A fixed-wing unmanned aerial vehicle cluster formation control method for mobile rigid formation

Abstract

The application discloses a kind of fixed-wing unmanned aerial vehicle cluster formation control method for mobile rigid formation, based on the three-dimensional rigid kinematics model of fixed-wing unmanned aerial vehicle, define a mobile rigid formation, the formation satisfies the non-complete constraint and input saturation constraint of fixed-wing unmanned aerial vehicle;Based on the multiple parent nodes of fixed-wing unmanned aerial vehicle in communication topology, a virtual parent node, i.e., convex combination system, is constructed using the geometric convex combination of special Euclidean group, and an additional angular velocity is designed as a control input, and the formation control of fixed-wing unmanned aerial vehicle cluster is realized by trajectory tracking control of fixed-wing unmanned aerial vehicle relative to virtual parent node.The application realizes the overall motion of formation formation, and has high practicability, and is more suitable for cooperative observation, patrol reconnaissance, escort and other task scenarios.

Description

Technical Field

[0001] This invention relates to a formation control method for unmanned swarm systems, specifically a formation control method for fixed-wing UAV swarms that is designed for mobile rigid formations and ensures formation feasibility. Background Technology

[0002] Formation control of fixed-wing UAV swarms refers to the process by which fixed-wing UAVs interact and coordinate to achieve predefined state constraints based on relative position and attitude, also known as formation. Intuitively, formation can be described by specific geometric figures. Fixed-wing UAV swarm formations have wide applications in various scenarios such as resource exploration, disaster relief, and border patrol. Currently, common formation control methods include the leader-follower method, virtual structure method, behavior-based method, and guided vector field method. However, most existing research results have overlooked the following two important issues.

[0003] First, the model of a fixed-wing UAV is essentially a rigid body model with nonholonomic constraints in three-dimensional space, which can simultaneously describe the evolution of the UAV's position and attitude. However, most existing research models fixed-wing UAVs as point mass models and describe their attitude kinematics as an integrator form with respect to Euler angles. Although the integrator model is simpler than the rigid body kinematic model, it ignores the coupling relationships between the degrees of freedom in three-dimensional rotation and cannot reflect the rotational control process based on rigid body angular velocity. Therefore, controllers designed based on point mass models cannot be directly applied to the formation control of fixed-wing UAV swarms.

[0004] Another issue is that existing research primarily focuses on achieving formation in fixed-wing UAV swarms, with little attention paid to the overall motion of the formation after formation, which is crucial in practical applications. For example, during aerial refueling, the tanker aircraft must always remain at a fixed position behind the receiver aircraft and follow its movement. In other words, the formation must remain unchanged under translation and rotation, functioning like a single, independently moving rigid body. Therefore, formation control must not only ensure the desired relative positions and attitudes of the fixed-wing UAVs within the swarm but also ensure that the formation moves as a unified whole. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention proposes a formation control method for fixed-wing UAV swarms based on a three-dimensional rigid body kinematic model of a fixed-wing UAV, specifically for moving rigid formations. On one hand, the rigid body model uses a rotation matrix to globally and uniquely describe the attitude of the fixed-wing UAVs, overcoming the singularity problem of Euler angles in the point mass model. On the other hand, once the moving rigid formation is formed, it remains unchanged under translation and rotation, functioning like an independently moving rigid body, thus realizing the overall motion of the formation.

[0006] The fixed-wing UAV swarm formation control method proposed in this invention has the following characteristics: A mobile rigid formation is defined by utilizing the group elements of a special Euclidean group, and this formation satisfies the nonholonomic constraints and input saturation constraints of the fixed-wing UAVs, ensuring the feasibility of formation control; For cases where fixed-wing UAVs have multiple parent nodes in the communication topology, a virtual parent node is constructed using a geometric convex combination of a special Euclidean group, also known as a convex combination system, transforming the formation control of the fixed-wing UAV swarm into trajectory tracking control of the fixed-wing UAVs relative to the virtual parent node; Furthermore, based on the concepts of motion coupling and input compensation, an additional angular velocity is designed as the control input, solving the problem of limited linear velocity direction for fixed-wing UAVs under nonholonomic constraints.

[0007] This invention provides a method for controlling the swarm formation of fixed-wing UAVs in a mobile rigid formation, comprising the following steps:

[0008] 1) Construct a model of a fixed-wing UAV and a communication topology diagram of the cluster. The model is a three-dimensional rigid body kinematics model, and the communication topology diagram has a root node, i.e., the leader, and there are no loops.

[0009] 2) Define the rigid moving formation of each fixed-wing UAV in the cluster relative to the leader. This formation is defined by the group elements of a special Euclidean group and satisfies nonholonomic constraints and input saturation constraints.

[0010] 3) Based on the leader configuration and rigid moving formation, an auxiliary system is constructed for any fixed-wing UAV in the cluster using group operations of a special Euclidean group.

[0011] 4) Based on the communication topology diagram, for any fixed-wing UAV in the cluster, if it has multiple parent nodes, construct a convex combination system of the parent node auxiliary system.

[0012] 5) By utilizing the relative configuration and relative velocity information between any fixed-wing UAV and the convex combination system in the cluster, an additional angular velocity is constructed, thereby designing a formation controller for the fixed-wing UAV cluster to achieve formation control of the fixed-wing UAV cluster for moving rigid formations.

[0013] Specifically, in step 1), the configuration of the fixed-wing UAV... and speed The kinematic model of the fixed-wing UAV swarm system is established as follows:

[0014]

[0015] in, configuration Time derivative; configuration Indicates the status of a fixed-wing drone; speed. For the control input of a fixed-wing unmanned aerial vehicle; superscript This indicates a Hat mapping; This is the sequence number of the fixed-wing UAV in the fixed-wing UAV swarm, with a value of [value missing]. All configurations Forming a special European group ,Right now:

[0016] ;in, and They represent the first The attitude matrix and position vector of a fixed-wing UAV; Special orthogonal group Elements in; For three-dimensional space Vectors in;

[0017] Construct a communication topology graph for a fixed-wing UAV swarm. Each node in the topology graph represents a fixed-wing UAV, and nodes are connected by directed edges, indicating the direction of information transmission. For two nodes connected by a directed edge, the node that sends the information is the parent node, and the node that receives the information is the child node. There is a root node in the topology graph, which is the leader of the fixed-wing UAV swarm, and it only sends information and does not receive information. All other nodes are followers. There are no loops in the topology graph, that is, there is no path that allows information sent from a node to return to that node.

[0018] In step 2), the configuration of the leader of the fixed-wing UAV swarm is denoted as... The position of the follower is denoted as , ;

[0019] if and The following conditions must be met: ,in , Represents special European groups Group elements in Represents the relative attitude matrix. Represents a relative position vector; then A rigid formation for the movement of followers relative to the leader;

[0020] The moving rigid formation satisfies the corresponding nonholonomic constraints and input saturation constraints, as follows:

[0021] Conditions to ensure input saturation constraints:

[0022]

[0023] in, For any positive constant; Defined as: ; The leader's angular velocity; This is the upper bound of the Euclidean norm of the leader's angular velocity; and These are the upper and lower bounds of the leader's forward linear velocity, respectively. and These are the upper and lower bounds of the forward linear velocity of the follower, respectively.

[0024] Conditions for guaranteeing nonholonomic constraints:

[0025]

[0026] in, , ; Represents the transpose matrix; The linear velocity of the leader;

[0027] make express The configuration of the parent node, Represents the rigid formation for moving parent nodes relative to the leader, defined as follows: ;but: ;in, This represents a rigid formation for the movement of followers relative to their parent node.

[0028] In step 3), the configuration of the auxiliary system for any fixed-wing UAV in the UAV swarm is constructed. Represented as:

[0029]

[0030] in, for The configuration of the parent node, A rigid formation for the movement of followers relative to their parent node;

[0031] The speed of the auxiliary system is defined as: ;in, for The speed of the parent node, For about The accompanying mapping;

[0032] In step 4), constructing the convex composite system of the parent node auxiliary system includes:

[0033] Suppose for any Its parent node has The configuration representation of all parent node auxiliary systems is as follows: The speed of all parent node auxiliary systems is expressed as ;

[0034] make representation configuration The convex combination makes Indicates speed convex combination; Iteratively expressed by the following formula:

[0035]

[0036]

[0037]

[0038]

[0039] in, ( ) are convex combination coefficients, satisfying ; exp and log represent the exponential and logarithmic mappings, respectively; Iteratively expressed by the following formula:

[0040]

[0041]

[0042]

[0043]

[0044] The tracking of multiple parent node auxiliary systems is achieved by tracking the convex composite system;

[0045] Step 5) includes the following process:

[0046] 51) Define relative configurations for: ;in, For the configuration of a convex combination system, For the follower's configuration; further define the relative velocity as: ;in, It is the speed of the convex combined system. It is the speed of the followers. It is about The accompanying mapping;

[0047] 52) Establish a kinematic model of the relative system, expressed as: ;in For relative control input;

[0048] 53) Relative control input Designed as follows: ;in, To control the gain; obtain the control input of the follower, expressed as: The obtained control input is the nominal control input;

[0049] 54) Set the linear velocity in the non-holonomic constraint direction to 0, and then construct an additional angular velocity to compensate for the lack of linear velocity; specifically:

[0050] Construct the following additional angular velocity : ;

[0051] in, This indicates that it belongs to a special orthogonal group. And around y Orthogonal matrices for axis rotation; This indicates that it belongs to a special orthogonal group. And around z Orthogonal matrix of axis rotation; superscript The Vee mapping is the inverse of the Hat mapping; Represents a logarithmic mapping;

[0052] 55) Using the nominal control input and additional angular velocity, design the following formation controller, where the angular velocity and linear velocity of the fixed-wing UAV are expressed as:

[0053]

[0054] in, To control the gain; The angular velocity of the follower; The linear velocity of the follower; This is the nominal angular velocity; For additional angular velocity, This is the actual linear velocity control input; To control the gain, .

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0056] This invention proposes a formation control method for fixed-wing UAV swarms in a moving rigid formation. By introducing a three-dimensional rigid body kinematic model based on a special Euclidean group, a global and unique description of the position and attitude of fixed-wing UAVs is achieved, overcoming the singularity problem of Euler angles in the mass model. This makes the formation controller designed based on this model more practical. Moreover, the moving rigid formation defined in this invention has the characteristic of remaining unchanged under translational and rotational motions. The entire formation can be regarded as an independently moving rigid body, realizing the overall motion of the formation. Therefore, it is more suitable for mission scenarios such as collaborative observation, reconnaissance, and escort. Attached Figure Description

[0057] Figure 1 The flowchart is shown below for the formation control algorithm provided by this invention.

[0058] Figure 2 This is a flowchart illustrating the specific implementation of the formation flight experiment of the present invention. Detailed Implementation

[0059] The present invention will be further described below with reference to the accompanying drawings and embodiments, but the scope of the invention is not limited in any way.

[0060] This invention provides a method for formation control of fixed-wing UAV swarms in a mobile rigid formation. The control algorithm flow is as follows: Figure 1 As shown, the process begins by establishing the kinematic model and communication topology of the fixed-wing UAV. Next, a mobile rigid formation is defined, followed by the construction of the auxiliary systems for the parent nodes. It is then determined whether the fixed-wing UAV has multiple parent nodes. If so, a convex composite system is constructed based on the auxiliary systems of these multiple parent nodes. Following this, based on the current state of the fixed-wing UAV and the state of the convex composite system, the angular velocity and linear velocity control inputs are calculated according to a given control law, causing the fixed-wing UAV to move under these control inputs. Finally, it is determined whether the fixed-wing UAV has formed a predefined formation. If so, the process ends; otherwise, the control inputs are recalculated based on the current state.

[0061] Figure 2This document outlines the procedure for a formation flight experiment based on the Optitrack positioning system and the Crazyfile UAV collaborative control platform. Since fixed-wing UAVs are typically large, large-scale formation flight experiments are difficult to conduct indoors. Therefore, the Crazyfile UAV was chosen as the experimental subject, as it is small and suitable for indoor flight. Although the Crazyfile UAV is a quadcopter, it is also a rigid body model with six degrees of freedom. Therefore, by artificially setting the vertical and lateral linear velocities to zero, a fixed-wing UAV model can be simulated. The specific experimental procedure is as follows: First, start the Optitrack positioning system and the Crazyfile UAV, and calibrate the Optitrack positioning system to achieve real-time positioning and broadcasting of the Crazyfile UAV. Second, check if the communication between the Optitrack positioning system and the control station PC is normal. If not, check the firewall, IP settings, etc. Third, check if the communication between the Crazyfile UAV and the control station PC is normal. If not, check the Crazyfile UAV power supply, PC serial port settings, etc. Subsequently, the formation control method proposed in this invention was used to write the formation flight program code on a PC based on C language or Python, and formation flight experiments were carried out on the Crazyfile UAV.

[0062] The specific implementation of the technical solution of the present invention includes the following steps:

[0063] 1) Constructing the kinematic model and communication topology diagram

[0064] consider The fixed-wing UAVs are labeled as follows: .make and They represent the first The attitude matrix and position vector of a fixed-wing UAV. Special orthogonal group The elements in, where Represents the transpose matrix; Represents the identity matrix; Represents the determinant of a matrix; For three-dimensional space Vectors in; For three-dimensional space The three-dimensional coordinates of the fixed-wing UAV. Therefore, the configuration (i.e., position and attitude) of the fixed-wing UAV can be represented as:

[0065]

[0066] because From the attitude matrix and position vector Uniquely determined, therefore configuration It can also be simply expressed as All configurations Forming a special European group ,Right now

[0067]

[0068] No. The angular velocity and linear velocity of the fixed-wing UAV are denoted as follows: and .in, Angular velocity Along the UAV body coordinate system The components of the axis; Linear velocity Along the UAV body coordinate system The components of the axis;

[0069] To facilitate the establishment of a kinematic model for a fixed-wing UAV, its velocities (including angular and linear velocities) are expressed in a special Euclidean group below. In Lie algebras, the Hat mapping is defined. as follows

[0070]

[0071] in, , Representing three-dimensional space The outer product in the middle, Special orthogonal group Lie algebras, defined as ; This refers to the Hat mapping. Applying the Hat mapping to angular velocity... ,So It can be represented as:

[0072]

[0073] Accordingly, the inverse of the Hat mapping is defined as the Vee mapping. ,Right now Therefore, special European-style groups The Lie algebra is defined as:

[0074]

[0075] Therefore, the speed of a fixed-wing UAV can be expressed as The elements in, i.e.

[0076]

[0077] From configuration and speed The kinematic model of a fixed-wing UAV swarm system can be established as follows:

[0078]

[0079] in, configuration The time derivative; from the perspective of the control system, configuration For fixed-wing drones, the speed This serves as the control input for the fixed-wing UAV. The model is built within a special Euclidean group, possessing globality and uniqueness, independent of local coordinates, and free from singularities. Furthermore, based on the kinematic model, for , define about The accompanying mapping as follows

[0080]

[0081] in, Indicates about The accompanying mapping, Represents special European groups The configuration in Represents special European groups Lie algebras express Any element in express The inverse matrix.

[0082] Although fixed-wing UAVs have six degrees of freedom, they are subject to nonholonomic constraints, which manifest as constraints along a rigid body coordinate system. y shaft and z The linear velocity of the shaft is 0, that is...

[0083]

[0084] Therefore, fixed-wing UAVs have only four control inputs, namely .

[0085] In a fixed-wing UAV swarm, the information exchange relationships between UAVs are described using a communication topology graph. Each node in the topology graph represents a fixed-wing UAV, and nodes are connected by directed edges, indicating the direction of information transmission. For two nodes connected by a directed edge, the node sending the information is called the parent node, and the node receiving the information is called the child node. Without loss of generality, it is assumed that there is a root node in the communication topology graph, i.e., the node that only sends information and does not receive information. This node can be regarded as the leader of the entire fixed-wing UAV swarm, used to guide the movement of the swarm. All other nodes are regarded as followers. In addition, it is assumed that there are no loops in the communication topology graph, i.e., there is no path that allows information sent from a certain node to return to that node.

[0086] 2) Define a moving rigid formation

[0087] The fixed-wing drone labeled 0 represents the leader, and the one labeled is... Fixed-wing drones represent followers, therefore Indicates the position of the leader. The position of the follower ( ).make Represents special European groups Group elements in, where Represents the relative attitude matrix. This represents a relative position vector. If... and Between satisfy

[0088]

[0089] So, it is called A rigid formation for the movement of followers relative to the leader.

[0090] Moving rigid formations In reality, what is given is the relative configuration of the followers with respect to the leader, not the absolute configuration of the followers. It's called a moving rigid formation because it's defined in the leader's rigid coordinate system, and the position vector within that system must remain constant. Intuitively, it can be viewed as the formation being fixed to the leader's rigid coordinate system and moving with the leader. Therefore, the formation remains unchanged with respect to the leader's translational and rotational motions, like an independently moving rigid body, hence the name "moving rigid formation."

[0091] As can be seen from the kinematic model, the fixed-wing UAV is subject to nonholonomic constraints, that is, along the rigid body coordinate system. y shaft and zThe linear velocity of the axis is 0. In addition, the fixed-wing UAV is subject to input saturation constraints, meaning both angular velocity and linear velocity have upper and lower bounds. Without loss of generality, assume the leader is subject to the following input saturation constraints: ,in The input saturation constraint imposed on the follower is ,in In the above saturation constraints, the symbol... Represents the Euclidean norm. The leader's angular velocity; The angular velocity of the follower; This is the upper bound of the Euclidean norm of the leader's angular velocity; This is the upper bound of the Euclidean norm of the follower's angular velocity; Forward linear velocity of the leader; The forward linear velocity of the follower; and These are the upper and lower bounds of the leader's forward linear velocity, respectively. and These are the upper and lower bounds of the forward linear velocity of the follower, respectively. Therefore, only moving rigid formations... This formation also satisfies the corresponding nonholonomic constraints and input saturation constraints, making it feasible or achievable for fixed-wing UAVs. To ensure a rigid mobile formation... The feasibility of this can be determined through derivation and analysis, which shows that the relative attitude matrix... and relative position vector The following conditions must be met.

[0092] To ensure input saturation constraints, relative position vectors Need to meet

[0093]

[0094] in, Let be any positive constant. Defined as:

[0095]

[0096] To ensure nonholonomic constraints, the relative attitude matrix Need to meet

[0097]

[0098] in, , ; Represents the transpose matrix; The linear velocity of the leader;

[0099] although This indicates a rigid formation in which followers move relative to the leader, but is determined by... This allows us to obtain a rigid formation of followers moving relative to their parent nodes. Let... express The configuration of the parent node, If we represent a rigid formation where the parent node moves relative to the leader, then for... have .and Jointly eliminate , can be obtained

[0100]

[0101] definition Then the above formula can be further simplified to:

[0102]

[0103] in, This indicates the rigid formation of the movement of the follower relative to its parent node.

[0104] 3) Constructing auxiliary systems

[0105] According to the definition of a mobile rigid formation, a fixed-wing UAV swarm can form a formation if and only if the position of the followers is... and Achieve consistency. Because... This includes information about the leader, i.e., the root node. According to the communication topology, no follower may necessarily obtain the leader's information. However, every follower can obtain information about its parent node, and this is defined by the rigid formation of the moving array. and Consistency is achieved if and only if and Therefore, the formation problem of fixed-wing UAV swarms is transformed into the formation problem of any follower to its parent node. Furthermore, the formation problem of followers to their parent nodes can be transformed into the tracking problem of followers to an auxiliary system.

[0106] Define an auxiliary system for each follower, the configuration of which is as follows:

[0107]

[0108] in, Configuration of the auxiliary system for followers; for The configuration of the parent node, For the rigid formation of the followers relative to their parent nodes; the velocity of the auxiliary system is defined as...

[0109]

[0110] in, for The speed of the parent node, For about The accompanying mapping; the kinematic model of the auxiliary system is

[0111]

[0112] Therefore, fixed-wing UAV swarms form a formation if and only if the position of the followers is... With auxiliary system configuration Consistency is achieved. Thus, the problem of followers queuing their parent nodes is transformed into the problem of followers tracking the auxiliary system.

[0113] 4) Constructing a convex composite system

[0114] According to the communication topology, any follower may have more than one parent node, and each parent node corresponds to an auxiliary system. Therefore, the follower needs to track multiple auxiliary systems simultaneously. To solve this problem, we utilize the geometric convex combination in a special Euclidean group to construct a convex combination system of multiple auxiliary systems, thus transforming the problem into the follower tracking the convex combination system.

[0115] Suppose for any Its parent node has The configuration of all parent node auxiliary systems can be represented as: The speed of all parent node auxiliary systems can be expressed as .make representation configuration The convex combination makes Indicates speed A convex combination. Then, The expression is given by iteratively from the following formula.

[0116]

[0117]

[0118]

[0119]

[0120] in, ( ) are convex combination coefficients, satisfying exp and log represent the exponential and logarithmic mappings, respectively; The expression is given by iteratively from the following formula.

[0121]

[0122]

[0123]

[0124]

[0125] Therefore, by convex combination configuration and convex combination speed The kinematic model of the convex combined system can be given as follows:

[0126]

[0127] Therefore, the problem of tracking a follower in a system with multiple parent nodes is transformed into the problem of tracking a convex composite system.

[0128] 5) Design a formation controller

[0129] The following design utilizes the relative configuration and relative velocity between the follower and the convex combination system to design a formation controller. First, the relative configuration is defined. as follows

[0130]

[0131] in, For the configuration of a convex combination system, For the follower's configuration, redefine the relative velocity. as follows

[0132]

[0133] in, It is the speed of the convex combined system. It is the speed of the followers. It is about The accompanying mapping. Therefore, the kinematic model of the relative system can be established as follows.

[0134]

[0135] As defined by relative configuration, a follower can track a convex composite system if and only if the relative system configuration... Converging to the identity matrix. Based on the logarithmic feedback-based stabilization control law in the special Euclidean group, relative control input... Can be designed as

[0136]

[0137] in, To control the gain. Therefore, the control input for the follower is:

[0138]

[0139] Note that fixed-wing UAVs are subject to nonholonomic constraints, lacking lateral and vertical linear velocities. The control inputs obtained above are omnidirectional, i.e., nominal control inputs, and cannot be directly applied to fixed-wing UAVs. Therefore, the linear velocities in the nonholonomic constraint directions are set to 0, and additional angular velocities are constructed to compensate for the effects of missing linear velocities.

[0140] make The vector form representing the nominal control input, i.e.

[0141]

[0142] in, This indicates a Vee mapping. and These represent the nominal angular velocity control input and the nominal linear velocity control input, respectively. express Along the UAV body coordinate system Components of the axis, express Along the UAV body coordinate system The axis components. Define the new linear velocity control input as...

[0143]

[0144] And said This is the actual linear velocity control input. Next, we will utilize... Construct additional angular velocity control input. First, construct a coordinate system around the rigid body. z Rotation matrix of axis Define a vector Then use this vector and the unit vector Construct a vector orthogonal to both, i.e.

[0145]

[0146] Therefore, This forms a set of orthogonal vectors in three-dimensional space, so the following orthogonal matrix can be constructed.

[0147]

[0148] Among them, symbols Represents the Euclidean norm;

[0149] This matrix belongs to a special orthogonal group. And it indicates that it is around z Rotation around the axis. Similarly, construct another coordinate system around the rigid body. yRotation matrix of axis Define a vector Then use this vector and the unit vector Construct a vector orthogonal to both, i.e.

[0150]

[0151] Therefore, This forms a set of orthogonal vectors in three-dimensional space, so the following orthogonal matrix can be constructed.

[0152]

[0153] This matrix belongs to a special orthogonal group. And it indicates that it is around y Axis rotation. Using matrices. and Construct the following additional angular velocity

[0154]

[0155] in, and For an orthogonal matrix constructed according to the above rules, Represents a logarithmic mapping. This represents the Vee mapping. Therefore, using the nominal control input and additional angular velocity, the following formation controller is designed, where the angular velocity and linear velocity of the fixed-wing UAV are...

[0156]

[0157] in, The nominal angular velocity, To control the gain, For additional angular velocity, This is the actual linear velocity control input.

[0158] By following the steps above, it is possible to achieve formation control of fixed-wing UAV swarms that can be used for mobile rigid formations and ensure formation feasibility.

[0159] It should be noted that the purpose of disclosing the embodiments is to help further understand the present invention. However, those skilled in the art will understand that various substitutions and modifications are possible without departing from the scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the embodiments, and the scope of protection of the present invention is defined by the scope of the claims.

Claims

1. A method for formation control of a fixed-wing UAV swarm aiming at a moving rigid formation, based on a three-dimensional rigid body kinematics model of a fixed-wing UAV, a moving rigid formation is defined, which satisfies the nonholonomic constraint and input saturation constraint of the fixed-wing UAV. Based on the fact that a fixed-wing UAV has multiple parent nodes in the communication topology, a virtual parent node, i.e., a convex combination system, is constructed using the geometric convex combination of special Euclidean groups, and an additional angular velocity is designed as a control input, and the formation control of the fixed-wing UAV cluster is realized through the trajectory tracking control of the fixed-wing UAV relative to the virtual parent node; including the following steps: 1) constructing a model of the fixed-wing UAV and a communication topology graph of the UAV cluster; the constructed model is a three-dimensional rigid body kinematics model; the communication topology graph of the UAV cluster has a root node, i.e., a leader, and does not have a loop; including: From the configuration g i and speed The kinematic model of the fixed-wing UAV cluster system is established and expressed as: wherein, is the shape g i of the time derivative; shape g i represents the state of the fixed-wing UAV; velocity is the control input of the fixed-wing UAV; the superscript ∧ represents the Hat mapping; i is the fixed-wing UAV number in the fixed-wing UAV cluster, taking values of 0, 1, 2, …, N; all shapes g i constitute a special Euclidean group SE(3), namely: wherein, R i and p i respectively represent the attitude matrix and the position vector of the i-th fixed-wing UAV; R i is an element in the special orthogonal group SO(3); p i is a vector in a three-dimensional space . constructing a communication topology graph of the fixed-wing UAV cluster, each node in the communication topology graph represents each fixed-wing UAV, and the nodes are connected by directed edges, representing the direction of information transmission; for two nodes connected by a directed edge, the node sending information is the parent node, and the node receiving information is the child node; the communication topology graph has a root node, i.e., the leader of the fixed-wing UAV cluster, which only sends information and does not receive information; other nodes except the leader are followers; there is no loop in the communication topology graph, i.e., there is no path that makes the information sent from a node return to the node; 2) defining the rigid movement formation of each fixed-wing UAV in the UAV cluster relative to the leader, which is defined by the group elements of the special Euclidean group and satisfies the non-holonomic constraint and the input saturation constraint; Let the position of the leader of the fixed-wing UAV cluster be denoted as g0, and the position of the follower be denoted as g i , i = 1, …, N; if g0and g i satisfy: where denote a group element in the special Euclidean group SE(3), denote a relative pose matrix, denote a relative position vector; then is a moving rigid formation of the follower relative to the leader. The movement rigid formation satisfies the corresponding non-holonomic constraint and input saturation constraint, respectively represented as: The condition for guaranteeing the input saturation constraint is: where c1 is an arbitrary positive constant; c2 is defined as: ω0is the leader's angular velocity; a L is an upper bound on the leader's angular velocity Euclidean norm; and β L are an upper and lower bound, respectively, on the leader's forward linear velocity; and β F are an upper and lower bound, respectively, on the follower's forward linear velocity; The condition for guaranteeing the non-holonomic constraint is: where e2 = [0 1 0] T , e3 = [0 0 1] T ; T denotes a transpose matrix; v0 is a linear velocity of the leader Let g pi denote g i the configuration of the parent, denote the moving formation of the parent relative to the leader, defined then: where, denote the moving formation of the follower relative to its parent; 3) Based on the leader position and the rigid moving formation, the auxiliary system of any fixed-wing UAV in the UAV cluster is constructed by using the group operation of special Euclidean group; its position g ai is expressed as: wherein g pi is g i the configuration of the parent node, is a moving rigid formation of followers relative to their parent node; The speed of the auxiliary system is defined as: wherein, is g i the speed of the parent node, is the adjoint map with respect to the velocity of the parent node. 4) according to the communication topology graph, for any fixed-wing UAV in the UAV cluster, if it has multiple parent nodes, a convex combination system of the parent node auxiliary system is constructed; Let g be any i node with M i parents, the configuration of all parent helper systems is denoted as the velocity of all parent helper systems is denoted as Let g ci represent the configuration of the convex combination, let ξ ci represent the velocity of the convex combination; g ci is iterated by the following formula, denoted as: wherein, is a convex combination coefficient satisfying exp and log denote exponential mapping and logarithmic mapping, respectively; ξ ci is iterated by the following equation, denoted as: The tracking of the convex combination system is used to realize the tracking of the multiple parent node auxiliary system by the follower; 5) using the relative position and velocity information between any fixed-wing UAV in the UAV cluster and the convex combination system, an additional angular velocity is constructed, and a formation controller of the fixed-wing UAV cluster is designed to realize the formation control of the fixed-wing UAV cluster for the movement rigid formation; including: 51) Define the relative configuration g LF is: where g ci is the configuration of the convex combination system, g i is the configuration of the follower; redefine the relative velocity as: where is the velocity of the convex combination system, is the velocity of the follower, is the adjoint map with respect to ; 52) Establish a kinematic model of the relative system, expressed as: where is the relative control input; 53) the relative control input is designed to: where k p > 0 is a control gain; the control input to the follower is denoted by: the resulting control input is the nominal control input; 54) set the linear velocity in the non-holonomic constraint direction to 0, and then construct the additional angular velocity to compensate for the missing linear velocity; specifically: The additional angular velocity Ω is constructed as follows AD : Ω AD = (log(R y )) ∨ + (log(R z )) ∨ ; where R y represents an orthogonal matrix belonging to the special orthogonal group SO(3) and rotating around the y-axis; R z represents an orthogonal matrix belonging to the special orthogonal group SO(3) and rotating around the z-axis; the superscript ∨ is the Vee mapping, which is the inverse mapping of the Hat mapping; log represents the logarithm mapping; 55) using the nominal control input and the additional angular velocity, the following formation controller is designed, i.e., the angular velocity and linear velocity of the fixed-wing UAV are represented as: ω i = Ω + k a Ω AD v i =Λ NH where ω i is the angular velocity of the follower; v i is the linear velocity of the follower; Ω is the nominal angular velocity; Ω AD is the additional angular velocity, Λ NH is the actual linear velocity control input; k a is the control gain, k a > 0; Through the above steps, the formation control of the fixed-wing UAV cluster for the movement rigid formation is realized.

2. The method of claim 1, wherein the method is characterized in that, In step 1), the special orthogonal group is represented as: p i = [x y z] T ; where T denotes the transpose matrix; I denotes the identity matrix; and det denotes the matrix determinant. A kinematics model of the fixed-wing UAV is established, and the angular velocity and linear velocity of the fixed-wing UAV are represented in the Lie algebra of the special Euclidean group SE(3); The Hat map ∧ is defined as follows: as follows: (a ∧ )b = a x b wherein x denotes the outer product in three-dimensional space is the Lie algebra of the special orthogonal group SO(3), ​ The Hat map A is applied to the angular velocity ω i , is represented as: The inverse mapping of the Hat mapping is defined as the Vee mapping ∨: i.e., (a ∧ ) ∨ = a; The Lie algebra of the special Euclidean group SE(3) is defined as: wherein is the Lie algebra of the special Euclidean group SE(3); The speed of the fixed-wing drone is denoted as the elements in, i.e.: For g e SE(3), define the adjoint map Adg g : is given by where Ad g denotes the adjoint map with respect to g; g denotes a configuration in the special Euclidean group SE(3); denotes the Lie algebra of the special Euclidean group SE(3); η ∧ denotes any element in g -1 denotes the inverse matrix of g; The fixed-wing UAV is subject to a non-holonomic constraint, which is represented as the linear velocity along the y-axis and z-axis of the rigid body coordinate system being 0, i.e., The four control inputs of the fixed-wing UAV are where are the angular velocities ω i are the components along the x, y, z axes of the UAV body coordinate system. are the linear velocities v i are the components along the x, y, z axes of the UAV body coordinate system.

3. The method of claim 1, wherein the method further comprises: In Step 2), the leader is subject to input saturation constraints where The follower is subject to input saturation constraints where where ω0is the leader's angular velocity; ω i is the follower's angular velocity; α L is an upper bound on the leader's angular velocity Euclidean norm; α F is an upper bound on the follower's angular velocity Euclidean norm; is the leader's forward linear velocity; is the follower's forward linear velocity; and β L are an upper and lower bound, respectively, on the leader's forward linear velocity; and β F are an upper and lower bound, respectively, on the follower's forward linear velocity.

4. The method of claim 1, wherein the method is characterized in that, In step 54) the matrix R y and R z is constructed from the additional angular velocity, wherein R y and R z are constructed as follows: An orthogonal matrix R z The construction method of the orthogonal matrix R is specifically: where ||·|| represents the Euclidean norm; the vector n is defined as: b = [Λ x 0 Λ z ] T ; using the vector and the unit vector e3 = [0 0 1] T , a vector n orthogonal to both is constructed ⊥ , that is: n ⊥ = e3 x n = [-Λ y Λ x 0] T ; {n, n ⊥ , e3} constitute a set of orthogonal vectors in three-dimensional space; wherein Λ x , Λ y , Λ z represent the components of Λ along the x, y, z axes of the UAV body coordinate system; Λ is a nominal linear velocity control input, Λ = [Λ x Λ y Λ z ] T ; An orthogonal matrix R y The construction method is specifically: where e2 is a unit vector, e2 = [0 1 0] T ; vector m is defined as m = [Λ x 0 Λ z ] T ; a vector m orthogonal to both is constructed ⊥ , i.e. m ⊥ = e2 x m = [Λ z 0 -Λ x ] T ; {m, m ⊥ , e2} form a set of orthogonal vectors in three-dimensional space.

5. The method of claim 4, wherein the fixed-wing UAV cluster formation control method for a mobile rigid formation is characterized in that, In step 55) the actual linear velocity control input Λ NH is: NH = [Λ x 0 0] T .

6. The method of claim 5, wherein the method further comprises: In step 55), the nominal angular velocity control input Ω is expressed as: Ω = [Ω x Ω y Ω z ] T ,Ω x ,Ω y ,Ω z denotes the components of Ω along the x, y, z axes of the drone body frame.

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