17) When reaching the sliding surface Then, the following conditions are met: (18) Combining formula (14), we can obtain: when ,have: (19) when ,have: (20) Combining formulas (19) and (20) with Lemma 2, we can obtain that when the following conditions are met... Afterwards, drones The tracking error will be in time Convergence to and in The asymptotic convergence to 0 is achieved; the next step is to design a controller that can achieve convergence of the position slip surface as much as possible.

[0036] Choose the Lyapunov function: (twenty one) right Differentiation yields: (twenty two) in, Due to the complex wind disturbances in mountainous environments, and the inherent quality errors during drone manufacturing and wear and tear during use, the precise quality and upper limit of external disturbances are crucial factors. [6] Difficult to obtain, therefore To address the aforementioned issues, which make it difficult to directly apply to controller design, RBFNN is used to process unknown functions. By fitting the data, we can obtain: (twenty three) On the position ring, It is a definition in compact set Unknown nonlinear function within, ; This represents a set of optimal position loop neural network weights, whose function is to minimize the position loop estimation error. minimize; The vector representing the basis functions of the neural network, where Let be the number of nodes in the position loop neural network. Each component in the equation is typically a Gaussian function. This represents the input vector of the position loop neural network. However, due to the optimal weights... It is usually an unknown constant matrix, whose definition is only used in theoretical stability proofs and other analytical processes, and therefore cannot be directly applied to actual controller design.

[0037] In this invention, The increase in the number of nodes in the RBF neural network will directly lead to a significant increase in the size of the adaptive parameters, which is similar to the situation in the attitude loop design in reference [1]. In order to ensure feasibility under the limited onboard computing resources of the UAV, the estimator form of the RBF network must be reconstructed to deal with the resulting computational bottleneck.

[0038] Define the following unknown variables: (twenty four) Therefore, we can further conclude that: (25) in, , This represents the number of nodes in the neural network. In fact, the parameters... It is difficult to obtain, and its existence has an unknown upper bound. , Indicates the unknown upper bound The estimate, Indicates to The estimation error.

[0039] In summary, the position loop controller and adaptive law are designed as follows: (26) (27) in, Representing drones exist Control torque in three directions; It is a diagonal matrix in which all diagonal elements are greater than 0. , . , satisfy: (28) in, ; Representing drones i Position ring in Predefined time sliding surfaces for position loops in three directions.

[0040] 2. Stability Analysis of Position Subsystem Controller Theorem 1: Considering the UAV position subsystem (7), under the action of the adaptive predefined time controller (26) and the adaptive law (27), it can be guaranteed that: (1) The sliding surface converges to the neighborhood of zero within a predefined time, and the estimation error is bounded.

[0041] (2) The position error and velocity error converge to the neighborhood of zero within a predefined time.

[0042] Proof (1): The Lyapunov function is selected as follows: (29) Differentiation yields: (30) Combining Lemma 1, we get: (31) Substituting formula (31) into formula (30) yields: (32) in Bounded, These represent taking the minimum and maximum eigenvalues ​​of the matrix, respectively. Therefore... Bounded, therefore the position is a sliding mold surface and estimation error It is bounded, therefore, there exists a bounded constant. satisfy Based on the definition of a sliding surface, we can conclude that there exists a bounded positive number. satisfy .

[0043] right Differentiation yields: (33) Combination From the definition and Lemma 4, we can obtain: (34) in .

[0044] Combining formulas (33) and (34), we can obtain (35) in .

[0045] Combining Lemma 3, we can obtain that At a predefined time Converging inward to: (36) Therefore, sliding surface At a predefined time Converging to: (37) In conclusion, (1) has been proven.

[0046] Proof (2): right Differentiation yields: (38) Combining formulas (13) and (14), we can obtain that after a predefined time... Later, when : (39) It can be known that: (40) Therefore, at the predefined time Within this range, the position error will converge to: (41) Based on the definition of a sliding surface, in this case, the speed error will converge to: (42) when Substituting into the definition of a sliding surface, we get: (43) In conclusion, (2) has been proven.

[0047] (II) Event Trigger Mechanism Design The event triggering mechanism is designed as follows: (44) in, These represent the pitch, roll, and yaw channels, respectively. It is a small positive number; This represents the virtual control torque on the attitude loop, i.e., the attitude loop controller designed below; This represents the actual control torque executed on the attitude loop, serving as the input to the attitude loop; Representing the At each trigger point, the actual executed control torque and the virtual control law can be determined to have the following relationship: (45) Combining formula (44), it is easy to obtain: (46) in, It is a 3×3 diagonal matrix, and each component on the diagonal... It satisfies formula (46). It is a 3-dimensional vector, and each of its components It satisfies formula (46). These represent pitch, roll, and yaw channels, respectively.

[0048] In other words, matrix For a positive definite vector, both its minimum and maximum eigenvalues ​​can be obtained. There exists a known upper bound.

[0049] (III) Attitude Subsystem Controller Design and Stability Analysis 1. Attitude Subsystem Controller Design Design a predefined time sliding surface for the attitude loop: (47) in (48) in It is a diagonal matrix in which all diagonal elements are greater than 0; This is a preset constant greater than 0; To ensure the continuity of the sliding surface, They respectively satisfy: (49) Combining formula (46), we can obtain: (50) in, .

[0050] Combining formula (47), we can obtain: (51) When reaching the sliding surface Then, the following conditions are met: (52) Combining formula (48), we can obtain: when ,have: (53) when ,have: (54) Combining formulas (53) and (54) with Lemma 2, we can obtain that when the following conditions are met... Afterwards, drones The attitude tracking error will be in time Convergence to and in The asymptotic convergence to 0 is achieved. The next step is to design a controller for the attitude loop that can achieve convergence of the attitude loop sliding surface as much as possible.

[0051] Choose the Lyapunov function: (55) right Differentiation yields: (56) in: (57) Due to the upper bound of the drone's rotational inertia and external disturbances [5] Difficult to obtain precisely The upper bound at any given time is unattainable. Similar to the design of the position loop, a radial basis function neural network is used to fit this unknown function, yielding: (58) On the attitude ring, It is a definition in compact set Unknown nonlinear function within, ; This represents a set of optimal attitude loop neural network weights, whose function is to minimize the attitude loop estimation error. minimize; The vector representing the basis functions of the neural network, where Let be the number of nodes in the attitude loop neural network. Each component in the equation is typically a Gaussian function. This represents the input vector of the pose loop neural network. However, due to the optimal weights... It is usually an unknown constant matrix, whose definition is only used in theoretical stability proofs and other analytical processes, and therefore cannot be directly applied to actual controller design.

[0052] In this invention, Using a scaling approach similar to that used for position loops, the following unknown variables are defined: (59) Therefore, we can further conclude that: (60) in, In fact, parameters It is also difficult to obtain, and its existence is beyond the known upper bound. .definition Indicates the unknown upper bound The estimate, They represent respectively to The estimation error.

[0053] In summary, the attitude loop controller and adaptive law are designed as follows: (61) (62) in, This represents the virtual control torque on the attitude loop, i.e., the attitude loop controller; This represents the actual control torque executed on the attitude loop, serving as the input to the attitude loop; j=1,2,3 , , It is a diagonal matrix in which all diagonal elements are greater than 0. , ( )satisfy: (63) in . Representing drones i The attitude loop has a predefined time sliding surface in the pitch, roll and yaw channels; 2. Stability Analysis of Attitude Subsystem Controller Theorem 2: Considering the UAV attitude subsystem (8), under the action of the event triggering mechanism (44), the adaptive update law (62), and the adaptive controller (61), it can be guaranteed that: (1) The attitude sliding surface and its adaptive estimation error can converge to the zero neighborhood and bounded stability respectively within a predefined time.

[0054] (2) The attitude error and angular velocity error converge to the neighborhood of zero within a predefined time.

[0055] (3) The time interval between two consecutive events is strictly greater than zero to avoid the occurrence of Zeno's phenomenon.

[0056] Proof (1): Choose the Lyapunov function: (64) Using a similar approach to position loops, by differentiating equation (64) and combining it with Lemma 1, we can obtain... (65) in .so Bounded, therefore the attitude-smoothing mold surface and estimation error Bounded, that is, there exists a bounded constant. satisfy Based on the definition of attitude slip surface, it can be concluded that there exists a bounded positive number. satisfy .

[0057] right By taking the derivative and combining it with Lemma 4, using the analytical process of formulas (33) to (35), we can obtain: At a predefined time Convergence to (66) in , , denoted as the number of nodes in the attitude loop neural network.

[0058] Sliding surface At a predefined time converged to (67) In conclusion, (1) has been proven.

[0059] Proof (2): Because the posture is always feasible, Both its inverse and its inverse are bounded. Therefore, and since the sliding surface is bounded, it exists. ,satisfy Furthermore, regarding Taking the derivative and combining it with the definition of the attitude slip surface, we can obtain: after a predefined time... back when : (68) Easy to obtain, when ,satisfy: (69) Therefore, at the predefined time Within this timeframe, the attitude error will converge to: (70) Based on the definition of a sliding surface, in this case, the speed error will converge to: (71) when Substituting into the definition of a sliding surface, we get: (72) In conclusion, (2) has been proven.

[0060] Proof (3): We prove by contradiction that the designed event triggering mechanism can avoid Zeno's phenomenon. Assume that the time interval between two adjacent triggering moments satisfies... We can obtain: (73) According to formula (44), at any time... All satisfy: (74) By comparing formulas (73) and (74), it can be found that they contradict each other. Therefore, it is assumed that... This is not true, which means there always exists a smallest normal number. This ensures that the trigger interval between any two adjacent times satisfies In summary, the designed control strategy can avoid the Zeno phenomenon, (3) Q.E.D.

[0061] IV. Formation Tracking Control Method Based on Adaptive Predefined Time Event Triggered Controller 1. Method and Step Design The controller is a further design based on reference [1]. Therefore, according to the inner and outer loop scheme designed in reference [1], the outer loop is the position subsystem controller and the inner loop is the attitude subsystem controller. In addition, in terms of the cooperative control method, the ideas of the classic navigator-follower method and the virtual structure method are integrated, and a virtual navigator is tracked. [7] This method enables coordinated control of the formation, eliminating the need for direct communication between drones and reducing the communication burden.

[0062] The adaptive predefined time event triggered formation tracking control method of the present invention includes the following steps: Step 1: Set the center of the quadcopter drone formation as the virtual navigator position, set the virtual navigator's trajectory as the path to be inspected, and assign the desired position of each other drone relative to the virtual navigator in the formation; establish a position subsystem (Formula 7), an attitude subsystem (Formula 8), a position loop error system (including Formulas 10 and 11), and an attitude loop error system (Formula 12) for each drone in the formation. In step 1, the specific design is as follows: drones The location subsystem is modeled as follows: (7) in, Representative to Differentiate, Representing drones In respectively Spatial position in three directions; Representing drones exist Velocity in three directions; Representing drones The quality; Representing drones exist Control torque in three directions; Representing drones Unknown external disturbance vector. ,in g It is the acceleration due to gravity; drones The attitude subsystem is modeled as follows: (8) in, Representative to Differentiate; Representing drones The posture; , , These represent the roll angle, pitch angle, and yaw angle of the drone, respectively. The rotation matrices are represented by the following formula (9); It is a drone Rotational angular velocity in the body coordinate system; It is the moment of inertia matrix, which is a diagonal matrix in which all elements on the diagonal are greater than 0; It is the input to the attitude loop; This represents the attitude disturbance moment, which has an upper bound but is unknown. Its corresponding It is a skew-symmetric matrix: (9) Assuming the center of this formation is a virtual navigator, and its position is... drones The deviation of the desired position in the formation from the center position is: Therefore, drones The position relative to the virtual navigator is The speed is acceleration is ; drones The position loop error system is modeled as follows: (10) in, They represent drones Compared to the position and speed errors of its virtual navigator; represent The second derivative; given the desired angle In this situation, the control commands output by the position subsystem can be used to obtain the UAV's... i Desired attitude and total lift: (11) in, Representing drones i Total lift; , , Representing drones i The expected pitch angle, expected roll angle, and expected yaw angle; drones Expected posture These represent its first and second derivatives, respectively.

[0063] drones The attitude loop error system is modeled as follows: (12) Step 2: The virtual navigator, following a preset motion trajectory, inputs its desired position information into the position loop error system of each UAV, and inputs the obtained position error into the position loop controller of the corresponding UAV; design the predefined time sliding surface of the position loop (Equations 13, 14, 15), the position loop controller, and the adaptive law (Equations 26, 27, 28).

[0064] Step 2 is designed as follows: The predefined time sliding surface design for the position loop is as follows: (13) in (14) in, It is a diagonal matrix in which all diagonal elements are greater than 0; This is a preset constant greater than 0; To ensure the continuity of the sliding surface, They respectively satisfy: (15); The position loop controller and adaptive law are designed as follows: (26) (27) in, Representing drones exist Control torque in three directions; It is a diagonal matrix in which all diagonal elements are greater than 0. , . , satisfy: (28) in, ; Representing drones i Position ring in Predefined time sliding surfaces for position loops in three directions.

[0065] In step 2, when unforeseen lateral winds or atmospheric turbulence interfere with UAV formation flight, some UAVs may deviate from their predetermined formation positions. To reduce position deviation, a position subsystem controller is designed, in which a position loop controller is constructed using a radial basis function neural network (RBFNN). This controller can perform online learning and approximate nonlinear unknown disturbance terms, enabling real-time identification and compensation of wind disturbance characteristics. Simultaneously, an adaptive law is used to estimate unknown variables, and the neural network parameter values ​​are corrected in real-time based on the system state, improving its approximation accuracy. A composite control strategy combining a predefined time sliding surface of the position loop and an adaptive law is used to achieve predefined time tracking of the UAVs' x, y, and z axes positions. This allows the disturbed UAVs to quickly and smoothly return to a pre-set point in the hexagonal formation within a predefined time, ensuring the stability of the reconnaissance formation and effectively eliminating reconnaissance blind spots caused by single-UAV position errors.

[0066] Step 3: In each UAV, the desired roll angle and desired pitch angle, and total thrust output from the position loop error system (Formula 11) are input into the attitude loop error system (Formula 12), and the obtained attitude error is input into the attitude loop controller of the corresponding UAV.

[0067] This step ensures that the attitude angle that each drone needs to maintain is calculated in real time and dynamically.

[0068] Step 4: Design a predefined time sliding surface for the attitude loop (including formulas 47, 48, and 49), an attitude loop controller, and an adaptive law (including formulas 61, 62, and 63) for each UAV, and design an event triggering mechanism (including formulas 44, 45, and 46).

[0069] In step 4, the specific design is as follows: The predefined time sliding surface design for the attitude loop is as follows: (47) in (48) in It is a diagonal matrix in which all diagonal elements are greater than 0; This is a preset constant greater than 0; To ensure the continuity of the sliding surface, They respectively satisfy: (49); Attitude loop controller and adaptive law: (61) (62) in, This represents the virtual control torque on the attitude loop, i.e., the attitude loop controller; This represents the actual control torque executed on the attitude loop, serving as the input to the attitude loop; , , , It is a diagonal matrix in which all diagonal elements are greater than 0. , ( )satisfy: (63) in, ; Representing drones i The attitude loop has a predefined time sliding surface in the pitch, roll and yaw channels.

[0070] In this step, considering the limited communication resources of quadcopter formations, an attitude subsystem controller and an event-triggered mechanism were designed for the attitude loop control of the UAVs in the formation. The event-triggered mechanism uses state as a condition; the attitude loop controller's control signal update and communication transmission are only executed when the attitude error exceeds a preset threshold and may affect the stability of the flight platform or the working state of the flight mission payload. This non-periodic signal transmission reduces the update frequency and significantly reduces the bandwidth burden on the UAV's internal communication network. Simultaneously, a radial basis function neural network (RBFNN) is integrated into the attitude loop controller of each UAV. This network enables autonomous learning to compensate for the time-varying aerodynamic interference caused by the complex environment of mountain flight, while continuously iteratively optimizing the neural network weights, improving the approximation performance of the neural network. Furthermore, an adaptive law is set in the attitude subsystem controller to estimate unknown parameters. The design of the attitude subsystem controller allows each UAV in the entire formation to quickly adjust its attitude within a predetermined time range to provide a stable imaging platform for the onboard reconnaissance payload, resulting in clearer and more stable images.

[0071] Step 5: Each drone flies according to the instructions of the position loop controller and attitude loop controller.

[0072] Specifically, by combining the quadcopter dynamics model, the torque commands of the attitude loop controller for each UAV are transformed into four sets of conflict-free, precise motor speed commands. The electronic speed controller, based on these motor speed commands, drives the motors of each quadcopter to the target speed, generating the required control torque and total thrust. This enables UAVs 01 through 06 to achieve six degrees of freedom control, ensuring that the UAV formation maintains a preset hexagonal formation for an extended period even in complex airflow environments throughout the mission. This allows for precise control of the UAV formation's position and attitude. It also ensures coordinated and efficient cooperation with ground forces throughout the mission to search for and lock onto the location of fleeing terrorists, facilitating the precise elimination of these terrorists.

[0073] 2. Example like Figure 3 As shown, taking the mountain search and suppression mission of the Armed Police Force as an example, after the previous stronghold was attacked, some remaining terrorists used the terrain as cover to move to another stronghold. In order to prevent them from successfully escaping and strengthen the forces of the other stronghold, it is necessary to dispatch multiple rotary-wing drones to conduct reconnaissance along the route and lock their positions so as to facilitate the ground troops to advance and eliminate them. The specific execution steps of the rotary-wing drone formation tracking and control method are as follows: Step 1: Formation system construction and error definition.

[0074] To effectively search for fleeing terrorists, a reconnaissance formation with a large coverage area and no blind spots needs to be constructed. A virtual navigator is assigned to the entire UAV formation system. The trajectory of this virtual navigator is set as the reconnaissance path along the terrorists' escape route. Subsequently, the desired position needs to be accurately assigned to each UAV in the formation. Taking a six-UAV formation numbered 01 to 06 as an example, a stable hexagonal search formation is established. Based on this, using a conventional quadcopter dynamics model, a position subsystem, attitude subsystem, position loop error system, and attitude loop error system are established for each UAV in the formation. This allows for real-time and continuous calculation of the difference between the actual pose state of each UAV and its corresponding desired pose state in the formation. This continuously updated error vector system forms the basis for maintaining the geometric structure of the formation and realizing multi-UAV cooperative search behavior.

[0075] Step 2: The virtual navigator moves along a predetermined trajectory. The desired position information of the virtual navigator is input into the position loop error system of each UAV. The obtained position error is input into the position loop controller of the corresponding UAV. The predefined time sliding surface of the position loop, the position loop controller, and the adaptive law are designed.

[0076] Step 3: In each UAV, the desired roll angle, desired pitch angle, and total thrust output from the position loop error system are input into the attitude loop error system, and the resulting attitude error is input into the attitude loop controller of the corresponding UAV.

[0077] Step 4: Design a predefined time sliding surface for the attitude loop, an attitude loop controller, and an adaptive law for each UAV, and design an event triggering mechanism.

[0078] Step 5: Each drone flies according to the instructions of the position loop controller and attitude loop controller.

[0079] 3. Experimental verification and analysis Numerical simulations were performed using Matlab / Simulink, simulating six quadcopter UAVs rapidly forming a hexagonal formation to conduct cover reconnaissance of a specific area during counter-terrorism operations. The flight time was set to 80 seconds, and the simulation step size was set to 0.01 seconds. The controller parameters for each UAV in the formation were set to be identical, as detailed in Table 1.

[0080] Desired yaw angle is The mass of the drone is The moment of inertia is The desired trajectory at the center of the formation is

[0081] To simulate complex airflow in mountainous terrain during flight, the aerodynamic disturbances of the attitude dual-loop system are set as follows: , .

[0082] The paranoia vector is set as follows: .

[0083] Table 1 Formation Controller Parameters

[0084] Initial state of drone 1: Unit: m Unit m / s The unit is rad. The unit is rad / s. The initial states of drones 2-6 are the same as those of drone 1, with the following initial positions:

[0085] .

[0086] The simulation results are as follows: Figure 4The demonstration showed the effectiveness of the formation in tracking the virtual navigator's preset trajectory under time-varying wind disturbances. The six drones formed the desired formation within 10 seconds, with a smooth trajectory. The formation remained stable throughout the tracking process, demonstrating the excellent handling effect of the adaptive controller on system uncertainties.

[0087] Through observation Figure 5 and Figure 6 As can be seen from the subgraph, the position and velocity errors of the six drones converged within 3 seconds. The error of each drone relative to the desired position remained within ±0.05m, and the velocity error fluctuated slightly in the neighborhood of zero after convergence.

[0088] Through analysis Figure 7 and Figure 8 As can be seen, despite strong external disturbances, the control strategy designed in this chapter can still track the position subsystem well to give the desired attitude and desired angular velocity, achieve convergence within 3 seconds, and maintain steady state.

[0089] Figure 9 The total lift of the six UAVs in the formation is given, and the control input of each UAV is always kept within the engineering allowable range. Figure 10 and Figure 11 The adaptive parameters of the position loop and attitude loop for each UAV are shown separately. It can be found that the adaptive parameters are bounded, which reflects the effectiveness of the designed adaptive law.

[0090] Figure 12 The study demonstrated the time interval for triggering events on drones in a formation. A total of 8,000 samples were taken during an 80-second formation tracking task. Events on drones 1 through 6 were triggered 1,523, 1,522, 1,526, 1,499, 1,526, and 1,512 times, respectively. Compared with the traditional time-triggered framework, this reduced data transmission volume by 80.96%, 80.97%, 80.92%, 81.26%, and 81.1%, respectively, effectively saving communication resources while maintaining control performance.

[0091] In summary, this invention considers more realistic scenarios when performing counter-terrorism missions in mountainous areas. Addressing the problem of rotorcraft UAV formation tracking in coverage reconnaissance missions, and considering the unknown airframe mass, moment of inertia, and upper bounds of external disturbances, it proposes an adaptive predefined time-triggered formation tracking control method. This method enables time-controllable formation formation. Simulation results show that this method has a faster convergence speed and higher convergence accuracy, consumes fewer communication resources than traditional time-triggered methods, and can accurately track pre-planned reconnaissance trajectories.

Claims

1. An adaptive predefined time event triggered formation tracking control method, characterized in that, The steps include the following: Step 1: Set the center of the quadcopter drone formation as the virtual navigator position, set the virtual navigator's trajectory as the path to be inspected, and assign the desired position of each other drone relative to the virtual navigator in the formation; establish a position subsystem, attitude subsystem, position loop error system and attitude loop error system for each drone in the formation. Step 2: The virtual navigator, following a preset motion trajectory, inputs its desired position information into the position loop error system of each UAV, and then inputs the obtained position error into the position loop controller of the corresponding UAV; design the predefined time sliding surface of the position loop, the position loop controller, and the adaptive law; Step 3: In each UAV, the desired roll angle, desired pitch angle, and total thrust output from the position loop error system are input into the attitude loop error system, and the obtained attitude error is input into the attitude loop controller of the corresponding UAV. Step 4: Design a predefined time sliding surface for the attitude loop, an attitude loop controller, and an adaptive law for each UAV, and design an event triggering mechanism; Step 5: Each drone flies according to the instructions of the position loop controller and attitude loop controller.

2. The adaptive predefined time event triggered formation tracking control method as described in claim 1, characterized in that, In step 1, the specific design is as follows: drones The location subsystem is modeled as follows: in, Representative to Differentiate, Representing drones In respectively Spatial position in three directions; Representing drones exist Velocity in three directions; Representing drones The quality; Representing drones exist Control torque in three directions; Representing drones Unknown external disturbance vector. ,in g It is the acceleration due to gravity; drones The attitude subsystem is modeled as follows: in, Representative to Differentiate; Representing drones The posture; , , These represent the roll angle, pitch angle, and yaw angle of the drone, respectively. The rotation matrices are represented by the following formula (9); It is a drone Rotational angular velocity in the body coordinate system; It is the moment of inertia matrix, which is a diagonal matrix in which all elements on the diagonal are greater than 0; It is the input to the attitude loop; This represents the attitude disturbance moment, which has an upper bound but is unknown. Its corresponding It is a skew-symmetric matrix: Assuming the center of this formation is a virtual navigator, and its position is... drones The deviation of the desired position in the formation from the center position is: drones The position relative to the virtual navigator is The speed is acceleration is ; drones The position loop error system is modeled as follows: in, They represent drones Compared to the position and speed errors of its virtual navigator; represent The second derivative; given the desired angle In this situation, the control commands output by the position subsystem can be used to obtain the UAV's... i Desired attitude and total lift: in, Representing drones i Total lift; , , Representing drones i The expected pitch angle, expected roll angle, and expected yaw angle; drones Expected posture These represent its first and second derivatives, respectively; drones The attitude loop error system is modeled as follows: 。 3. The adaptive predefined time event triggered formation tracking control method as described in claim 1, characterized in that, Step 2 is designed as follows: The predefined time sliding surface design for the position loop is as follows: in in, It is a diagonal matrix in which all diagonal elements are greater than 0; This is a preset constant greater than 0; To ensure the continuity of the sliding surface, They respectively satisfy: ； The position loop controller and adaptive law are designed as follows: in, Representing drones exist Control torque in three directions; It is a diagonal matrix in which all diagonal elements are greater than 0. , ; , satisfy: in, ; Representing drones i Position ring in Predefined time sliding surfaces for position loops in three directions.

4. The adaptive predefined time event triggered formation tracking control method as described in claim 1, characterized in that, In step 4, the specific design is as follows: The predefined time sliding surface design for the attitude loop is as follows: in in It is a diagonal matrix in which all diagonal elements are greater than 0; This is a preset constant greater than 0; To ensure the continuity of the sliding surface, They respectively satisfy: ； Attitude loop controller and adaptive law: in, This represents the virtual control torque on the attitude loop, i.e., the attitude loop controller; This represents the actual control torque executed on the attitude loop, serving as the input to the attitude loop; , , , It is a diagonal matrix in which all diagonal elements are greater than 0; , ( )satisfy: in, ; Representing drones i The attitude loop has a predefined time sliding surface in the pitch, roll and yaw channels.

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