A guaranteed-cost cooperative formation control design method for a swarm of quadrotor UAVs

Abstract

The present invention discloses a method for designing guaranteed performance cooperative formation control for a swarm of quadrotor drones. The method comprises: constructing a quadrotor drone dynamics model with an external unknown disturbance, establishing a state-space equation containing two-level subsystems based on the dynamics model; defining the inter-neighbor formation tracking error based on the topological structure between the leader and followers, and designing a preset performance function to constrain the convergence behavior of the inter-neighbor formation tracking error so that it never violates the performance function boundary; constructing a state transition equation based on adaptive dynamic surface control technology, and designing a predetermined time filter to avoid the complex computational problems of traditional recursive frameworks; and designing a virtual controller, a parameter update law, and a predetermined time cooperative formation controller for the first-level and second-level subsystems based on the state transition equation. This method ensures that the inter-neighbor formation tracking error achieves a predetermined time convergence characteristic, and the convergence time can be adjusted by the controller gain, thereby increasing the degree of freedom in controller design.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicle (UAV) technology, and in particular to a method for designing performance-guaranteed collaborative formation control for a cluster of quad-rotor UAVs. Background Art

[0002] In recent years, quadrotor drones (UAVs) have been widely used in environmental monitoring, personnel search, and data collection due to their low cost, high maneuverability, vertical takeoff and landing, and hovering capabilities. However, a single UAV is clearly unable to complete increasingly complex flight missions, necessitating a collaborative operation platform for multiple quadrotors to achieve desired control objectives. Coordinated formation control of swarms of quadrotors is fundamental to executing these complex missions. However, unknown interference from the external environment and the highly nonlinear mechanical structure of these drones complicate the coordinated formation control of swarms.

[0003] It is worth noting that formation control schemes based on traditional adaptive backstepping control technology ignore the computational burden caused by repeated differentiation of virtual control signals. In addition, finite-time or fixed-time formation control schemes cannot directly provide a clear relationship between controller gain and tracking error convergence time, making it difficult to achieve the control goal of ensuring error convergence within the desired time by adjusting the controller gain. More importantly, for the cooperative formation control of quadrotor UAV clusters, the large overshoot and steady-state error region of the formation tracking error between adjacent groups may reduce the formation performance and even cause UAV collisions. Therefore, it is urgent to design a cooperative formation control method with tracking performance guarantee to improve the formation tracking performance of quadrotor UAV clusters. Summary of the Invention

[0004] In view of the problems that the above-mentioned existing technologies cannot achieve transient performance constraints on the tracking errors of adjacent formations of quadrotor drone clusters and cannot clearly define the relationship between system convergence time and control gain, the present invention provides a performance-guaranteed collaborative formation control design method for quadrotor drone clusters, which introduces a preset performance function into the recursive framework of the collaborative formation of quadrotor drone clusters to achieve convergence constraints on the tracking errors of adjacent formations, and designs a predetermined time filter to avoid the computational complexity problems of traditional adaptive backstepping control schemes. The designed non-singular predetermined time collaborative formation controller ensures that the tracking errors of adjacent formations converge to a small area near the origin within a predetermined time, and the convergence time can be adjusted by the controller gain.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A guaranteed performance collaborative formation control design method for a swarm of quadrotor drones includes the following steps:

[0007] S1. Construct a dynamic model of a quadrotor drone with external unknown disturbances and establish a state-space equation containing two-level subsystems based on the dynamic model.

[0008] S2. Based on the topological structure between the leader and follower quadrotor drones, define the inter-neighbor formation tracking error, design a preset performance function and error conversion equation, and convert the inter-neighbor formation tracking error constrained by inequality into an equivalent inter-neighbor formation tracking error without constraints;

[0009] S3. Based on the adaptive dynamic surface control method, construct the state transition equation and design the predetermined time filter;

[0010] S4. Based on the state transition equation, construct the Lyapunov function of the first-level subsystem Designing a virtual controller Parameter update law of the first-level subsystem And the parameter update law

[0011] S5. Construct the Lyapunov function of the second-level subsystem Design of a scheduled time cooperative formation controller Parameter update law of the second-level subsystem Parameter update law And the parameter update law

[0012] S6. Construct the overall Lyapunov function, prove the stability of the closed-loop system based on the scheduled time Lyapunov stability theory, and determine the control gain of the scheduled time cooperative formation controller.

[0013] In a preferred embodiment of the present invention, in step S1, the quadrotor UAV dynamics model is:

[0014]

[0015] Among them, 1≤ι≤N, N represents the number of followers in the quadrotor drone cluster, φ ι ,θ ι and ψ ι They are respectively represented as the roll angle, pitch angle and yaw angle of the ιth quadrotor drone; as well as They are respectively represented as the roll angular velocity, pitch angular velocity and yaw angular velocity of the ιth quadrotor drone; as well as They are respectively represented as the roll angle acceleration, pitch angle acceleration and yaw angle acceleration of the ιth quadrotor drone; z, as well as Respectively represent the position coordinates, velocity and acceleration of the ιth quadrotor drone in the z-axis direction; x, as well as Respectively represent the position coordinates, velocity and acceleration of the ι-th quadrotor drone in the x-axis direction; y, as well as Respectively represent the position coordinate, velocity and acceleration of the ith quadrotor drone in the y-axis direction; u ι,f ,u ι,φ ,u ι,θ and u ι,ψ denote the total lift, roll angle control input, pitch angle control input, and yaw angle control input of the ιth quadrotor drone, respectively; is the mass of the ιth quadrotor drone; is the distance between the center of mass of the ιth quadrotor drone and the center of the rotor; as well as Represent the rotational inertia of the ιth quadrotor drone in three directions; is the drag coefficient; is an unknown external disturbance and satisfies G ι is the acceleration due to gravity; and Respectively and ι is the serial number of the quadrotor drone;

[0016] The state space equation containing the two-level subsystem is:

[0017]

[0018] in,

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] In a preferred embodiment of the present invention, in step S2, the topological structure of the quadrotor drone leader and the quadrotor drone follower is defined as follows:

[0029] A directed graph G = (X, Z) is used to describe the information exchange between quadrotor drones, where X = {1, 2, ..., N} is the vertex set consisting of N quadrotors; Z∈X×X represents the edge set; (j, ι) means that the ι-th quadrotor drone can obtain the j-th quadrotor drone information; Represents the adjacent set of the ι-th quadrotor drone; the adjacent matrix of the directed graph G Defined as: if (j, ι)∈Z, then a ι,j =1; otherwise, a ι,j =0;

[0030] The degree matrix is ​​defined as in

[0031] The Laplacian matrix of a directed graph G is defined as:

[0032] Extended directed graph Used to describe the information interaction between a swarm of quadrotor drones including the leader, where To expand the directed graph The point set, the quadrotor drone labeled 0 represents the leader; To expand the directed graph The edge set of

[0033] Extended directed graph The Laplacian matrix of where d=[d1,d2,...,d N ] T ; D = diag{d1, d2, ..., d N}, d ι =1 means that the ιth quadrotor drone can receive the leader's information, otherwise, d ι =0;

[0034] If there exists an extended directed graph G with the leader as the root and with paths to other followers, then the extended directed graph is a spanning tree;

[0035] Inter-neighbor formation tracking error The definition is as follows:

[0036]

[0037] in, represents the reference trajectory, Represents the expected inter-neighbor formation distance.

[0038] In a preferred embodiment of the present invention, the inequality relationship is constructed Constrain the convergence behavior of the tracking error between neighbor formations, and For the positive constant to be designed, preset performance function Defined as:

[0039]

[0040] Where t represents time, c i,j and T i,j They represent the expected minimum convergence rate and maximum convergence time, and Represent the preset initial value and steady-state final value respectively;

[0041] The construction error conversion equation is:

[0042]

[0043] in, is the error variable;

[0044] Based on the error conversion equation, the equivalent adjacent formation tracking error is converted to Defined as:

[0045]

[0046] In a preferred embodiment of the present invention, in step S3, based on the equivalent adjacent formation tracking error Construct the state transition equation:

[0047]

[0048] in, is the output signal of the predetermined time filter, is the input signal of the predetermined time filter, is the filtering error.

[0049] In a preferred embodiment of the present invention, the predetermined time filter is:

[0050]

[0051] in, and T p is the control gain to be designed, is the time-varying bounded function to be designed; for The estimated value of Represents the output signal of the predetermined time filter The derivative of .

[0052] In a preferred embodiment of the present invention, step S4 specifically includes:

[0053] According to the state transition equation, the Lyapunov function of the first-level subsystem of the quadrotor drone is constructed.

[0054]

[0055] in, and They are and The estimated value of the first-level subsystem of the ι-th quadrotor drone is Lyapunov function Taking the derivative with respect to time t, we get:

[0056]

[0057] in, Representative reference trajectory The derivative of

[0058] Using interval type 2 fuzzy logic system Estimating composite terms Satisfy

[0059]

[0060] represents the approximation error, is a bounded positive constant, is the weight vector The transpose of is the interval type 2 fuzzy logic system basis function vector The input vector, Represents the preset performance function The derivative of

[0061] Design a virtual controller for the first-level subsystem of a quadrotor drone

[0062]

[0063] in,

[0064]

[0065] is the control gain to be designed, is the interval type 2 fuzzy logic system basis function vector The transpose of

[0066] Design of parameter update law for the first-level subsystem of quadrotor UAV and parameter update law

[0067]

[0068]

[0069] Where θ = 2 + γ,

[0070] Virtual Controller Parameter update law And the parameter update law The time derivative of the Lyapunov function introduced into the first-order subsystem We get the first inequality:

[0071]

[0072] in,

[0073] In a preferred embodiment of the present invention, step S5 specifically includes:

[0074] Constructing the Lyapunov function of the second-level subsystem of the quadrotor drone

[0075]

[0076] in, as well as They are as well as estimated value of;

[0077] The Lyapunov function of the second-level subsystem of the quadrotor drone Taking the derivative with respect to time t, we get:

[0078]

[0079] in, is an unknown nonlinear function, and the interval type 2 fuzzy logic system The adopted estimate Satisfy is the weight vector The transpose of is the interval type 2 fuzzy logic system basis function vector The input vector, is the estimation error, is a bounded positive constant; Represents filtering error The derivative of hour, when hour,

[0080] Design of a time-scheduled cooperative formation tracking controller for quadrotor drones

[0081]

[0082] in, is the control gain to be designed, is the time-varying bounded function to be designed, Filter output signal The time derivative of is the interval type 2 fuzzy logic system basis function vector The transpose of

[0083] Design of parameter update law for the second-level subsystem of quadrotor UAV Parameter update law And the parameter update law

[0084]

[0085]

[0086]

[0087] in, Represents filtering error The absolute value of

[0088] Schedule the time for the coordinated formation tracking controller Parameter update law Parameter update law And the parameter update law The time derivative of the Lyapunov function introduced into the second-level subsystem We get the second inequality:

[0089]

[0090] In a preferred embodiment of the present invention, in step S6, the overall Lyapunov function is based on the Lyapunov function of the first-level subsystem. and the Lyapunov function of the second-level subsystem We get:

[0091]

[0092] Compared with the prior art, the present invention has the following beneficial effects:

[0093] 1. The present invention adopts an interval type-2 fuzzy logic system to perform online fuzzy modeling of the nonlinear coupling terms in the controlled quadrotor UAV, and designs a compensation function to reduce the adverse effects caused by approximation errors and external unknown interference, thereby improving the robustness and formation tracking performance of the controlled quadrotor UAV; the designed predetermined time filter not only avoids the complex iterative differential solution process, but also ensures the predetermined time convergence characteristics of the filtering error.

[0094] 2. Different from the finite-time control method and the fixed-time control method, the present invention proposes a collaborative formation control protocol with adaptive predetermined time for tracking accuracy, which ensures that the formation tracking error converges to a region near the origin within the predetermined time, effectively avoids potential singularity problems, and can determine the minimum upper limit of the formation tracking error convergence time through an easily adjustable controller gain.

[0095] 3. Unlike the traditional exponential decay performance function, the present invention introduces a fixed-time preset performance function to improve the steady-state performance and transient performance of the quadrotor drone, ensuring that the formation tracking error always converges within the preset performance range and never violates the preset maximum overshoot and maximum allowable steady-state error boundaries.

[0096] In order to make the above-mentioned objects, features and advantages of the present invention more clearly understood, embodiments of the present invention are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0098] Figure 1 This is a schematic diagram of the design process of a guaranteed performance collaborative formation control method for a cluster of quadrotor UAVs;

[0099] Figure 2 1 is a schematic structural diagram of a guaranteed performance collaborative formation control method for a cluster of quadrotor drones according to an embodiment of the present invention;

[0100] Figure 3 2. Schematic diagram of the communication topology structure of a swarm formation of four-rotor drones according to an embodiment of the present invention;

[0101] Figure 4 This is an actual formation trajectory diagram of a cluster of four-rotor drones in three-dimensional space in an embodiment of the present invention;

[0102] Figure 5 This is a state response trajectory diagram of the attitude subsystem of the quadrotor drone cluster in an embodiment of the present invention;

[0103] Figure 6 : is a state response trajectory diagram of the position subsystem of the quadrotor drone cluster in an embodiment of the present invention;

[0104] Figure 7 : This is a formation tracking error trajectory diagram of the attitude subsystem of the quadrotor drone cluster in an embodiment of the present invention;

[0105] Figure 8 : is a formation tracking error trajectory diagram of the quadrotor drone cluster position subsystem in an embodiment of the present invention;

[0106] Figure 9 This is a control input trajectory diagram of the attitude subsystem of the quadrotor drone cluster in an embodiment of the present invention;

[0107] Figure 10 This is a control input trajectory diagram of the quadrotor drone cluster position subsystem in an embodiment of the present invention. DETAILED DESCRIPTION

[0108] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0109] Please refer to Figure 1 and Figure 2 The present invention provides a method for designing guaranteed performance collaborative formation control for a cluster of quadrotor UAVs, comprising the following steps:

[0110] Step S1: construct a dynamic model of a quadrotor drone with external unknown disturbances, and establish a state space equation containing two-level subsystems based on the dynamic model.

[0111] Step S11: Based on the dynamics principle of the quadrotor drone, a quadrotor drone dynamics model with external unknown disturbance is established:

[0112]

[0113] Among them, 1≤ι≤N, N represents the number of followers in the quadrotor drone cluster, φ ι ,θ l and ψ lThey are respectively represented as the roll angle, pitch angle and yaw angle of the ιth quadrotor drone; as well as They are respectively represented as the roll angular velocity, pitch angular velocity and yaw angular velocity of the ιth quadrotor drone; as well as They are respectively represented as the roll angle acceleration, pitch angle acceleration and yaw angle acceleration of the ιth quadrotor drone; z, as well as Respectively represent the position coordinates, velocity and acceleration of the ιth quadrotor drone in the z-axis direction; x, as well as Respectively represent the position coordinates, velocity and acceleration of the ι-th quadrotor drone in the x-axis direction; y, as well as Respectively represent the position coordinate, velocity and acceleration of the ith quadrotor drone in the y-axis direction; u ι,f ,u ι,φ ,u ι,θ and u ι,ψ denote the total lift, roll angle control input, pitch angle control input, and yaw angle control input of the ιth quadrotor drone, respectively; is the mass of the ιth quadrotor drone; is the distance between the center of mass of the ιth quadrotor drone and the center of the rotor; as well as Represent the rotational inertia of the ιth quadrotor drone in three directions; is the drag coefficient; is an unknown external disturbance and satisfies G ι is the acceleration due to gravity; and Respectively and ι is the serial number of the quadrotor drone.

[0114] Step S12: Based on the above dynamic model (1), a state space equation containing two-level subsystems is established:

[0115]

[0116] in,

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] Step S2: Based on the topological structure between the leader and follower quadrotor drones, define the inter-neighbor formation tracking error, design a preset performance function and error conversion equation, and convert the inter-neighbor formation tracking error constrained by the inequality into an equivalent inter-neighbor formation tracking error without constraints.

[0127] Step S21: Define the topology between the leader and followers:

[0128] In the present invention, the leader of the quadrotor drone is defined as the reference trajectory, and the follower is defined as N quadrotor drones forming a quadrotor drone cluster.

[0129] A directed graph G = (X, Z) is used to describe the information exchange between quadrotor drones, where X = {1, 2, ..., N} is the vertex set consisting of N quadrotors; Z∈X×X represents the edge set; (j, ι) means that the ι-th quadrotor drone can obtain the j-th quadrotor drone information; Represents the adjacent set of the quadrotor drone; the adjacent matrix of the directed graph G Defined as: If So otherwise, The degree matrix is ​​defined as in The Laplacian matrix of a directed graph G is defined as: Extended directed graph Used to describe the information interaction between a swarm of quadrotor drones including the leader, where To expand the directed graph The point set, the quadrotor drone labeled 0 represents the leader; To expand the directed graph The Laplacian matrix of the extended directed graph G is defined as where d=[d1,d2,…,d N ] T ; D = diag{d1,d2,...,d N}, d ι=1 means that the ιth quadrotor drone can receive the leader's information, otherwise, d ι = 0. If there exists an extended directed graph G with the leader as the root and paths to other followers, then the extended directed graph is a spanning tree.

[0130] Step S22: Based on the topological structure obtained in step S21, define the tracking error between adjacent formations

[0131]

[0132] in, represents the reference trajectory, represents the expected inter-neighbor formation distance, and the inter-neighbor formation tracking error represents the tracking error between follower quadrotors.

[0133] Furthermore, the formation tracking error is defined as the tracking error between each follower quadrotor and its reference trajectory:

[0134]

[0135] in, Reference trajectory and is the control input u ι,z ,u ι,x ,u l,y and the yaw angle ψ l The calculation formula is as follows:

[0136]

[0137] Step S23: Construct an inequality relationship Constrain the convergence behavior of the tracking error between neighbor formations, and For the positive constant to be designed, preset performance function Defined as:

[0138]

[0139] Where t represents time, c i,j and T i,j They represent the expected minimum convergence rate and maximum convergence time, and Represent the preset initial value and steady-state final value respectively.

[0140] Step S24: To reduce the increase in the design complexity of the cooperative formation controller caused by the introduction of the preset performance function, the following error conversion equation is constructed to convert the inter-neighbor formation tracking error constrained by the inequality into an equivalent inter-neighbor formation tracking error without constraints:

[0141]

[0142] in, is the error variable.

[0143] Step S25: Based on the error conversion equation (6) obtained in step S24, an additional term is introduced: Solving for error variables and formation neighbor tracking error Zero point inconsistency problem, equivalent adjacent formation tracking error Defined as:

[0144]

[0145] Based on the above equivalent error transformation, the tracking error of adjacent formations is The convergence constraint problem is equivalent to ensuring the equivalent tracking error between adjacent formations The boundedness problem.

[0146] Step S3: Based on the adaptive dynamic surface control method, construct a state transition equation and design a predetermined time filter.

[0147] Step S31: Based on the equivalent adjacent formation tracking error obtained in step S25 Construct the state transition equation:

[0148]

[0149] in, is the output signal of the predetermined time filter, is the input signal of the predetermined time filter, is the filtering error.

[0150] Step S32: To solve the complex calculation problem in the traditional backstepping control scheme, the following predetermined time filter is designed:

[0151]

[0152] in, and T p is the control gain to be designed, is the time-varying bounded function to be designed; for The estimated value of Represents the output signal of the predetermined time filter The derivative of .

[0153] Step S4: Based on the state transition equation, construct the Lyapunov function of the first-level subsystem Designing a virtual controller Parameter update law of the first-level subsystem And the parameter update law

[0154] According to the state transition equation obtained in step S31, the Lyapunov function of the first-level subsystem of the ι-th quadrotor drone is constructed.

[0155]

[0156] in, and They are and estimated value.

[0157] Furthermore, the Lyapunov function of the first-level subsystem of the ι-th quadrotor drone is Taking the derivative with respect to time t, we can get:

[0158]

[0159] in, Representative reference trajectory The derivative of

[0160] Using interval type 2 fuzzy logic system Estimating composite terms Satisfy

[0161]

[0162] represents the approximation error, is a bounded positive constant, is the weight vector The transpose of is the interval type 2 fuzzy logic system basis function vector The input vector, Represents the preset performance function The derivative of .

[0163] Design a virtual controller for the first-level subsystem of a quadrotor drone

[0164]

[0165] in,

[0166]

[0167] is the control gain to be designed, is the interval type 2 fuzzy logic system basis function vector The transpose of .

[0168] Design the parameter update law for the first-level subsystem of the ι-th quadrotor drone and parameter update law

[0169]

[0170]

[0171] Where θ = 2 + γ,

[0172] Parameter update law and For adaptive parameters and Calculation and update of the parameters, dynamically adjust the update rate of the parameters; due to the unknown parameters and Cannot be used for controller design, so adaptive parameters are used and Estimate unknown parameters and The estimated values ​​obtained are used for controller design.

[0173] Furthermore, the virtual controller Parameter update law And the parameter update law Substituting into formula (11), we can get:

[0174]

[0175] in,

[0176] Step S5: Construct the Lyapunov function of the second-level subsystem Design of a scheduled time cooperative formation controller Parameter update law of the second-level subsystem Parameter update law And the parameter update law

[0177] Constructing the Lyapunov function of the second-level subsystem of the ι-th quadrotor drone

[0178]

[0179] in, as well as They are as well as estimated value.

[0180] Furthermore, the Lyapunov function of the second-level subsystem of the ι-th quadrotor drone is Taking the derivative with respect to time t, we get:

[0181]

[0182] in, For unknown nonlinear functions, an interval type-2 fuzzy logic system The adopted estimate Satisfy is the weight vector The transpose of is the interval type 2 fuzzy logic system basis function vector The input vector, is the estimation error, is a bounded positive constant; Represents filtering error The derivative of hour, when hour,

[0183] Design a time-scheduled cooperative formation tracking controller for the first quadrotor drone

[0184]

[0185] in, is the control gain to be designed, is the time-varying bounded function to be designed, Filter output signal The time derivative of is the interval type 2 fuzzy logic system basis function vector The transpose of .

[0186] Design the parameter update law for the second-level subsystem of the ι-th quadrotor drone Parameter update law And the parameter update law

[0187]

[0188]

[0189]

[0190] in, Represents filtering error The absolute value of .

[0191] Further, the scheduled time cooperative formation tracking controller Parameter update law Parameter update law And the parameter update law Substituting into formula (17), we can get:

[0192]

[0193] Step S6: Construct the overall Lyapunov function Based on the scheduled time Lyapunov stability theory, the stability of the closed-loop system is proved and the control gain of the scheduled time cooperative formation controller is determined.

[0194] Construct the Lyapunov function of the entire quadrotor drone swarm system:

[0195]

[0196] Furthermore, by taking the derivative of the Lyapunov function V of the entire quadrotor drone swarm system with respect to time t, we can obtain:

[0197]

[0198] in,

[0199]

[0200] Based on the Lyapunov stability theory of predetermined time, Will be at the scheduled time Converges within the region:

[0201]

[0202] Furthermore, the error variable will converge to the region:

[0203]

[0204] Based on the above stability analysis, the designed virtual controller is used Parameter update law Parameter update law Scheduled time cooperative formation tracking controller Parameter update law Parameter update law And the parameter update law It can ensure that all signals of the closed-loop system of the quadcopter UAV cluster are bounded, and then determine the control gain of the scheduled time cooperative formation controller. Based on the above stability analysis, the designed scheduled time cooperative formation control method ensures that the formation tracking error converges to a small neighborhood of the origin within the scheduled time, achieving the tracking error between adjacent formations. Track performance constraints to ensure they never exceed preset performance ranges

[0205] At this point, the design of the guaranteed performance collaborative formation control method for the quadrotor UAV cluster is completed. The effectiveness of the algorithm of the present invention is verified by MATLAB.

[0206] In the Simulink environment, a formation control system of three (N=3) quadrotor drones is simulated. Leader 0 represents the reference trajectory. The communication topology is as follows: Figure 3 The system parameters of the quadrotor UAV are shown in Table 1.

[0207] Table 1: Quadrotor UAV model parameters

[0208]

[0209] Reference trajectory is set as the leader. The initial positions of the three followers (ι=1, 2, 3) are set as:

[0210]

[0211]

[0212]

[0213] The expected formation neighbor distance is set as:

[0214]

[0215]

[0216]

[0217] The external disturbance is set as:

[0218]

[0219]

[0220] The controller gain is selected as:

[0221]

[0222]

[0223] The following results were obtained through MATLAB simulation experiments: Figure 4 This is the actual formation trajectory diagram of the quadrotor drone cluster in three-dimensional space. Figure 5 and Figure 6 The state response trajectory diagram of the attitude subsystem and position subsystem of the quadrotor swarm is shown in Figure 2. From the figure, we can see that under different initial conditions, the output trajectories of the three followers track the reference trajectory within the predetermined time. Figure 7 and Figure 8 The following figure shows the formation tracking error trajectory of the attitude subsystem and position subsystem of the quadrotor drone cluster. We can intuitively see that the formation tracking error converges within the pre-specified performance range and never violates the given maximum allowable overshoot and steady-state area. Figure 9 and Figure 10 The control input trajectory diagrams for the attitude and position subsystems of a quadrotor swarm are shown in Figure 2. Based on these simulation results, the invented guaranteed-cost collaborative formation control design method achieves a predetermined time convergence of the formation tracking error of a quadrotor swarm system, with the minimum upper bound of the convergence time directly adjusted via a single controller gain. Furthermore, the transient performance of the formation tracking error (such as the maximum allowable overshoot and convergence rate) can be adjusted according to user needs, effectively increasing the design flexibility of the collaborative formation control method.

[0224] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A guaranteed cost cooperative formation control design method for a swarm of quadrotor drones, characterized by: The following steps are involved: S1. Construct a dynamic model of a quadrotor drone with external unknown disturbances and establish a state-space equation containing two-level subsystems based on the dynamic model. S2. Based on the topological structure between the leader and follower quadrotor drones, define the inter-neighbor formation tracking error, design a preset performance function and error conversion equation, and convert the inter-neighbor formation tracking error constrained by inequality into an equivalent inter-neighbor formation tracking error without constraints; S3. Based on the adaptive dynamic surface control method, construct the state transition equation and design the predetermined time filter; S4. Based on the state transition equation, construct the Lyapunov function V of the first-level subsystem ι,j,1 , design virtual controller ρ ι,j,1 , the parameter update law of the first-level subsystem And the parameter update law S5. Construct the Lyapunov function V of the second-level subsystem ι,j,2 , design the scheduled time cooperative formation controller u ι,j , the parameter update law of the second-level subsystem Parameter update law And the parameter update law S6. Construct the overall Lyapunov function, prove the stability of the closed-loop system based on the scheduled time Lyapunov stability theory, and determine the control gain of the scheduled time cooperative formation controller; In step S1, the dynamic model of the quadrotor drone is: Among them, 1≤ι≤N, N represents the number of followers in the quadrotor drone cluster, φ ι ,θ ι and ψ ι They are respectively represented as the roll angle, pitch angle and yaw angle of the ιth quadrotor drone; as well as They are respectively represented as the roll angular velocity, pitch angular velocity and yaw angular velocity of the ιth quadrotor drone; as well as They are respectively represented as the roll angle acceleration, pitch angle acceleration and yaw angle acceleration of the ιth quadrotor drone; z, as well as Respectively represent the position coordinates, velocity and acceleration of the ιth quadrotor drone in the z-axis direction; x, as well as Respectively represent the position coordinates, velocity and acceleration of the ι-th quadrotor drone in the x-axis direction; y, as well as Respectively represent the position coordinate, velocity and acceleration of the ith quadrotor drone in the y-axis direction; u ι,f ,u ι,φ ,u ι,θ and u ι,ψ denote the total lift, roll angle control input, pitch angle control input, and yaw angle control input of the ιth quadrotor drone, respectively; is the mass of the ιth quadrotor drone; is the distance between the center of mass of the ιth quadrotor drone and the center of the rotor; as well as Respectively represent the rotational inertia of the ι-th quadrotor drone in three directions; Δ ι,j is the drag coefficient; is an unknown external disturbance and satisfies G ι is the acceleration due to gravity; S ι,o and C ι,o Respectively and ι is the serial number of the quadrotor drone; The state space equation containing the two-level subsystem is: in, In step S2, the topological structure of the quadrotor leader and the quadrotor follower is defined as follows: A directed graph G = (X, Z) is used to describe the information exchange between quadrotor drone clusters, where X = {1, 2, ..., N} is the vertex set consisting of N quadrotor drones; Z∈X×X represents the edge set; (j, ι) represents that the jth quadrotor drone can obtain the information of the jth quadrotor drone; Represents the adjacent set of the ι-th quadrotor drone; the adjacent matrix of the directed graph G Defined as: if (j, ι)∈Z, then a ι,j =1; otherwise, a ι,j =0; The degree matrix is ​​defined as in The Laplacian matrix of a directed graph G is defined as: Extended directed graph Used to describe the information interaction between a swarm of quadrotor drones including the leader, where To expand the directed graph The point set, the quadrotor drone labeled 0 represents the leader; To expand the directed graph The edge set of Extended directed graph The Laplacian matrix of in D=diag{d1,d2,...,d N }, d ι =1 means that the ιth quadrotor drone can receive the leader's information, otherwise, d ι =0; If there is an extended directed graph with the leader as the root and paths to other followers Then the extended directed graph is a spanning tree; Neighbor formation tracking error e ι,j The definition is as follows: in, represents the reference trajectory, represents the expected inter-neighbor formation distance; Constructing inequality relations Constrain the convergence behavior of the tracking error between neighbor formations, Λ ι,j and For the positive constant to be designed, preset performance function Defined as: Where t represents time, c i,j and T i,j They represent the expected minimum convergence rate and maximum convergence time, and Represent the preset initial value and steady-state final value respectively; The construction error conversion equation is: in, is the error variable; Based on the error conversion equation, the equivalent adjacent formation tracking error ζ ι,j (t) is defined as:

2. The method for designing guaranteed cost cooperative formation control for a swarm of quadrotor drones according to claim 1 is characterized in that: In step S3, based on the equivalent adjacent formation tracking error ζ ι,j (t), construct the state transition equation: Where ι = 1, 2, ..., N, j = 1, 2, ..., 6; is the output signal of the predetermined time filter, ρ ι，j，1 is the input signal of the predetermined time filter, ∈ ι,j,1 is the filtering error.

3. The method for designing guaranteed cost cooperative formation control for a swarm of quadrotor drones according to claim 2, characterized in that: The predetermined time filters are: in, 0<γ<1, τ ι,j and T p is the control gain to be designed, η ι，j,1 (t) is the time-varying bounded function to be designed; is Φ ι,j,1 The estimated value of Represents the output signal of the predetermined time filter The derivative of .

4. The method for designing guaranteed cost cooperative formation control for a swarm of quadrotor drones according to claim 3 is characterized in that: Step S4 specifically includes: According to the state transition equation, the Lyapunov function V of the first-level subsystem of the quadrotor drone is constructed. i,j,1 : in, and Y ι,j,1 and Ψ ι,j,1 estimated value of; The Lyapunov function V of the first-level subsystem of the ι-th quadrotor drone is ι,j,1 Taking the derivative with respect to time t, we get: in, The reference trajectory The derivative of Using interval type 2 fuzzy logic system Estimating composite terms Satisfy β ι,j,1 (χ ι,j,1 ) represents the approximation error, is a bounded positive constant, is the weight vector The transpose of is the interval type 2 fuzzy logic system basis function vector The input vector, Represents the preset performance function The derivative of Design of a virtual controller for the first-level subsystem of a quadrotor drone ι,j,1 : in, a ι,j,1 is the control gain to be designed, is the interval type 2 fuzzy logic system basis function vector The transpose of Design of parameter update law for the first-level subsystem of quadrotor UAV and parameter update law Where, θ=2+γ, The virtual controller ρ ι,j,1 , parameter update law And the parameter update law The time derivative of the Lyapunov function introduced into the first-order subsystem We get the first inequality: in, 5. The method for designing guaranteed cost cooperative formation control for a swarm of quadrotor drones according to claim 4, characterized in that: Step S5 specifically includes: Constructing the Lyapunov function V of the second-level subsystem of the quadrotor drone ι,j,2 : in, as well as Y ι,j,2 ,Ψ ι,j,2 and Φ ι,j,1 estimated value of; The Lyapunov function V of the second-level subsystem of the quadrotor drone is ι,j,2 Taking the derivative with respect to time t, we get: in, is an unknown nonlinear function, and the interval type 2 fuzzy logic system The adopted estimate Satisfy is the weight vector The transpose of χ i,j,2 is the interval type 2 fuzzy logic system basis function vector The input vector, β ι,j,2 (χ ι,j,2 ) is the estimation error, is a bounded positive constant; Represents the filtering error ∈ ι,j,1 The derivative of; when j=1,2,3, When j=4,5,6, Design of a time-scheduled cooperative formation tracking controller for quadrotor drones ι,j : Among them, a ι,j,2 is the control gain to be designed, η ι,j,2 (t) is the time-varying bounded function to be designed, Filter output signal The time derivative of is the interval type 2 fuzzy logic system basis function vector The transpose of Design of parameter update law for the second-level subsystem of quadrotor UAV Parameter update law And the parameter update law Among them, |∈ ι,j,1 | represents the filtering error ∈ ι,j,1 The absolute value of The scheduled time cooperative formation tracking controller u ι,j , parameter update law Parameter update law And the parameter update law The time derivative of the Lyapunov function introduced into the second-level subsystem We get the second inequality:

6. The method for designing guaranteed cost cooperative formation control for a swarm of quadrotor drones according to claim 5, characterized in that: In step S6, the overall Lyapunov function is based on the Lyapunov function V of the first-level subsystem. ι,j,1 and the Lyapunov function V of the second-level subsystem ι,j,2 We get:

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