An unmanned helicopter formation fault-tolerant method based on a time-varying topology method of a full-drive system

Abstract

The application discloses a kind of unmanned helicopter formation fault-tolerant methods under time-varying topology based on all-drive system method, including steps as follows: first, establish the high-order all-drive system model of unmanned helicopter, and divide into position outer loop subsystem and attitude inner loop subsystem;For the composite disturbance of unmanned helicopter actuator failure, external disturbance, design decentralized preset time composite disturbance observer to realize real-time accurate estimation of composite disturbance within preset time and be used for the design of controller;Based on all-drive system theory, preset time formation fault-tolerant controller and attitude tracking fault-tolerant controller are designed for the inner and outer loops of unmanned helicopter.The controller is designed according to all-drive system theory and preset time control method, so that the formation tracking error can reach stable convergence within a predetermined time, improve the maneuvering response speed of unmanned helicopter, and at the same time ensure the stability of multi-unmanned helicopter system under time-varying topology and fault conditions.

Description

Technical Field

[0001] This invention relates to the field of fault-tolerant control, and more particularly to a fault-tolerant method for unmanned helicopter formation under time-varying topology based on an all-drive system approach. Background Technology

[0002] Unmanned helicopters are low-altitude aircraft widely used in agriculture and industrial production, offering advantages such as: minimal impact from terrain and strong environmental adaptability; high payload capacity, flexible maneuverability, and long loiter time; strong stealth capabilities, enabling ultra-low-altitude and ground-hugging flight in special environments. When multiple unmanned helicopters cooperate, the efficiency of search and rescue, monitoring and reconnaissance, and cargo transportation missions can be effectively improved, thereby enhancing overall system performance. Therefore, research on formation control of multiple unmanned helicopters has become a current research hotspot.

[0003] Currently, it is noteworthy that most existing research on unmanned helicopter control is based on first-order state-space models, leading to complex controller structures and difficulties in practical applications. Establishing an unmanned helicopter model requires consideration of constraints from physical theorems such as Newton's laws and the law of angular momentum. These theorems are mostly presented in the form of second-order or higher-order differential equations. Converting a second-order or higher-order system model into a first-order state-space model would destroy the original system's all-drive characteristics. However, all-drive system theory based on higher-order all-drive system models can effectively preserve the key performance of the control system and directly design controllers that can eliminate nonlinear terms, ultimately obtaining a linear time-invariant system with desired characteristic structures. Therefore, research on formation control of multiple unmanned helicopters based on all-drive system theory is a cutting-edge issue worthy of close attention.

[0004] During flight, the communication range between unmanned helicopters is often limited, potentially leading to the failure of existing communication links and the establishment of new ones, resulting in a dynamically changing communication topology among multiple unmanned helicopters. In this situation, existing formation control methods for multiple unmanned helicopters under fixed topologies become inapplicable. Furthermore, each unmanned helicopter inevitably encounters unpredictable malfunctions during missions, such as actuator failures, sensor failures, and component failures. If these malfunctions are not effectively addressed, they will affect the normal flight of the unmanned helicopters and the formation of the entire unmanned helicopter swarm. In conclusion, considering time-varying topology conditions, researching fault-tolerant formation control methods for multiple unmanned helicopters has significant theoretical research value and practical application value. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a fault-tolerant method for unmanned helicopter formation under time-varying topology based on the all-drive system approach. This method ensures that the unmanned helicopter swarm can maintain its formation and flight attitude under time-varying topology and fault conditions, thereby improving the maneuver response speed of unmanned helicopters and the robustness and fault tolerance of the formation system.

[0006] Technical solution: This invention provides a fault-tolerant method for unmanned helicopter formation under time-varying topology based on the all-drive system approach, specifically including the following steps:

[0007] S1. The structure of the multi-unmanned helicopter formation system is regarded as a leader-follower structure, in which one virtual unmanned helicopter is the leader node and the other unmanned helicopters are the follower nodes. The switching topology of the multi-unmanned helicopter formation system is constructed.

[0008] S2. Analyze the motion characteristics of the unmanned helicopter and establish a system model of the unmanned helicopter; based on the impact of actuator failure on the system performance, construct an actuator failure model, and finally obtain an all-wheel drive system model of the unmanned helicopter with actuator failure.

[0009] S3, construct a distributed preset time composite interference observer to ensure that each follower unmanned helicopter can accurately estimate the composite interference composed of external interference and actuator failure within a preset time.

[0010] S4, based on the theory of all-drive systems, uses the formation error signal to design a preset time-tolerant controller for the position outer loop of the unmanned helicopter, so that the position tracking error converges to zero within a preset time, and gives the condition that the dwell time of the switching topology needs to meet.

[0011] S5. The desired attitude signal of the unmanned helicopter is obtained through attitude decoupling, and the first and second derivatives of the attitude signal are obtained with the help of a preset time integral filter. Then, based on the theory of all-drive system, a preset time fault-tolerant controller is designed for the attitude inner loop of the unmanned helicopter to ensure that the attitude tracking error converges to zero within a preset time.

[0012] Furthermore, in step S1, the directed communication topology graph of the N unmanned helicopters when switching signals σ(t) is G. σ(t) ={V,E σ(t)}, where V={v1,v2,...,v N}、E σ(t) ={(v i ,v j ):v i ,v j ∈V} are the set of nodes and the set of edges, respectively; defined As graph G σ(t) The adjacency matrix, where, This indicates whether there is communication between the i-th and j-th unmanned helicopters. If the i-th unmanned helicopter can receive information from the j-th unmanned helicopter, then... otherwise Directed graph G σ(t) in-degree matrix D σ(t) Defined as in Define the Laplace matrix L σ(t) For L σ(t) =D σ(t) -A σ(t) ;

[0013] When considering a virtual leader, the directed graph G σ(t) Transform into a new directed graph And the definition diagram The adjacency matrix B σ(t) for in, This indicates whether there is communication between the i-th unmanned helicopter and the virtual leader. If the i-th unmanned helicopter can receive information from the virtual leader, then... otherwise

[0014] Furthermore, in step S2, the system model of the unmanned helicopter is as follows:

[0015]

[0016] Among them, P i =[x i ,y i ,z i ] T and V i =[u i ,v i ,ω i ] T Let x represent the position and velocity of the unmanned helicopter i, respectively, and x... i y i z i These represent the positions along the x-axis, y-axis, and z-axis in the geocentric coordinate system, respectively. i v i w i Let m represent the velocities along the x-axis, y-axis, and z-axis in the geocentric coordinate system, respectively. i Let represent the mass of the unmanned helicopter i, g represent the acceleration due to gravity, and e3 = [0, 0, 1]. T , f represents the rotation matrix from the machine body to the geocentric coordinate system. i f represents the force generated by the main rotor. dVi Θ represents external disturbances on the outer ring of the location.i =[φ i ,θ i ,ψ i ] T and Ω i =[p i ,q i ,r i ] T Let φ represent the attitude angle and attitude angular velocity of the unmanned helicopter i relative to the geocentric coordinate system, respectively, and φ i θ i ψ i These represent the roll angle, pitch angle, and yaw angle, respectively. i q i r i These represent the roll, pitch, and yaw angular velocities, respectively. This represents the attitude state matrix from the body coordinate system to the geocentric coordinate system. The diagonal moment of inertia matrix, Let τ represent a skew-symmetric matrix. i τ represents the control torque of the unmanned helicopter i. dΩi To account for external disturbances to the attitude inner loop, the specific expressions for the matrices in the unmanned helicopter model are given as follows:

[0017]

[0018]

[0019]

[0020] Where C, S, and T represent cos(·), sin(·), and tan(·), respectively, and J xxi J yyi and J zzi It is the inertial constant;

[0021] External force f of unmanned helicopter i =[0,0,-T mi ] T , Represents the main rotor thrust, of which and These are parameters for the unmanned helicopter system. The collective pitch angle of the main rotor; the control torque τ of the unmanned helicopter i. i Defined as in Indicates the collective pitch angle of the tail rotor. Indicates the longitudinal periodic pitch angle. The coefficient matrix A represents the lateral periodic pitch angle and the control torque. i and control input matrix B i The definition is as follows:

[0022]

[0023] Wherein, parameter τ mi , and All of these are related to the system structure of unmanned helicopters.

[0024] Furthermore, the actuator fault model in step S2 is as follows:

[0025]

[0026] in, For the output of the actuator, For the input of the actuator, This represents the input control quantity of the main rotor collective pitch actuator. This represents the input control quantity of the longitudinal periodic variable pitch angle actuator. This represents the input control quantity of the transverse periodic variable pitch actuator. This represents the input control quantity for the tail rotor collective pitch actuator; Represents the identity matrix, Λ i =diag{ρ 1i ,ρ 2i ,ρ 3i ,ρ 4i} represents a partial failure factor vector, ρ mi ∈[0,1)(m=1,2,3,4) represents a partial failure factor, Δ i =[δ 1i (t),δ 2i (t),δ 3i (t),δ 4i (t)] T Denotes the time-varying migration fault function vector, δ 1i (t), δ 2i (t), δ 3i (t), δ 4i (t) represents the variable offset fault function;

[0027] The following model of the all-wheel drive system of an unmanned helicopter with actuator failure is established:

[0028] (1) Location outer ring all-drive subsystem

[0029]

[0030] in, U xi U yi U zi These represent the position control values ​​along the x, y, and z axes, respectively. dVi =R i f dVi / m i ;

[0031] (2) Attitude Inner Ring All-Drive Subsystem

[0032]

[0033] in, G i =Π i (Θ i B i , Λ 2i =diag{ρ 2i ,ρ 3i ,ρ 4i}, Δ 2i =[δ 2i (t),δ 3i (t),δ 4i (t)] T .

[0034] Furthermore, the distributed preset time composite interference observer in step S3 is constructed as follows:

[0035]

[0036]

[0037] in, These represent the auxiliary variables that interfere with the observer. They are D 1i and D 2i The estimated value; m 1i and m 2i These are design parameters, time-varying scalar functions. Its derivative ρ is a positive real number, T d This indicates a time constant that can be preset.

[0038] Furthermore, the preset time-tolerant controller design for the outer loop of the position in step S4 is as follows:

[0039]

[0040] Among them, e pi =P i -P0-s i P0 represents the location of the virtual unmanned helicopter, s i This represents the ideal relative distance between unmanned helicopter i and the virtual unmanned helicopter. These are design parameters. Preset time T p Satisfy T p >T d ;

[0041] Dwell time when switching topologies in ∈ p It is a positive integer. All are positive definite matrices, and q is the number of communication topologies.

[0042] Furthermore, the expression for attitude decoupling in step S5 is as follows:

[0043]

[0044]

[0045] The preset time integral filter is designed as follows:

[0046]

[0047]

[0048]

[0049] Where, Θ di =[φ di ,θ di ,ψ di ] T , φ di θ di ψ is obtained through attitude decoupling. di Provided by a virtual unmanned helicopter. ε 1i ε 2i and ε 3i For positive design parameters, and The preset time constant and satisfying

[0050] Furthermore, in step S5, the attitude inner loop preset time fault-tolerant controller is designed as follows:

[0051]

[0052] in, These are design parameters, preset time. Provided by the designed filter,

[0053] Compared with the prior art, the significant advantages of this invention are as follows:

[0054] 1. By establishing a high-order all-drive system model for unmanned helicopters, the system is divided into an outer position subsystem and an inner attitude subsystem. A distributed preset time disturbance observer is designed so that each unmanned helicopter can accurately estimate the composite disturbance composed of actuator failure and external disturbance within a preset time, thereby achieving effective compensation for the subsequent controller.

[0055] 2. Based on the theory of all-drive systems, a time-preset formation fault-tolerant controller and attitude fault-tolerant controller are designed to ensure that the unmanned helicopter swarm can maintain its formation and flight attitude under time-varying topology and fault conditions, which significantly improves the maneuver response speed of unmanned helicopters and the robustness and fault tolerance of the formation system. Attached Figure Description

[0056] Figure 1 This is a flowchart of the present invention;

[0057] Figure 2 A schematic diagram of a multi-unmanned helicopter formation;

[0058] Figure 3 Force diagram of an unmanned helicopter;

[0059] Figure 4 (a) in the diagram is the communication topology diagram of the first type of multi-unmanned helicopter.

[0060] (b) is the communication topology diagram of the second type of multi-unmanned helicopter.

[0061] (c) is the communication topology diagram of the third type of multi-unmanned helicopter;

[0062] Figure 5 This is a schematic diagram of the switching signal σ(t);

[0063] Figure 6 A 3D formation rendering of multiple unmanned helicopters;

[0064] Figure 7 This is a diagram showing the formation tracking error of multiple unmanned helicopters. Detailed Implementation

[0065] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0066] The technical solution of this embodiment first establishes a full-drive system model of the unmanned helicopter. For the combined interference of unmanned helicopter actuator failure and external disturbances, a distributed, preset-time combined interference observer is designed to achieve real-time and accurate estimation of the combined interference within a preset time, which is then used in the controller design. This ensures that the combined interference of each unmanned helicopter can be effectively compensated. Based on the full-drive system theory, a preset-time formation fault-tolerant controller and an attitude tracking fault-tolerant controller are designed for the inner and outer loops of the unmanned helicopter. This invention designs the controller based on the full-drive system theory and the preset-time control method, enabling the formation tracking error to achieve stable convergence within a predetermined time, improving the maneuver response speed of the unmanned helicopter, and simultaneously ensuring the stability of the multi-unmanned helicopter system under time-varying topology and fault conditions.

[0067] like Figure 1 As shown, the specific implementation steps of this embodiment are as follows:

[0068] Step 1: Treat the structure of the multi-unmanned helicopter formation system as a leader-follower structure, where one virtual unmanned helicopter acts as the leader node and the other unmanned helicopters act as follower nodes, and construct the switching topology diagram of the multi-unmanned helicopter formation system.

[0069] like Figure 2 As shown, N unmanned helicopters achieve the desired formation pattern through a time-varying communication topology and virtual unmanned helicopters. The communication topology when the unmanned helicopters switch signals σ(t) can be represented by a directed graph: G σ(t) ={V,E σ(t)}, where V={v1,v2,...,v N}、E σ(t) ={(v i ,v j ):v i ,v j ∈V} are the set of nodes and the set of edges, respectively. i Let be the position of the i-th UAV; the switching signal σ(t) is defined as σ(t): [0,+∞)→{1,2,…,q}, where q is the number of communication topologies; define The time interval is an infinite sequence of time intervals and t0 = 0; the dwell time τ0 satisfies 0 < τ0 ≤ t k+1 -t k The communication topology remains unchanged during the dwell time τ0; definition As graph G σ(t) The adjacency matrix, This indicates whether there is communication between the i-th and j-th unmanned helicopters. Specifically, if the i-th unmanned helicopter can receive information from the j-th unmanned helicopter, then... otherwise Directed graph Gσ(t) in-degree matrix D σ(t) Defined as in Define the Laplace matrix L σ(t) For L σ(t) =D σ(t) -A σ(t) When considering a virtual leader, the directed graph G... σ(t) Transform into a new directed graph And the definition diagram The adjacency matrix B σ(t) for This indicates whether there is communication between the i-th unmanned helicopter and the virtual leader. Specifically, if the i-th unmanned helicopter can receive information from the virtual leader, then... otherwise

[0070] Step 2: Analyze the motion characteristics of the unmanned helicopter and establish a system model of the unmanned helicopter; further consider the impact of actuator failure on the system performance, construct an actuator failure model, and finally obtain the unmanned helicopter all-drive system model with actuator failure.

[0071] During flight, the flight status control of the unmanned helicopter mainly relies on the collective pitch angle of the main rotor. tail rotor collective pitch Longitudinal periodic pitch angle and lateral periodic pitch angle Figure 3 The force diagram of the unmanned helicopter is presented, where O I x I y I z I Using a geocentric coordinate system, O i x i y i z i Using the body coordinate system, and based on the Newton-Euler method, the system model of the unmanned helicopter is established as follows:

[0072]

[0073] Among them, P i =[x i ,y i ,z i ] T V i =[u i ,v i ,ω i ] T Let x represent the position and velocity of unmanned helicopter i, respectively. i y i zi Let u represent the x-axis, y-axis, and z-axis coordinates of the unmanned helicopter i in the geocentric coordinate system, respectively. i v i ω i Let m represent the velocities of unmanned helicopter i along the x, y, and z axes in the geocentric coordinate system, respectively; i Let e3 represent the mass of the unmanned helicopter i, and g represent the acceleration due to gravity; e3 = [0, 0, 1] T T denotes matrix transpose; f represents the rotation matrix from the machine body to the Earth coordinate system. i f represents the force generated by the main rotor. dVi Θ represents external disturbances on the outer ring of the location. i =[φ i ,θ i ,ψ i ] T and Ω i =[p i ,q i ,r i ] T Let φ represent the attitude angle and attitude angular velocity of the unmanned helicopter i relative to the geocentric coordinate system, respectively. i θ i ψ i Let p represent the attitude angles of unmanned helicopter i along the x-axis, y-axis, and z-axis in the geocentric coordinate system, respectively. i q i r i These represent the attitude angular velocities of unmanned helicopter i along the x-axis, y-axis, and z-axis in the geocentric coordinate system, respectively. This represents the attitude state matrix from the body coordinate system to the geocentric coordinate system. The diagonal moment of inertia matrix, Let τ represent a skew-symmetric matrix. i τ represents the control torque of the unmanned helicopter i. dΩi To account for external disturbances to the attitude inner loop, the specific expressions for the matrices in the unmanned helicopter model are given as follows:

[0074]

[0075]

[0076]

[0077] Where C, S, and T represent cos(·), sin(·), and tan(·), respectively; J xxi J yyi and J zzi These are the inertial constants, respectively.

[0078] External force f of unmanned helicopter i =[0,0,-T mi ] T , Represents the main rotor thrust, of which and These are the system parameters of the unmanned helicopter i; the control torque τ of the unmanned helicopter i. i It can be defined as The coefficient matrix A represents the main rotor collective pitch coupling coefficient and the control torque. i and control input matrix B i The definition is as follows:

[0079]

[0080] Wherein, parameter τ mi , and All of these are related to the system structure of unmanned helicopters;

[0081] make For the control input of the outer loop of the position, These represent the position control values ​​in the x-axis, y-axis, and z-axis directions, respectively. As the control input for the attitude inner loop, the system model of the unmanned helicopter i can be divided into the following two subsystems:

[0082] (A1) Location outer ring subsystem

[0083]

[0084] Where, d Vi =R i f dVi / m i ;

[0085] (A2) Attitude Inner Loop Subsystem

[0086]

[0087] in,

[0088] In formation control, the actuator output of unmanned helicopter i Actuator failures may occur, which can be modeled as follows:

[0089]

[0090] in, For actuator input, This represents the input control quantity of the main rotor collective pitch actuator. This represents the input control quantity of the longitudinal periodic variable pitch angle actuator. This represents the input control quantity of the transverse periodic variable pitch actuator. This represents the input control quantity for the tail rotor collective pitch actuator; Represents the identity matrix, Λ i =diag{ρ 1i ,ρ 2i ,ρ 3i ,ρ 4i}, ρ mi ∈[0,1)(m=1,2,3,4) represents a partial failure factor, Δ i =[δ 1i (t),δ 2i (t),δ 3i (t),δ 4i (t)] T Denotes the time-varying offset fault function, δ 1i (t), δ 2i (t), δ 3i (t), δ 4i (t) represents the variable offset fault function; this actuator fault includes three fault conditions:

[0091] When 0 < ρ mi <1,δ mi When (t) = 0, it indicates that the actuator has experienced a partial failure.

[0092] When ρ mi =0,δ mi When (t)≠0, it indicates that the actuator has an offset fault;

[0093] When 0 < ρ mi <1,δ mi When (t)≠0, it indicates that the actuator has experienced a mixed fault, including failure and offset faults;

[0094] Finally, the model of the i-drive system of an unmanned helicopter with actuator failure can be established as follows:

[0095] (B1) Position outer ring all-drive subsystem

[0096]

[0097] in, U xi U yi U zi These represent the position control values ​​in the x-axis, y-axis, and z-axis directions, respectively.

[0098] (B2) Attitude Inner Ring All-Drive Subsystem

[0099]

[0100] in, G i =Π i (Θ i B i , Λ 2i =diag{ρ 2i ,ρ 3i ,ρ 4i}, Δ 2i =[δ 2i (t),δ 3i (t),δ 4i (t)] T .

[0101] Step 3: Construct a distributed, preset-time composite interference observer to ensure that each follower unmanned helicopter can accurately estimate the composite interference consisting of external interference and actuator failure within a preset time.

[0102] The distributed, pre-set time composite interference observer is constructed as follows:

[0103]

[0104]

[0105] in, These represent the auxiliary variables that interfere with the observer; They are D 1i and D 2i The estimated value; m 1i and m 2i These are design parameters; time-varying scalar functions. Its derivative ρ is a positive real number, T d This represents a preset time constant. For convenience, μ will be used below to represent μ(t,T). d ).

[0106] For z 1i Taking the derivative, we get

[0107]

[0108] Substituting equation (7) into equation (9), we get

[0109]

[0110] Choose Lyapunov functions as And on Taking the derivative, we get

[0111]

[0112] Where, ζ 1i =D 1i -m 1i sign(z 1i ).

[0113] Suppose there exists a positive constant β 1i Satisfy ||D 1i ||≤β 1i Then when m 1i >β 1i ζ can be found 1i and z 1i The sign is opposite, i.e., z 1i ζ 1i ≤0. Therefore, we can obtain

[0114]

[0115] Based on the preset time control theory, it can be found that: when t≥T d At that time, z 1i If ≡0, then t≥T d hour, Therefore, the designed interference observer (7) is able to detect interference within a preset time T. d Composite interference D of inner position outer loop subsystem (5) 1i Make an estimate.

[0116] The same method can be used to demonstrate that the interference observer (8) can function within a preset time T. d Composite disturbance D of the inner attitude inner loop subsystem (6) 2i Make an estimate.

[0117] In summary, if composite interference observers (7) and (8) are designed for each unmanned helicopter, and the design parameters satisfy... m 1i >β 1i and m 2i >β 2i Then when t≥T d hour,

[0118] Step 4: Based on the theory of all-drive systems, design a preset time-tolerant controller for the position outer loop of the unmanned helicopter so that the position tracking error converges to zero within a preset time, and give the condition that the dwell time of the switching topology needs to meet.

[0119] For the outer loop of the position, the position tracking error of the unmanned helicopter i is defined as follows:

[0120] e pi =P i -P0-s i (13)

[0121] P0 represents the virtual location of the unmanned helicopter, s i This represents the ideal relative distance between unmanned helicopter i and the virtual unmanned helicopter.

[0122] make but The second derivative can be calculated as

[0123]

[0124] in, Preset time T p Satisfy T p >T d .

[0125] Based on the theory of all-drive systems, the preset time-tolerant controller for the outer loop of the position is designed as follows:

[0126]

[0127] in, It is a design parameter, e pj Position tracking error of unmanned helicopter j.

[0128] When t≥T d hour, Substituting equation (15) into equation (14), we get:

[0129]

[0130] definition and Then equation (16) becomes:

[0131]

[0132] Among them, Q σ(t) =L σ(t) +B σ(t) It is a positive definite matrix.

[0133] make The following linear system can be obtained:

[0134]

[0135] in,

[0136] Due to the existence of topology switching, it is difficult to construct a Lyapunov function that can describe the energy of the entire formation error. Therefore, for t∈[t k ,t k+1 Fixed directed graph Introduce the following piecewise positive definite Lyapunov function:

[0137]

[0138] in, It is a positive definite matrix;

[0139] right Taking the derivative, we get:

[0140]

[0141] Choose appropriately Can be allocated arbitrarily The eigenvalues ​​of such that they satisfy . Then we can obtain

[0142]

[0143] Where, ∈ p It is a positive integer.

[0144] For convenience, μ′ will be used to represent μ(t,T) in the following text. p ).

[0145] definition in, If it is a positive definite matrix, then we can obtain:

[0146]

[0147] According to equations (21) and (22), we can obtain:

[0148]

[0149] Differentiating both sides of equation (22), we get:

[0150]

[0151] Combining equations (23) and (24), we can obtain:

[0152]

[0153] For t∈[t] k ,t k+1 Piecewise Lyapunov function V p It can be deduced that:

[0154]

[0155] Because of e pi From the continuity, we can obtain:

[0156]

[0157] in, All are positive definite matrices, and q is the number of communication topologies.

[0158] Combining equations (26) and (27), we can derive:

[0159]

[0160] because so:

[0161]

[0162] Based on the recursive method, we can derive from equation (29)

[0163]

[0164] Since the dwell time τ0 satisfies τ0≤t / k, then

[0165]

[0166] If the length of stay but Based on the preset time control theory, the position tracking error variable can be identified. It can achieve time stability, that is, when t∈[T] p If ,∞), then e pi =P i -P0-s i Keep it at zero.

[0167] Step 5: Obtain the desired attitude signal of the unmanned helicopter through attitude decoupling, and obtain the first and second derivatives of the attitude signal with the help of a preset time integral filter; then, based on the theory of all-drive system, design a preset time fault-tolerant controller for the attitude inner loop of the unmanned helicopter to ensure that the attitude tracking error converges to zero within a preset time.

[0168] according to and We can obtain:

[0169]

[0170] Expanding the above equation (32), we get:

[0171]

[0172] The desired roll angle φ can be obtained through attitude decoupling. di and desired pitch angle θ di :

[0173]

[0174] Desired yaw angle ψ of unmanned helicopter formation di Provided by a virtual unmanned helicopter, due to the desired attitude signal Θ di =[φ di ,θ di ,ψ di ] T In practice, it may not be differentiable, so the following preset time integral filter is designed to obtain... and

[0175]

[0176] in, ε 1i ε 2i and ε 3i For design parameters, and The preset time constant and satisfying

[0177] When the design parameters meet but and Can be done at the scheduled time and Acquisition, that is, when hour, when hour,

[0178] For the inner attitude loop, the attitude tracking error of the unmanned helicopter is defined as:

[0179] e θi =Θ i -Θ di (36)

[0180] make but The second derivative can be calculated as:

[0181]

[0182] Among them, the preset time T p satisfy

[0183] Based on the theory of all-drive systems, the preset time-tolerant controller for the outer loop of the position is designed as follows:

[0184]

[0185] in, These are design parameters.

[0186] When t≥T d hour, Substituting equation (38) into equation (37), we can obtain

[0187]

[0188] definition The following linear system can be obtained:

[0189]

[0190] in,

[0191] Introduce the following positive definite Lyapunov function:

[0192]

[0193] Among them, H θi It is a positive definite matrix;

[0194] right Taking the derivative, we get:

[0195]

[0196] Choose appropriately A can be assigned arbitrarily. θi The eigenvalues ​​of such that they satisfy . Then we can obtain

[0197]

[0198] Additionally, for convenience, μ″ will be used below to represent μ(t,T) θ ).definition Then we can obtain:

[0199]

[0200] According to equations (43) and (44), we can obtain:

[0201]

[0202] Differentiating both sides of equation (44), we get:

[0203]

[0204] Combining equations (45) and (46), we can obtain:

[0205]

[0206] Based on the pre-defined time control theory, it can be found that when t∈[T] θ When ,∞), the attitude tracking error variable e θi =Θ i -Θ di Keep it at zero.

[0207] In this embodiment of the invention, one virtual unmanned helicopter and four unmanned helicopters are selected to form the entire formation system. Possible switching topologies include: Figure 4 As shown in (a), (b), and (c), UH1 to UH4 represent four unmanned helicopters, and Leader represents a virtual unmanned helicopter. Figure 5 A schematic diagram of the switching signal σ(t) is presented. The system parameters for each unmanned helicopter are set as follows: g = 9.8 m·s -2 m i =8.2kg, J i = diag{0.18,0.34,0.28} kg·m 2 ,

[0208] A i =diag{-48.1757,-25.5048,-0.9808}s -1 .

[0209] The initial state of each unmanned helicopter is: P1(0) = [2, 10, 1] T m, P2(0) = [-2, 13, 1.5] T m, P3(0) = [-2, 17, 0.5] T m, P4(0) = [2, 20, 2] T m.

[0210] The initial attitude of each unmanned helicopter is: Θ1(0)=[0.4,0.3,0.8] T rad, Θ2(0)=[0.3,0.2,-0.5] T rad, Θ3(0)=[-0.5,0.1,-0.2] T rad, Θ4(0)=[0.6,0.1,0.4] T rad.

[0211] The desired trajectory of the virtual unmanned helicopter is: P0 = [15sin(0.2t), 15cos(0.2t), 0.2t]T m, ψ0=cos(0.2t)rad, where t is the time variable; the expected relative distance is: s1=[-2,2,0] T m, s2 = [2, 2, 0] T m, s3 = [-2, -2, 0] T m, s4 = [2, -2, 0] T m.

[0212] The parameters of the interference observer are set as follows: T d =3s, i=1,2,3,4; the outer loop controller parameters for the position of each unmanned helicopter are set as follows: T p =4s, i=1,2,3,4; the parameters of the integral filter are set as follows: ε 3i =ε 3i =ε 3i =0.1, i = 1, 2, 3, 4; the attitude inner loop controller parameters for each unmanned helicopter are set as follows: T θ =5s, i=1,2,3,4.

[0213] Furthermore, to illustrate the fault tolerance capability of the present invention, the actuator fault parameters for multiple unmanned helicopters are set as follows:

[0214] For the first unmanned helicopter, when t < 1s, Λ1 = 0, Δ1 = 0; when t ≥ 1s, Λ1 = diag{0.5, 0.3, 0.2, 0.1}, Δ1 = [0.01sin(0.5t), 0.02sin(0.5t), 0.02cos(0.5t), 0.01cos(0.5t)]. T ;

[0215] For the second unmanned helicopter, when t < 1.5s, Λ2 = 0, Δ2 = 0; when t ≥ 1.5s, Λ2 = diag{0.3, 0, 0, 0.4}, Δ2 = [0.02cos(0.5t), 0, 0, 0.02sin(0.5t)]. T ;

[0216] For the third unmanned helicopter, when t < 1s, Λ3 = 0, Δ3 = 0; when t ≥ 1s, Λ3 = diag{0, 0.2, 0.1, 0}, Δ3 = [0, 0.01sin(0.5t)cos(0.5t), 0.02sin(0.5t) + 0.02cos(0.5t), 0)] T ;

[0217] For the fourth unmanned helicopter, when t < 2s, Λ4 = 0, Δ4 = 0; when t ≥ 2s, Λ4 = diag{0.4, 0.2, 0, 0}, Δ4 = [0.03sin(0.5t) - 0.03cos(0.5t), 0, 0.03cos(0.5t) - 0.03sin(0.5t), 0] T .

[0218] To verify the effectiveness of the preset time formation fault-tolerant control of the multi-unmanned helicopters in this invention, simulation verification was performed using the Simulink module in Matlab. Figure 6 It presents a 3D formation rendering of multiple unmanned helicopters. Figure 7 The simulation results present a formation tracking error diagram for multiple unmanned helicopters. The simulation results show that the position tracking error e for all unmanned helicopters is... pi After 4 seconds, the yaw angle tracking error ψ approaches 0. i -ψ0 approaches 0 after 5 seconds, completing the preset control target. Therefore, it can be concluded that the multi-unmanned helicopter formation system can achieve the expected formation task by using the preset time formation fault-tolerant controller designed in this invention in the event of actuator failure and communication topology switching.

[0219] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A fault-tolerant method for unmanned helicopter formation based on time-varying topology of all-wheel drive system method, characterized in that, Specifically, the steps include the following: S1. The structure of the multi-unmanned helicopter formation system is regarded as a leader-follower structure, in which one virtual unmanned helicopter is the leader node and the other unmanned helicopters are the follower nodes. The switching topology of the multi-unmanned helicopter formation system is constructed. S2. Analyze the motion characteristics of the unmanned helicopter and establish a system model of the unmanned helicopter; based on the impact of actuator failure on the system performance, construct an actuator failure model, and finally obtain an all-wheel drive system model of the unmanned helicopter with actuator failure. S3, construct a distributed preset time composite interference observer to ensure that each follower unmanned helicopter can accurately estimate the composite interference composed of external interference and actuator failure within a preset time. S4, based on the theory of all-drive systems, uses the formation error signal to design a preset time-tolerant controller for the position outer loop of the unmanned helicopter, so that the position tracking error converges to zero within a preset time, and gives the condition that the dwell time of the switching topology needs to meet. S5. The desired attitude signal of the unmanned helicopter is obtained through attitude decoupling, and the first and second derivatives of the attitude signal are obtained by means of a preset time integral filter. Then, based on the theory of all-drive system, a preset time fault-tolerant controller is designed for the attitude inner loop of the unmanned helicopter to ensure that the attitude tracking error converges to zero within a preset time. In step S1, An unmanned helicopter is switching signals. The directed graph of the communication topology at that time is ,in, , These are the set of nodes and the set of edges; defined As a diagram The adjacency matrix, where, Indicates the first The unmanned helicopter and the first Is there communication between the unmanned helicopters? If the first The unmanned helicopter can receive the first Information about the unmanned helicopter, ,otherwise Directed graph in-degree matrix Defined as ,in Define the Laplace matrix. for ; When considering virtual leaders, directed graphs Transform into a new directed graph And the definition graph adjacency matrix for ,in, Indicates the first Is there communication between the unmanned helicopter and the virtual leader? If the first If an unmanned helicopter can receive information from a virtual leader, then... ,otherwise ; In step S2, the system model of the unmanned helicopter is as follows: ， in, and These represent unmanned helicopters. Position and velocity, and , , These represent the coordinates in the geocentric coordinate system. axis, axis, Position in the axial direction , , These represent the coordinates in the geocentric coordinate system. axis, axis, Velocity in the axial direction, Indicates unmanned helicopter quality Represents gravitational acceleration. , This represents the rotation matrix of the machine body to the geocentric coordinate system. This represents the force generated by the main rotor. This indicates external interference on the outer ring of the location. and These represent unmanned helicopters. Relative to the attitude angle and attitude angular velocity in the geocentric coordinate system, and , , These represent the roll angle, pitch angle, and yaw angle, respectively. , , These represent the roll, pitch, and yaw angular velocities, respectively. This represents the attitude state matrix from the body coordinate system to the geocentric coordinate system. The diagonal moment of inertia matrix, Represents an oblique symmetric matrix. Indicates unmanned helicopter The control torque, To account for external disturbances to the attitude inner loop, the specific expressions for the matrices in the unmanned helicopter model are given as follows: ， ， ， ， in, , , They are respectively represented as , , , , and It is the inertial constant; External force of unmanned helicopter , Represents the main rotor thrust, of which and These are parameters for the unmanned helicopter system. Indicates the collective pitch angle of the main rotor; unmanned helicopter Control torque Defined as ,in Indicates the collective pitch angle of the tail rotor. Indicates the longitudinal periodic pitch angle. Indicates the lateral periodic pitch angle; The coefficient matrix represents the main rotor collective pitch coupling coefficient and the control torque coefficient matrix. and control input matrix The definition is as follows: ， ， Among them, parameters , , , , , , , , , and All of these are related to the system structure of unmanned helicopters.

2. The fault-tolerant method for unmanned helicopter formation under time-varying topology based on the all-drive system method according to claim 1, characterized in that, The actuator fault model in step S2 is as follows: ， in, For the output of the actuator, For the input of the actuator, This represents the input control quantity of the main rotor collective pitch actuator. This represents the input control quantity of the longitudinal periodic variable pitch angle actuator. This represents the input control quantity of the transverse periodic variable pitch actuator. This represents the input control quantity for the tail rotor collective pitch actuator; Represents the identity matrix. , representing a partial failure factor vector, Indicates partial failure factors. ; Represents the time-varying offset fault function vector. , , , Indicates the variable offset fault function; The following model of the all-wheel drive system of an unmanned helicopter with actuator failure is established: 1) Location outer ring all-drive subsystem ， in, , , , They represent axis, axis, Position control quantity in the axial direction. , , ; 2) Attitude Inner Ring All-Drive Subsystem ， in, , , , , , , .

3. The fault-tolerant method for unmanned helicopter formation under time-varying topology based on the all-drive system method according to claim 2, characterized in that, In step S3, the distributed preset time composite interference observer is constructed as follows: ， ， in, , These represent the auxiliary variables that interfere with the observer. , They are and The estimated value; , , , , , , and These are design parameters, time-varying scalar functions. Its derivative , It is a positive real number. This indicates a time constant that can be preset.

4. The fault-tolerant method for unmanned helicopter formation under time-varying topology based on the all-drive system method according to claim 3, characterized in that, The preset time-tolerant controller design for the outer loop position in step S4 is as follows: ， in, , Indicates the location of the virtual unmanned helicopter. Indicates unmanned helicopter The ideal relative distance to the virtual unmanned helicopter , These are design parameters. preset time satisfy ; Dwell time when switching topologies ,in , It is a positive integer. , All are positive definite matrices. The number of communication topologies.

5. The fault-tolerant method for unmanned helicopter formation under time-varying topology based on the all-drive system method according to claim 4, characterized in that, The expression for attitude decoupling in step S5 is as follows: ， The preset time integral filter is designed as follows: ， in, , , Obtained through attitude decoupling Provided by a virtual unmanned helicopter. , , , , , , , and For positive design parameters, , and The preset time constant and satisfying .

6. The fault-tolerant method for unmanned helicopter formation under time-varying topology based on the all-drive system method according to claim 5, characterized in that, In step S5, the attitude inner loop preset time fault-tolerant controller is designed as follows: ， in, , , , These are design parameters, preset time. , Provided by the designed filter, .

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