Multi-task cooperative constraint four rotor unmanned aerial vehicle cluster finite / fixed time multi-formation control method

Abstract

The application discloses a kind of multi-task cooperative constraint under quadrotor unmanned aerial vehicle cluster finite / fixed time multi-formation control method, the method establishes the six degrees of freedom kinematics and dynamics model of quadrotor unmanned aerial vehicle, based on the multiple cooperative relationship between unmanned aerial vehicles in algebraic graph theory;Design a distributed multi-formation control hierarchical framework based on inner and outer loop model;According to the homogeneity theory and double limit homogeneity theory, the finite / fixed time multi-formation control law of quadrotor unmanned aerial vehicle cluster is designed respectively, and the virtual control input of each quadrotor unmanned aerial vehicle is obtained;Based on attitude back solution, the desired attitude of unmanned aerial vehicle is obtained, and the desired attitude tracking is completed through the bottom attitude control algorithm, to realize the rapid multi-formation behavior of cluster.The application realizes the rapid grouping control of large-scale quadrotor unmanned aerial vehicle cluster, and is suitable for large-scale quadrotor unmanned aerial vehicle cluster to cooperatively execute complex tasks such as wide-area search and regional coverage.

Description

Technical Field

[0001] This invention belongs to the field of cooperative control of quadrotor UAV swarm systems, specifically involving a method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints. Background Technology

[0002] Quadrotor drones, with their advantages of low cost, high flexibility, and ease of operation, offer significant advantages over fixed-wing quadrotor drones in low-altitude missions, thus demonstrating great application potential in both military and civilian fields. However, as mission complexity increases, a single quadrotor drone swarm often cannot meet the demands of distributed, multi-cooperative missions. For example, in multi-target cooperative search, multi-target tracking and encirclement, and cooperative saturation attacks, relying solely on a single formation cannot efficiently complete the cooperative tasks. In such cases, it is necessary to divide the swarm system into multiple subgroups, improving the overall system efficiency through the mutual coordination of formation configurations between these subgroups. Considering the requirements of quadrotor drone swarms performing multi-cooperative missions and the time constraints of these missions, quadrotor drones often need to quickly form formations of different configurations during mission execution. Through the coordination between these formations, energy consumption is saved, thereby efficiently completing the mission. Therefore, studying the finite-time / fixed-time swarm formation control problem of quadrotor UAV swarms under multiple cooperative task constraints, driving swarm quadrotor UAVs to quickly generate and maintain a cooperative task configuration of a specific shape, satisfying the multiple cooperative constraints and timeliness constraints of the task, improving the formation generation speed, and reducing the energy consumption in the formation generation process are key issues that urgently need to be solved. Summary of the Invention

[0003] The purpose of this invention is to provide a finite / fixed-time multi-formation control method for quadrotor UAV swarms under multi-task cooperative constraints, in order to solve the adaptation problem of multi-formation control algorithms to the motion of quadrotor UAV swarms, as well as the fast convergence problem of multi-formation control methods.

[0004] To achieve the above objectives, the present invention employs the following technical solution: A finite / fixed-time multi-formation control method for quadrotor UAV swarms under multi-task cooperative constraints, including: A six-degree-of-freedom kinematic and dynamic model of a quadrotor UAV is established, which is decomposed into a translational subsystem and a rotational subsystem. Virtual control inputs are defined, and the translational subsystem of the quadrotor UAV is simplified. Based on the multi-task collaboration requirements of quadrotor UAV swarms, the quadrotor UAV swarms are grouped and clustered. The graphs and subgraphs in algebraic graph theory are used to describe the multi-collaboration relationships between quadrotor UAVs. The communication topology between quadrotor UAV sub-formations is established. Based on the inter-group and intra-group collaboration relationships, the control objective of the quadrotor UAV finite / fixed-time multi-formation control problem under multi-collaboration task constraints is set. Construct a multi-swarm control architecture for quadrotor UAV clusters based on inner and outer loop models; Based on homogeneity theory and double-limit homogeneity theory, finite-time multi-formation control laws and fixed-time multi-formation control laws for quadrotor UAV swarms are constructed respectively. Each quadrotor UAV updates its virtual control input based on the cooperative position error and cooperative velocity error within the subgroup. Based on the virtual control input, and using the quadrotor UAV swarm multi-formation control architecture, each quadrotor UAV obtains the desired attitude angle through attitude inverse kinematics; then, the underlying attitude controller is used to track the desired attitude angle, and the virtual control input in step four is recalculated based on the updated pose information; steps four and five are repeated until the quadrotor UAV swarm achieves multi-formation behavior.

[0005] Furthermore, the six-degree-of-freedom kinematics and dynamics model of the quadcopter UAV is expressed as follows: ; In the formula, the superscript dots on the parameters represent their derivatives, and the number of dots indicates the order of the derivative, the same applies below; For the index subscript of the quadcopter drone, For quadcopter drones quality Represents gravitational acceleration. Indicates quadcopter drone The position vector of the centroid relative to the ground coordinate system; Represents the real number space; the superscript parameter T indicates transpose, the same applies below; pitch angle Yaw angle and roll angle For quadcopter drones attitude variables relative to the ground coordinate system Indicates quadcopter drone Along the body coordinate system The translational air damping coefficient of a triaxial rotor causes a quadcopter drone to... The control input for pose state change is ,in, This represents the total thrust generated by all rotors. , These represent the quadcopter drone body. , The differential thrust generated by the shaft This indicates that the aircraft is surrounded by air. The force generated by the shaft Quadrone drone Around the body coordinate system Moment of inertia, It is differential thrust Through length of The lever arm generates a force around the body The angular acceleration term of the axis.

[0006] Furthermore, the six-degree-of-freedom kinematic and dynamic model is decomposed into a translational subsystem and a rotational subsystem, wherein the compact form of the translational subsystem can be integrated as follows: ; In the formula, This indicates a swarm of quadcopter drones; Representing the ground coordinate system The unit vector along the axial direction; Indicates quadcopter drone The normalized translational air damping matrix consists of diagonal elements. Represents a diagonal matrix; Indicates quadcopter drone attitude variables relative to the ground coordinate system For quadcopter drones The orthogonal rotation matrix from the body coordinate system to the ground coordinate system; For a six-degree-of-freedom kinematics and dynamics model, the virtual control input is defined as follows: ; in Indicates quadcopter drone Virtual control input for the translational subsystem; This indicates a swarm of quadcopter drones; Quadrone drone The translational subsystem can be rewritten as the following model: ; In the formula, , The three-axis components are for virtual control input.

[0007] Furthermore, the multi-cooperative relationships among quadrotor UAVs are described using graphs and subgraphs in algebraic graph theory, as follows: This diagram illustrates the communication topology between quadcopter drones, where... for A swarm of quadcopter drones, Indicates quadcopter drone Node index; Represents the set of edges connecting nodes. Communication topology diagram The adjacency matrix, Weight coefficients between edges; Quadrotor UAV The neighbor set is represented as Define the in-degree matrix ,in, Then the communication topology diagram The Laplace matrix can be expressed as ; Based on the requirements of multi-task collaboration, the cluster will... The quadcopter drone serves as a follower, and is divided according to mission requirements. Subgroups ,in Indicates the first Subgroups; right , Indicates quadcopter drone The subgroup number to which it belongs; , Indicates the number is The set of quadcopter UAV nodes in the subgroup; if Then quadcopter drone and They are grouped into the same subgroup and work together to execute the same subtask; definition , Indicates the first Communication topology subgraph of each subgroup Let the set of edges and the adjacency matrix be the graph; define For subgraph The number of quadcopter drones following within the area, Define offset variable ,in Indicates the first The number of quadcopter drones in each subgroup; then the subgraph The set of quadcopter drone nodes within can be represented as .

[0008] Furthermore, considering the virtual navigators of each subgroup, define Subgraph With the Virtual navigators of individual groups Navigation information matrix between, navigation reception flag Indicates quadcopter drone Can receive from virtual navigator Navigation information, otherwise ; Representation matrix The diagonal elements correspond to the first element in each subgroup. A navigation and reception marker for a quadcopter drone; If there is no communication connection between the quadcopter drones in each subgroup and the navigators in other subgroups, then the global navigation information matrix of the entire system can be represented as follows: ; For subgraph With the Virtual navigators of individual groups The navigation information matrix between them; if all the following quadcopter drones are considered as a whole, then the communication relationships between them can be represented by the adjacency matrix mentioned above. Perform block matrix representation, i.e. ,in, This indicates the first block after the adjacency matrix is ​​divided. OK Sub-blocks of a column, describing a set and The coupling relationship between them Then it represents a set The coupling relationships within the cluster system; the Laplace matrix of the cluster system is also represented in the form of a block matrix as follows: ,in Subgraph The Laplace matrix, and has ,right ; For set and The Laplace matrix between them.

[0009] Furthermore, the communication topology of a quadrotor drone swarm with multiple cooperative relationships should meet the following conditions: definition Subgroup and its virtual navigator Augmented communication topology between them For the corresponding set of nodes, set of edges, and adjacency matrix; for the augmented communication topology graph Its corresponding communication topology subgraph The graph is connected; within each subgroup, at least one quadcopter drone can communicate directly with the virtual navigator of the subgroup, i.e. Define the Laplacian matrix of the augmented graph. Then the matrix It is a positive definite matrix; adjacency matrix The in-degree balance condition is satisfied, that is, we have ,matrix The sum of the rows is zero; Based on the multi-cooperative mission requirements of quadcopter drones, the quadcopter drone swarm is divided into several subgroups according to the mission, and each subgroup has its corresponding navigation intelligent agent.

[0010] Furthermore, the control objective of the finite / fixed-time multi-formation control problem of quadrotor UAVs under multi-cooperative task constraints is defined as follows: Given bounded initial conditions for the system; under the action of a multi-swarm control law, what are the state variables of a quadrotor UAV swarm? , satisfy: , ,and , , , ,in, , For quadcopter drones The virtual navigator of the subgroup Position vector and velocity vector at any given moment; If the convergence time is bounded and depends on the initial state of the system, then the quadcopter UAV is said to converge in a finite time. Internally, it enables group formation.

[0011] Furthermore, a multi-swarm control architecture for quadrotor UAV swarms based on an inner and outer loop model is constructed, including: The six-degree-of-freedom kinematic and dynamic model can be decomposed into a translational subsystem of the outer loop and a rotational subsystem of the inner loop: Outer loop: In the translational subsystem, the output of each quadcopter UAV calculated by the finite-time multi-formation control law or the fixed-time multi-formation control law designed in step four is used as the virtual control input; Inner loop: It is responsible for converting the virtual control input calculated by the outer loop into the desired attitude angle and total thrust of the quadcopter UAV through the inverse attitude solution. Then, through the underlying attitude tracking controller, the deviation between these desired attitude angles and the current actual attitude angles is converted into control torque, which is applied to the propeller of the quadcopter to drive the UAV to perform the corresponding flight state.

[0012] Furthermore, based on homogeneous theory, the following finite-time multi-swarm control law for quadrotor UAV swarms is designed: ; In the formula, , For the power exponent parameter, satisfying , ; With a positive controller gain, a quadcopter drone swarm system can achieve group formation within a limited time. , , Refers to any variable, It is a symbolic function; , For quadcopter drones The cooperative position error vector and the cooperative velocity error vector; For quadcopter drones The velocity vector of the virtual navigator in the subgroup; Based on the double-limit homogeneous theory, the following fixed-time multi-group control law is designed: ; In the formula, , For the power exponent parameter, satisfying , ; The controller gain is positive.

[0013] Furthermore, let the desired attitude angle be... Quadrone drone Actual total thrust of the position subsystem The desired attitude angles are as follows: ; in, These are the desired pitch angle, desired roll angle, and desired yaw angle, respectively. For quadcopter drones The quality; Represents gravitational acceleration; For virtual control input, Its three-axis components.

[0014] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the multi-task cooperative constraint quadrotor UAV swarm finite / fixed time multi-formation control method.

[0015] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the multi-task cooperative constraint quadrotor UAV swarm finite / fixed-time multi-formation control method.

[0016] Compared with the prior art, the present invention has the following technical features: 1. This invention proposes a finite-time / fixed-time multi-formation control method for quadrotor UAVs under multi-cooperative task constraints, which can improve the overall efficiency of the cluster system through the mutual cooperation of formation configurations among subgroup quadrotor UAVs and the cooperation of sub-formations within and between groups; 2. This invention considers the multi-cooperative constraints and time-sensitivity constraints of tasks. Based on homogeneous system theory and double-limit homogeneous system theory, it designs finite-time and fixed-time multi-formation control algorithms, which improve the formation speed and reduce the energy consumption in the formation process. Attached Figure Description

[0017] Figure 1 For the quadcopter UAV and its control input in a three-dimensional coordinate system; Figure 2 This is the communication topology between quadcopter UAVs in this embodiment of the invention; Figure 3 This describes the motion trajectory and sub-formation configuration of a quadcopter UAV swarm in three-dimensional space within a finite-time group formation in Embodiment 1 of the present invention. Figure 4 The above are the position and velocity tracking curves of subgroup 1 of the quadcopter UAV swarm in Embodiment 1 of the present invention; Figure 5 The position and velocity tracking curves of subgroup 2 of the quadcopter UAV swarm in Embodiment 1 of the present invention are shown. Figure 6 The position and velocity tracking curves of subgroup 3 of the quadcopter UAV swarm in Embodiment 1 of the present invention are shown. Figure 7 The above are the position error tracking curves of all quadcopter drones in the quadcopter drone cluster of Embodiment 1 of the present invention; Figure 8 The speed error tracking curves of all quadcopter drones in the quadcopter drone cluster of Embodiment 1 of the present invention are shown. Figure 9 This describes the motion trajectory and sub-formation configuration of a quadcopter UAV swarm in three-dimensional space at a fixed time in Embodiment 2 of the present invention. Figure 10 The above are the position and velocity tracking curves of subgroup 1 of the quadcopter UAV swarm in Embodiment 2 of the present invention; Figure 11 The above are the position and velocity tracking curves of subgroup 2 of the quadcopter UAV swarm in Embodiment 2 of the present invention; Figure 12 The above are the position and velocity tracking curves of subgroup 3 of the quadcopter UAV swarm in Embodiment 2 of the present invention; Figure 13 The above are the position error tracking curves of all quadcopter drones in the quadcopter drone cluster of Embodiment 2 of the present invention; Figure 14 The speed error tracking curves of all quadcopter drones in the quadcopter drone cluster in Embodiment 2 of the present invention are shown. Figure 15 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0018] This invention considers the complex dynamic coupling relationships of quadrotor UAVs and the problem of rapid formation of quadrotor UAVs under multi-task cooperative constraints, and provides a finite / fixed-time multi-formation control method for quadrotor UAV swarms under multi-task cooperative constraints, including the following steps: Step 1: Establish a six-degree-of-freedom kinematic and dynamic model of the quadrotor UAV, decompose it into a translational subsystem and a rotational subsystem, define virtual control inputs, and simplify the translational subsystem of the quadrotor UAV.

[0019] First, construct a swarm system comprising multiple quadcopter UAVs; a six-degree-of-freedom kinematic and dynamic model is developed. (1) In the formula, the superscript dots on the parameters represent their derivatives, and the number of dots indicates the order of the derivative, the same applies below; For the index subscript of the quadcopter drone, For quadcopter drones quality Represents gravitational acceleration, a state variable. , These represent quadcopter drones. The position vector and velocity vector of the center of mass relative to the ground coordinate system; Represent the space of real numbers; for Quadcopter Drone exist Position in three axes for Quadcopter Drone exist Three-axis velocity; superscript parameter T indicates transpose, the same applies below; pitch angle Yaw angle and roll angle For quadcopter drones Attitude angle relative to the ground coordinate system Indicates quadcopter drone Along the body coordinate system The translational air damping coefficient of a triaxial rotor causes a quadcopter drone to... The control input for pose state change is ,in, This represents the total thrust generated by all rotors. , These represent the quadcopter drone body. , The differential thrust generated by the shaft This indicates that the aircraft is surrounded by air. The force generated by the shaft Quadrone drone Around the body coordinate system The moment of inertia of rotation, so as to revolve around Taking the rolling motion of the shaft as an example, in the formula... This is an inter-axis angular rate coupling term. It is differential thrust Through length of The lever arm generates a force around the body The angular acceleration term of the axis.

[0020] For simplicity, the six-degree-of-freedom kinematic and dynamic model can be decomposed into a translational subsystem and a rotational subsystem, where the compact form of the translational subsystem can be integrated as follows: (2) In the formula, This indicates a swarm of quadcopter drones; Representing the ground coordinate system The unit vector along the axial direction; Indicates quadcopter drone The normalized translational air damping matrix consists of diagonal elements. Represents a diagonal matrix; Indicates quadcopter drone attitude variables relative to the ground coordinate system For quadcopter drones The orthogonal rotation matrix from the body coordinate system to the ground coordinate system is specifically expressed as: (3) Similarly, the compact form of the rotating subsystem can be expressed as: (4) In the formula, Indicates quadcopter drone Attitude change rate vector; This indicates a quadcopter drone. The attitude angular velocity relative to the body coordinate system, Angular velocity of attitude in the body coordinate system Three-axis components; For quadcopter drones The diagonal matrix of rotational inertia about the three axes of the fuselage; For use in quadcopter drones Attitude control torque The angular velocity transfer matrix is ​​specifically represented as follows: (5) For the six-degree-of-freedom kinematic and dynamic model defined by equation (2), the virtual control input is defined as follows: (6) in Indicates quadcopter drone Virtual control input for the translational subsystem.

[0021] According to equations (1) and (6), the quadcopter drone The translational subsystem can be rewritten as the following model: (7) In the formula, , The three-axis components are for virtual control input.

[0022] Step 2: Based on the multi-task collaboration requirements of the quadrotor UAV swarm, the quadrotor UAV swarm is grouped and clustered. The multi-collaboration relationship between quadrotor UAVs is described using graphs and subgraphs in algebraic graph theory. The communication topology between quadrotor UAV sub-formations is established. Based on the inter-group and intra-group collaboration relationships, the control objective of the quadrotor UAV finite / fixed-time multi-formation control problem under multi-collaboration task constraints is set.

[0023] Specifically, the multi-cooperative relationships among quadrotor UAVs are described using graphs and subgraphs from algebraic graph theory, as follows: This diagram illustrates the communication topology between quadcopter drones, where... for A swarm of quadcopter drones, Indicates quadcopter drone The node index (the quadcopter drone is a node in the topology); This represents the set of edges connecting nodes. Communication topology diagram The adjacency matrix, The weight coefficients between the edges are the weights of the directed communication edges between nodes. Then there is Quadrone drone The neighbor set is represented as Define the in-degree matrix ,in, Then the communication topology diagram The Laplace matrix can be expressed as .

[0024] Based on the requirements of multi-task collaboration, the cluster will... The quadcopter drone serves as a follower, and is divided according to mission requirements. Subgroups ,in Indicates the first Subgroups; , ,right ; , , These are the union operator, intersection operator, and empty set, respectively.

[0025] right , Indicates quadcopter drone The subgroup number to which it belongs, i.e. , Indicates the number is The set of quadcopter drone nodes in the subgroup; if Then quadcopter drone and They are grouped into the same subgroup and work together to execute the same subtask; definition Indicates the first The communication topology subgraph of each subgroup, in which , Let the set of edges and adjacency matrix be the values ​​in the subgraph; define... For subgraph The number of quadcopter drones inside, Define offset variable ,in Indicates the first The number of quadcopter drones in each subgroup is 0, meaning the number in the 0th subgroup is 0. ;then subgraph The set of quadcopter drone nodes within can be represented as .

[0026] Considering the virtual navigators of each subgroup, define Subgraph With the Virtual navigators of individual groups Navigation information matrix between, navigation reception flag Indicates quadcopter drone Can receive from virtual navigator Navigation information, otherwise ; Representation matrix The diagonal elements correspond to the first element in each subgroup. A navigation and reception marker for a quadcopter drone.

[0027] Note that there is no communication connection between the quadcopter drones in each subgroup and the navigators in other subgroups, then the global navigation information matrix of the entire system can be represented as follows: ; For subgraph With the Virtual navigators of individual groups The navigation information matrix between them; if all the following quadcopter drones are considered as a whole, then the communication relationships between them can be represented by the adjacency matrix mentioned above. Perform block matrix representation, i.e. ,in, This indicates the first block after the adjacency matrix is ​​divided. OK Sub-blocks of a column, describing a set and The coupling relationship between them Then it represents a set The coupling relationships within the system; the Laplace matrix of the entire system is also represented in the form of a block matrix as follows: ,in Subgraph The Laplace matrix, and has ,right ; For set and The Laplace matrix between them.

[0028] The communication topology of a quadrotor drone swarm with multiple cooperative relationships should meet the following conditions: definition Subgroup and its virtual navigator Augmented communication topology between them For the corresponding set of nodes, set of edges, and adjacency matrix; for the augmented communication topology graph Its corresponding communication topology subgraph The graph is connected; within each subgroup, at least one quadcopter drone can communicate directly with the virtual navigator of the subgroup, i.e. Furthermore, define the Laplacian matrix of the augmented graph. Then the matrix It is a positive definite matrix; its adjacency matrix is... The in-degree balance condition is satisfied, that is, we have ,matrix The sum of the rows is zero; This indicates that the set does not belong to the current set. Other nodes Accumulate.

[0029] Based on the multi-cooperative mission requirements of quadcopter drones, the quadcopter drone swarm is divided into several subgroups according to the mission. Each subgroup has its corresponding virtual navigator. Virtual Navigator The dynamics can be described by the following second-order integrator model: (8) in , , They represent the first Sub-image Inner Virtual Navigator Position, velocity, and acceleration input; for ,use Subgraph Internal quadcopter drone and its virtual navigator The positional offset between them Let it be its three-axis components; consider that all subgroups are of fixed shape, i.e., for , It is a constant vector.

[0030] The control objective of the finite / fixed-time multi-formation control problem of quadrotor UAVs under multi-cooperative task constraints is defined as follows: Given the bounded initial conditions of the system, that is, the state variables (position, velocity, etc.) at the initial moment are within a bounded range; if under the action of the multi-formation control law, the state variables (position vector, velocity vector) of the quadcopter UAV cluster in step one (2) are... , satisfy: , ,and , , , ,in, , For quadcopter drones The virtual navigator of the subgroup Position vector and velocity vector at any given moment; If the convergence time is bounded and depends on the initial state of the system, then the quadcopter UAV is said to converge in a finite time. Within a fixed time, a quadcopter drone swarm can achieve cluster formation. In particular, if the convergence time of the system has a fixed upper bound that is independent of the initial state of the system, then the quadcopter drone swarm is said to achieve cluster formation within a fixed time.

[0031] Step 3: Considering the strong coupling and nonlinear characteristics of quadrotor UAVs, construct a multi-swarm control architecture for quadrotor UAV clusters based on inner and outer loop models.

[0032] Specifically, the quadrotor UAV swarm multi-formation control architecture based on the inner and outer loop model is as follows: Based on the six-degree-of-freedom kinematic and dynamic model of the quadcopter UAV established in step one, it can be seen that the quadcopter UAV Control input for pose state changes , , It will first cause quadcopter drones attitude angular velocity components , , The change in attitude variables leads to the change in attitude variables. , as well as The attitude change does not depend on the translational motion of the quadcopter UAV, but rather on the attitude angular velocity and the total thrust generated by all the rotors of the quadcopter UAV. .

[0033] According to step one, the six-degree-of-freedom kinematic and dynamic model can be decomposed into a translational subsystem (outer loop) and a rotational subsystem (inner loop): Outer ring (translational channel): responsible for handling cluster formation tasks; in the translational subsystem, the output calculated by each quadcopter UAV through the finite-time multi-formation control law or fixed-time multi-formation control law designed in step four is directly used as the resultant force expected to be received by the quadcopter UAV, that is, the virtual control input defined by formula (6) in step one. .

[0034] Inner loop (attitude channel): Responsible for processing the virtual control inputs calculated by the outer loop. The attitude inverse kinematics in step five is used to transform the desired attitude angles (desired roll angle, desired pitch angle, desired yaw angle) and total thrust of the quadcopter UAV. Subsequently, the underlying attitude tracking controller (attitude tracking control algorithm) converts the deviation between these desired attitude angles and the current actual attitude angles into control torque (i.e.,...). The propellers of the quadcopter act on the drone to drive it to perform the corresponding flight states.

[0035] Step 4: Based on homogeneity theory and double-limit homogeneity theory, construct finite-time multi-formation control laws and fixed-time multi-formation control laws for quadrotor UAV swarms, respectively. Each quadrotor UAV updates its virtual control input based on the cooperative position error and cooperative velocity error within its subgroup.

[0036] In this step, based on the graph theory grouping structure established in step two, and utilizing the simplified translational subsystem from step one, a finite-time multi-formation control law is designed according to homogeneity theory, and a fixed-time multi-formation control law is designed according to double-limit homogeneity theory. Each quadrotor UAV collects the position / velocity information of its neighbors and the leader within its subgroup, calculates the cooperative position error and cooperative velocity error, and then calculates its own virtual control input. This is used to drive the multi-squadron control architecture constructed in step three.

[0037] For ease of expression, let's use Taking axis control law design as an example, subscripts and suffixes are omitted. "According to the six-degree-of-freedom kinematics and dynamics model, since the quadcopter UAV has the same dynamic structure on all three axes, it can be..." The control law for the axes is extended to the three-axis channels via the Kronecker product.

[0038] quadcopter drones Define its virtual navigator relative to its subgroups. The position and velocity tracking errors are respectively expressed as: and ;in , For quadcopter drones Position vector and velocity vector; For quadcopter drones The positional offset between the virtual navigator and its subgroups; , Virtual Navigator The position vector and velocity vector.

[0039] Furthermore, define the joint position and velocity tracking error within the subgroup: (9) In the formula , These represent quadcopter drones. The cooperative position error and cooperative velocity error; These are the weight coefficients in the adjacency matrix; , quadcopter drone Position and velocity tracking errors; This is the navigation reception flag in the navigation information matrix; Indicates quadcopter drone In the set of subgroups A collection of neighboring quadcopter drones.

[0040] For the set of quadcopter drone nodes in the subgroup ,definition , Let the position tracking error and velocity tracking error be in vector form. , Corresponding to the first in each subgroup Position tracking error and speed tracking error of a quadcopter drone.

[0041] Further definition , Let the coordinated position error and coordinated velocity error be in vector form. , Corresponding to the first in each subgroup The cooperative position error and cooperative speed error of a quadcopter drone.

[0042] Based on the graph theory knowledge from step two, we can obtain... , .

[0043] Based on homogeneous theory, the following finite-time multi-swarm control law for quadrotor UAV swarms is designed: (10) In the formula, , For the power exponent parameter, satisfying , ; With a positive controller gain, a quadcopter drone swarm system can achieve group formation within a limited time. , , Refers to any variable, For example, a symbolic function; The other similar functions in equations (10) and (11) are all of this form; , For quadcopter drones The cooperative position error vector and the cooperative velocity error vector; For quadcopter drones The velocity vector of the virtual navigator in the subgroup.

[0044] Based on the double-limit homogeneous theory, the following fixed-time multi-group control law is designed: (11) In the formula, , For the power exponent parameter, satisfying , ; A positive controller gain is used to adjust convergence performance; thus, the swarm control task of the quadcopter UAV swarm system can be completed within a fixed time.

[0045] The virtual control input obtained in this step It will be directly used as the output of the outer loop in the inner and outer loop control architecture of step three, and will provide the core input for the attitude inverse solution of step five.

[0046] Step 5: Based on the virtual control input and the quadcopter drone swarm multi-formation control architecture, each quadcopter drone obtains the desired attitude angle through attitude inverse kinematics; then, the underlying attitude controller is used to track the desired attitude angle, and the virtual control input in step 4 is recalculated based on the updated pose information. Steps 4 and 5 are repeated until the quadcopter drone swarm achieves multi-formation behavior.

[0047] This step is the execution and closed-loop process of the control method of this invention. It uses the virtual control input calculated in step four. Combining the inner and outer loop control architecture from step three, the attitude inverse kinematics is used to convert it into the total thrust actually acting on the quadcopter UAV body. The desired attitude angles (desired roll angle, desired pitch angle, desired yaw angle) are then tracked by the underlying attitude controller, which drives the UAV to update its pose (position and attitude variables). The updated pose information is then used as feedback to re-enter the calculation process in step four, thus forming a complete closed-loop control system until all UAVs complete the formation task.

[0048] Based on the dynamic coupling relationship in step one (i.e., translation depends on total thrust and attitude, and attitude is independent of translation), the defined virtual control input is used. Perform the inverse kinematics of the desired attitude of the quadcopter UAV; let the desired attitude angle be... .

[0049] In the inner and outer loop control architecture, the output of the outer loop... This represents the desired net force acceleration vector of the quadrotor drone; based on the characteristics of the rotation matrix and the relationship between the inner and outer loop control variables, the quadrotor drone's... Actual total thrust of the position subsystem The desired attitude angles are as follows: (12) in, These are the desired pitch angle, desired roll angle, and desired yaw angle, respectively; the desired yaw angle can be set by the user or given by the flight mission requirements. For quadcopter drones The quality; It represents the acceleration due to gravity.

[0050] Each quadcopter UAV calculates its own virtual control input based on control law (10) or control law (11), and solves its actual total thrust according to equation (12). The desired attitude angle is tracked by a commonly used underlying attitude controller (such as an underlying attitude controller based on a PID control strategy).

[0051] In summary, regarding the inclusion The quadcopter drone swarm adopts the multi-swarm control architecture in step three and the finite-time / fixed-time group formation control law designed in step four. The swarm can quickly achieve group formation, meeting the multi-swarm control requirements under time constraints and multi-cooperative task constraints.

[0052] Example: In this embodiment of the invention, the basic parameters of the quadcopter drone are as follows: quadcopter drone mass Quadrone drones The moments of inertia of the three axes are respectively , , , Aerodynamic damping coefficient .

[0053] The quadcopter drone swarm system is configured to include 13 quadcopter drones, i.e. All quadrotor drones in the cluster are isomorphic. The output of the mission planning stage is that the quadrotor drone swarm system needs to be divided into three subgroups according to mission requirements. The communication topology between the quadrotor drones is as follows: Figure 2 As shown, based on the communication topology connection relationship, there are Subgroup indexes are represented as , , . , , Subgroups The virtual navigator. Based on the multi-cooperative mission requirements of quadcopter drones, each of the three subgroups has a corresponding navigator agent. Subgroup Virtual Navigator The dynamics can be described by the following second-order integrator model: ; in , , Representing subgroups Inner Navigator Position, velocity, and acceleration input. For ,use Subgroup Internal quadcopter drone and its leader The positional offset between them, considering that all sub-formations have a fixed shape, i.e., for , Let the vector be constant. The navigation-following relationship between the quadcopter drone and the subgroup of virtual navigators can be represented as: , , For each quadcopter drone, its initial position and velocity vector are randomly set within a bounded interval. The desired sub-formation configuration is represented by the positional offset between the quadcopter drone and its virtual navigator. In this embodiment, according to mission requirements, the three groups of quadcopter drones need to form trapezoidal, triangular, and diamond formations, respectively. The formation offsets are set as follows: , and .

[0054] To better illustrate the effectiveness of the quadrotor UAV swarm multi-swarm control architecture and algorithm based on the inner and outer loop model proposed in this invention, the multi-swarm control method of this invention is simulated and verified using MATLAB Simulink in the embodiments.

[0055] The expected trajector ...ies for each subgroup in Example 1 are as follows: ; Furthermore, the finite-time multi-programmable control law for the quadrotor UAV designed based on homogeneous theory in step four of Example 1 is as follows: ; In the formula, , , To obtain a positive controller gain, based on step four, set the control parameters as follows: , , , .

[0056] In step five of Example 1, each quadcopter drone calculates its own virtual control input using a finite-time multi-programmable control law, and then solves its actual control input using equation (12). Expected roll angle and desired pitch angle Under the action of the underlying attitude controller, the desired attitude is tracked. By repeating steps four and five above, the cluster can achieve multi-squad control behavior within a finite time.

[0057] The simulation results of Example 1 are as follows: Figures 3-8 As shown. Figure 3 The diagram shows the motion trajectories of a quadcopter drone swarm forming three sub-formations in a 3D environment. Different colors represent different sub-groups; dashed lines represent the motion trajectory of the virtual navigator, and solid lines represent the motion trajectories of the following quadcopter drones. Figure 3It can be seen that the quadcopter drones in each subgroup can track the movement trajectory of the virtual navigator in their respective subgroup and form the desired sub-formation (trapezoidal, triangular and diamond formations). Figures 4-6 The position and velocity tracking curves of each subgroup of quadcopter drones are presented. From the position tracking curves, it can be seen that the tracking error between the position of each subgroup of quadcopter drones and their position offset relative to the subgroup leader quickly becomes consistent. As indicated by the control objective in step two, the quadcopter drones within each subgroup have generated a preset sub-formation. Simultaneously, the velocity tracking curves of each subgroup of quadcopter drones show that the quadcopter drones within each subgroup have achieved consistent speed. Therefore, through Example 1, it can be concluded that each following quadcopter drone has achieved trajectory tracking of the subgroup leader and generated a preset sub-formation. Furthermore, Figure 7 and Figure 8 The position and velocity tracking error curves of all quadcopter drones in the cluster are shown respectively. It can be seen that the three-axis position and velocity errors of all quadcopter drones in the cluster converge to 0 in a finite time. The proposed finite-time group formation control algorithm achieves finite-time uniform convergence of position and velocity tracking errors.

[0058] The effectiveness of the fixed-time multi-group control law proposed in this invention is illustrated based on Example 2.

[0059] Example 2 also considers a quadcopter drone swarm system containing 13 quadcopter drones. The communication topology and desired formation are consistent with Example 1. According to the search mission requirements, the navigator trajectory of each subgroup needs to be reset as follows: ; The initial position and velocity state vectors of each quadcopter UAV are randomly set.

[0060] Furthermore, step four in Example 2 employs a fixed-time multi-group control law of the following form: ; The controller gain in the fixed-time multi-group control law is set to... The exponent parameter is set to .

[0061] Similarly, in step five of Example 2, each quadcopter UAV calculates its own virtual control input based on the control law and then solves for its actual control input. Expected roll angle and desired pitch angle Under the action of the underlying attitude controller, the desired attitude is tracked. By repeating steps four and five, the cluster can achieve multi-squad control behavior within a fixed time.

[0062] The simulation results of Example 2 are as follows: Figures 9-14 As shown. Figure 9 The three-dimensional motion trajectory of the quadcopter drone swarm is given. It can be seen that under the action of the fixed-time control law, the quadcopter drone swarm system can form and maintain three different shapes of sub-formations within a fixed time. Each quadcopter drone can track the motion trajectory of the virtual leader of the sub-group, thus achieving the fixed-time group formation goal described in step two. Figures 10-12 The position and velocity tracking curves of each subgroup of quadcopter UAVs are shown separately. Figure 13 , Figure 14 The position and velocity tracking errors of each subgroup are displayed. It can be seen that the tracking errors of the quadcopter UAVs in all three subgroups converge to zero within a fixed time. Therefore, the effectiveness of the fixed-time group formation control law described in step four is verified.

[0063] In summary, the results of the two embodiments above demonstrate that, under the proposed finite-time / fixed-time grouping and formation control scheme and algorithm for quadrotor UAV swarms, each quadrotor UAV can quickly form groups and generate sub-formation configurations, completing multiple collaborative tasks in groups, thereby improving formation generation speed and significantly enhancing task collaboration efficiency.

[0064] Through the detailed description of the embodiments, a more in-depth and specific understanding should be gained of the technical means and effects adopted by the present invention to achieve the intended purpose. The accompanying drawings are provided for reference and illustration only and are not intended to limit the present invention.

[0065] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints, characterized in that, include: A six-degree-of-freedom kinematic and dynamic model of a quadrotor UAV is established, which is decomposed into a translational subsystem and a rotational subsystem. Virtual control inputs are defined, and the translational subsystem of the quadrotor UAV is simplified. Based on the multi-task collaboration requirements of quadrotor UAV swarms, the quadrotor UAV swarms are grouped and clustered. The graphs and subgraphs in algebraic graph theory are used to describe the multi-collaboration relationships between quadrotor UAVs. The communication topology between quadrotor UAV sub-formations is established. Based on the inter-group and intra-group collaboration relationships, the control objective of the quadrotor UAV finite / fixed-time multi-formation control problem under multi-collaboration task constraints is set. Construct a multi-swarm control architecture for quadrotor UAV clusters based on inner and outer loop models; Based on homogeneity theory and double-limit homogeneity theory, finite-time multi-formation control laws and fixed-time multi-formation control laws for quadrotor UAV swarms are constructed respectively. Each quadrotor UAV updates its virtual control input based on the cooperative position error and cooperative velocity error within the subgroup. Based on the virtual control input, and using the quadrotor UAV swarm multi-formation control architecture, each quadrotor UAV obtains the desired attitude angle through attitude inverse kinematics; then, the underlying attitude controller is used to track the desired attitude angle, and the virtual control input in step four is recalculated based on the updated pose information; steps four and five are repeated until the quadrotor UAV swarm achieves multi-formation behavior.

2. The method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints according to claim 1, characterized in that, The six-degree-of-freedom kinematics and dynamics model of the quadcopter UAV is represented as follows: ； In the formula, the superscript dots on the parameters represent their derivatives, and the number of dots indicates the order of the derivative, the same applies below; For the index subscript of the quadcopter drone, For quadcopter drones quality Represents gravitational acceleration. Indicates quadcopter drone The position vector of the centroid relative to the ground coordinate system; Represents the real number space; the superscript parameter T indicates transpose, the same applies below; Pitch angle Yaw angle and roll angle For quadcopter drones attitude variables relative to the ground coordinate system Indicates quadcopter drone Along the body coordinate system The translational air damping coefficient of a triaxial rotor causes a quadcopter drone to... The control input for pose state change is ,in, This represents the total thrust generated by all rotors. , These represent the quadcopter drone body. , The differential thrust generated by the shaft This indicates that the aircraft is surrounded by air. The force generated by the shaft Quadrone drone Around the body coordinate system Moment of inertia, It is differential thrust Through length of The lever arm generates a force around the body The angular acceleration term of the axis.

3. The method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints according to claim 1, characterized in that, The six-degree-of-freedom kinematic and dynamic model is decomposed into a translational subsystem and a rotational subsystem, wherein the compact form of the translational subsystem can be integrated as follows: ； In the formula, This indicates a swarm of quadcopter drones; Representing the ground coordinate system The unit vector along the axial direction; Indicates quadcopter drone The normalized translational air damping matrix consists of diagonal elements. Represents a diagonal matrix; Indicates quadcopter drone attitude variables relative to the ground coordinate system For quadcopter drones The orthogonal rotation matrix from the body coordinate system to the ground coordinate system; For a six-degree-of-freedom kinematics and dynamics model, the virtual control input is defined as follows: ； in Indicates quadcopter drone Virtual control input for the translational subsystem; This indicates a swarm of quadcopter drones; Quadrone drone The translational subsystem can be rewritten as the following model: ； In the formula, , The three-axis components are for virtual control input.

4. The method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints according to claim 1, characterized in that, The multi-cooperative relationships among quadrotor UAVs are described using graphs and subgraphs from algebraic graph theory, as follows: This diagram illustrates the communication topology between quadcopter drones, where... for A swarm of quadcopter drones, Indicates quadcopter drone Node index; This represents the set of edges connecting nodes. Communication topology diagram The adjacency matrix, Weight coefficients between edges; Quadrotor UAV The neighbor set is represented as Define the in-degree matrix ,in, Then the communication topology diagram The Laplace matrix can be expressed as ; Based on the requirements of multi-task collaboration, the cluster will... The quadcopter drone serves as a follower, and is divided according to mission requirements. Subgroups ,in Indicates the first Subgroups; right , Indicates quadcopter drone The subgroup number to which it belongs; , Indicates the number is The set of quadcopter drone nodes in the subgroup; if Then quadcopter drone and They are grouped into the same subgroup and work together to execute the same subtask; definition , Indicates the first Communication topology subgraph of each subgroup Let the set of edges and the adjacency matrix be the graph; define For subgraph The number of quadcopter drones following within the area, Define offset variable ,in Indicates the first The number of quadcopter drones in each subgroup; then the subgraph The set of quadcopter drone nodes within can be represented as .

5. The method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints according to claim 1, characterized in that, Considering the virtual navigators of each subgroup, define Subgraph With the Virtual navigators of individual groups Navigation information matrix between, navigation reception flag Indicates quadcopter drone Can receive from virtual navigator Navigation information, otherwise ; Representation matrix The diagonal elements correspond to the first element in each subgroup. A navigation and reception marker for a quadcopter drone; If there is no communication connection between the quadcopter drones in each subgroup and the navigators in other subgroups, then the global navigation information matrix of the entire system can be represented as follows: ; For subgraph With the Virtual navigators of individual groups The navigation information matrix between them; if all the following quadcopter drones are considered as a whole, then the communication relationships between them can be represented by the adjacency matrix mentioned above. Perform block matrix representation, i.e. ,in, This indicates the first block after the adjacency matrix is ​​divided. OK Sub-blocks of a column, describing a set and The coupling relationship between them Then it represents a set The coupling relationships within the cluster system; the Laplace matrix of the cluster system is also represented in the form of a block matrix as follows: ,in Subgraph The Laplace matrix, and has ,right ; For set and The Laplace matrix between them.

6. The method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints according to claim 1, characterized in that, The control objective of the finite / fixed-time multi-formation control problem of quadrotor UAVs under multi-cooperative task constraints is defined as follows: Given bounded initial conditions for the system; Under the multi-swarm control law, the state variables of a quadrotor drone swarm are... , satisfy: , ,and , , , ,in, , For quadcopter drones The virtual navigator of the subgroup Position vector and velocity vector at any given moment; If the convergence time is bounded and depends on the initial state of the system, then the quadcopter UAV is said to converge in a finite time. Internally, it enables group formation.

7. The method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints according to claim 1, characterized in that, Constructing a multi-swarm control architecture for quadrotor UAV swarms based on inner and outer loop models, including: The six-degree-of-freedom kinematic and dynamic model can be decomposed into a translational subsystem of the outer loop and a rotational subsystem of the inner loop: Outer loop: In the translational subsystem, the output of each quadcopter UAV calculated by the finite-time multi-formation control law or the fixed-time multi-formation control law designed in step four is used as the virtual control input; Inner loop: It is responsible for converting the virtual control input calculated by the outer loop into the desired attitude angle and total thrust of the quadcopter UAV through the inverse attitude solution. Then, through the underlying attitude tracking controller, the deviation between these desired attitude angles and the current actual attitude angles is converted into control torque, which is applied to the propeller of the quadcopter to drive the UAV to perform the corresponding flight state.

8. The method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints according to claim 1, characterized in that, Based on homogeneous theory, the following finite-time multi-swarm control law for quadrotor UAV swarms is designed: ； In the formula, , For the power exponent parameter, satisfying , ; With a positive controller gain, a quadcopter drone swarm system can achieve group formation within a limited time. , , Refers to any variable, It is a symbolic function; , For quadcopter drones The cooperative position error vector and the cooperative velocity error vector; For quadcopter drones The velocity vector of the virtual navigator in the subgroup; Based on the double-limit homogeneous theory, the following fixed-time multi-group control law is designed: ； In the formula, , For the power exponent parameter, satisfying , ; The controller gain is positive.

9. The method for finite / fixed-time multi-formation control of quadrotor UAV swarms under multi-task cooperative constraints according to claim 1, characterized in that, Desired attitude angle is Quadrone drone Actual total thrust of the position subsystem The desired attitude angles are as follows: ； in, These are the desired pitch angle, desired roll angle, and desired yaw angle, respectively. For quadcopter drones The quality; Represents gravitational acceleration; For virtual control input, Its three-axis components.

10. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the multi-task cooperative constraint quadrotor UAV swarm finite / fixed time multi-formation control method as described in any one of claims 1-9.

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