Multi-UAV tracking control method and system considering disturbances and sensor failures

Abstract

This invention discloses a multi-UAV tracking control method and system considering disturbances and sensor faults, relating to the field of UAV tracking control technology. The method includes: constructing dynamic models for each UAV in a multi-quadrotor UAV system, considering external disturbances and sensor faults; based on the dynamic models, constructing sensor fault parameters characterizing UAV state loss, and modeling unknown time-varying external disturbances in the models as the output of a finite-dimensional linear generator, constructing disturbance parameters characterizing external disturbances; for the inner and outer loop control of the UAV system, introducing the estimation of sensor fault parameters, constructing estimates of synchronization error and velocity error, and designing a virtual controller, a real controller, and their corresponding adaptive laws, fault adaptive laws, and disturbance adaptive laws oriented towards disturbance parameters based on the error estimates; real-time acquisition of state information of each UAV, and using the designed controllers and adaptive laws to achieve tracking control of the multi-quadrotor UAV system.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) tracking and control technology, and in particular to a multi-UAV tracking and control method and system that takes into account disturbances and sensor malfunctions. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the widespread application of quadcopter unmanned aerial vehicles (UAVs) in rescue, detection, surveillance, and military fields, and the development of multi-agent systems, current research is increasingly focusing on the application of multiple UAVs. Compared to a single UAV, multiple UAVs can communicate and collaborate with other UAVs to perform larger and more complex tasks, such as formation flying missions. Among the challenges, the nonlinearity, high coupling, underactuated structure, and uncertainty of multi-UAV dynamic models are currently being studied. Traditional methods such as backstepping, sliding mode control, and PID control are used to minimize the impact of these characteristics. Currently, an adaptive fuzzy control strategy has been proposed. This strategy approximates a continuous nonlinear function with unknown parameters and unknown boundaries in a strictly feedback-switching nonlinear system to address these challenges.

[0004] In practical applications, faults are an unavoidable problem in the control field. Sensor aging and signal processing issues can lead to collisions between UAVs or even cause the entire system to collapse. Currently, two common fault handling methods exist: fault diagnosis technology and fault-tolerant control technology. For example, existing technologies propose observer-based fault detection filters for fault diagnosis, observer-based controllers for systems with actuator faults, and fuzzy adaptive formation control strategies combined with fixed-time controllers to address actuator faults. While the control process involves both actuator and sensor faults, existing technologies often only consider actuator faults. For multiple UAVs, sensor faults can lead to more serious consequences due to information transmission within the topology; therefore, mitigating the impact of unknown sensor faults is crucial.

[0005] Furthermore, the actual operating environment may impose unknown disturbances on the UAV, such as wind disturbances, which can prevent the closed-loop system from achieving the desired stability. To stabilize a quadcopter, existing technologies propose using the traditional PID control method to adjust the speed of the four rotors; however, this method is only applicable to local analysis of nonlinear systems. Building upon the aforementioned PID method, this paper combines PID with fuzzy control methods to simultaneously study attitude stabilization and precise trajectory tracking. For example, based on three-dimensional fuzzy control and traditional PD control methods, corresponding attitude and position controllers are designed to obtain better dynamic responses. However, using the aforementioned linearization methods to handle the strongly nonlinear dynamics of multiple UAVs results in low approximation accuracy, making it difficult to accurately and effectively estimate external disturbances, thus preventing the tracking control of multiple UAVs from achieving the desired stability of the closed-loop system. Summary of the Invention

[0006] To address the shortcomings of the prior art, this invention provides a multi-UAV tracking control method and system that considers disturbances and sensor failures. Through adaptive fault compensation and adaptive fuzzy disturbance suppression, it solves the UAV trajectory tracking problem under the influence of sensor failures and disturbances.

[0007] In a first aspect, the present invention provides a multi-UAV tracking and control method that takes into account disturbances and sensor failures.

[0008] A multi-UAV tracking control method considering disturbances and sensor failures includes:

[0009] For a multi-quadrotor unmanned aerial vehicle (UAV) system, a dynamic model of each UAV is constructed, taking into account external disturbances and sensor failures.

[0010] Based on the dynamic model, sensor fault parameters characterizing the state loss of the UAV are constructed, and the unknown time-varying external disturbances in the model are modeled as the output of a finite-dimensional linear generator to construct disturbance parameters characterizing the external disturbances.

[0011] For the inner and outer loop control of the UAV system, the estimation of sensor fault parameters is introduced, and the estimation of synchronization error and speed error is constructed. Based on the error estimation, a virtual controller, a real controller and their corresponding adaptive laws, fault adaptive laws and disturbance adaptive laws for disturbance parameters are designed.

[0012] The system collects real-time status information of each UAV and uses the designed controller and adaptive law to achieve tracking and control of the multi-quadrotor UAV system.

[0013] Secondly, the present invention provides a multi-UAV tracking and control system that takes into account disturbances and sensor failures.

[0014] A multi-UAV tracking and control system that takes into account disturbances and sensor failures includes:

[0015] The model building module is used to build dynamic models of each UAV for a multi-quadrotor UAV system, taking into account external disturbances and sensor failures.

[0016] The fault and disturbance characterization module is used to construct sensor fault parameters that characterize the state loss of UAVs based on the dynamic model, and to model unknown time-varying external disturbances in the model as the output of a finite-dimensional linear generator to construct disturbance parameters that characterize external disturbances.

[0017] The controller design module is used for the inner and outer loop control of the UAV system. It introduces the estimation of sensor fault parameters, constructs the estimation of synchronization error and speed error, and designs the virtual controller, the actual controller and their corresponding adaptive laws, fault adaptive laws and disturbance adaptive laws for disturbance parameters based on the error estimation.

[0018] The tracking and control module is used to collect the status information of each UAV in real time and realize the tracking and control of the multi-quadrotor UAV system using the designed controller and adaptive law.

[0019] Thirdly, the present invention also provides an electronic device, comprising: a memory for storing executable instructions; and a processor for implementing the above-described multi-UAV tracking control method that takes into account disturbances and sensor failures when executing the executable instructions stored in the memory.

[0020] Fourthly, the present invention also provides a computer-readable storage medium storing executable instructions for causing a processor to execute the executable instructions to implement the above-described multi-UAV tracking control method that takes into account disturbances and sensor failures.

[0021] Fifthly, the present invention also provides a computer program product comprising executable instructions stored in a computer-readable storage medium; wherein, when the processor of an electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, the above-mentioned multi-UAV tracking and control method considering disturbances and sensor failures is implemented.

[0022] The above one or more technical solutions have the following beneficial effects:

[0023] This invention provides a multi-UAV tracking control method and system considering disturbances and sensor failures. It solves the UAV trajectory tracking problem under the influence of sensor failures and disturbances through adaptive fault compensation and adaptive fuzzy disturbance suppression. First, this invention proposes a dynamic estimator for nonlinear multi-UAV systems based on adaptive laws to compensate for fault losses. This estimator is applicable to both the inner and outer loop systems of the UAVs. Compared to traditional methods, this invention reconstructs the ideal state during actuator design and directly compensates for the state loss interval, eliminating the need for observer design. Second, for multi-UAV systems with unknown time-varying disturbances, this invention proposes an adaptive anti-interference strategy. This involves first performing coordinate transformation on the dynamic system to make the system model non-prior, overcoming the system model transformation problem caused by state reconstruction, and then achieving stable UAV trajectory tracking under the influence of disturbances through the adaptive anti-interference strategy.

[0024] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0025] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0026] Figure 1 This is an overall flowchart of the multi-UAV tracking and control method considering disturbances and sensor failures as described in an embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram of a quadcopter drone in an embodiment of the present invention;

[0028] Figure 3 This is the communication topology of the multi-UAV system in this embodiment of the invention;

[0029] Figure 4 This is a schematic diagram of the multi-UAV formation tracking trajectory in an embodiment of the present invention;

[0030] Figure 5 Here are the estimated values ​​of sensor fault parameters in this embodiment of the invention; where (a) is... The trajectory, (b) is The trajectory of i, i = 1, 2, 3, 4.

[0031] Figure 6 In the embodiments of the present invention, x d and q i,11 The trajectory; where (a) represents fault-free compensation and (b) represents fault-compensated compensation, i = 1, 2, 3, 4.

[0032] Figure 7 In the embodiments of the present invention, y d and q i,12 The trajectory; where (a) is without fault compensation; (b) is with fault compensation, i = 1, 2, 3, 4.

[0033] Figure 8 Here are the perturbations and estimates in the x-direction in this embodiment of the invention; where (a) is the trajectory of follower 1, (b) is the trajectory of follower 2, (c) is the trajectory of follower 3, and (d) is the trajectory of follower 4.

[0034] Figure 9 Here are the perturbations and estimates in the y-direction in this embodiment of the invention; where (a) is the trajectory of follower 1, (b) is the trajectory of follower 2, (c) is the trajectory of follower 3, and (d) is the trajectory of follower 4.

[0035] Figure 10 Here are the perturbations and estimates in the z-direction in this embodiment of the invention; where (a) is the trajectory of follower 1, (b) is the trajectory of follower 2, (c) is the trajectory of follower 3, and (d) is the trajectory of follower 4.

[0036] Figure 11 In this embodiment of the invention, x is the control input signal in the x direction; where (a) is the trajectory of follower 1, (b) is the trajectory of follower 2, (c) is the trajectory of follower 3, and (d) is the trajectory of follower 4.

[0037] Figure 12 In this embodiment of the invention, y is the control input signal in the y direction; where (a) is the trajectory of follower 1, (b) is the trajectory of follower 2, (c) is the trajectory of follower 3, and (d) is the trajectory of follower 4.

[0038] Figure 13 The z-direction control input signal is shown in the embodiment of the present invention; where (a) is the trajectory of follower 1, (b) is the trajectory of follower 2, (c) is the trajectory of follower 3, and (d) is the trajectory of follower 4. Detailed Implementation

[0039] It should be noted that the following detailed descriptions are exemplary and are intended only to describe specific embodiments and to provide further explanation of the invention, and are not intended to limit the scope of exemplary embodiments of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0040] Example 1

[0041] This embodiment provides a multi-UAV tracking and control method that considers disturbances and sensor malfunctions, such as Figure 1 As shown, the specific steps include:

[0042] Step S1: For the multi-quadcopter UAV system, construct a dynamic model for each UAV that takes into account external disturbances and sensor failures.

[0043] For a multi-quadcopter unmanned aerial vehicle (UAV) system, to represent the information exchange between each UAV, this embodiment first describes the directed graph of the system. Specifically, consider the directed graph G = (Z, H, P), where... Let Z = (1, ..., n) represent the set of edges, and let Z = (1, ..., n) represent the set of vertices. Let Z be the adjacency matrix. i Z j H represents the path of information from agent i to j; the set of neighbors is defined as E. i ={Z j |(Z j Z i ∈H,i≠j)},a ij >0 indicates that agent i has received information from agent j; otherwise, a ij =0; Let be the in-degree matrix, where It is a Laplace matrix; Represents an augmented graph, in which and definition b i >0 indicates that agent i can directly obtain information from agent j; otherwise, b i =0.

[0044] At this point, let's assume assumption 1: For a leader-follower multi-agent system, there is at least one directed path from the root to all other nodes, in the communication graph. It exists in the form of a spanning tree.

[0045] Secondly, based on the directed graph of the aforementioned multi-UAV system, consider as follows: Figure 2 The quadcopter drone shown is used to construct a nonlinear dynamic model of a multi-quadcopter drone system, which includes a dynamic model of the drone's position system and a dynamic model of the drone's attitude system.

[0046] (1) For the dynamic model of the UAV position system, the reference system is defined by its position as the geocentric structure G. i,E ={O i,e ,x i,e ,y i,e ,z i,e}, where O i,e ,xi,e ,y i,e ,z i,e Let G represent the origin, horizontal, vertical, and longitudinal positions of the i-th UAV in the geocentric coordinate system E, respectively, and let G be the attitude structure defined by its attitude. i,B ={O i,b ,x i,b ,y i,b ,z i,b}, where O i,b ,x i,b ,y i,b ,z i,b These represent the origin, horizontal, vertical, and lateral positions of the i-th UAV in attitude coordinate system B, respectively, as follows: Figure 2 As shown, vector [x] i ,y i ,z i ] T Description in O i,e The horizontal, vertical, and mid-range position vectors, vector [φ] i ,θ i ,ψ i ] T Indicates in O i,b The attitude vectors of roll, pitch, and yaw are represented by the force generated by each horizontal rotor. Given k = 1, 2, 3, 4, the dynamic model of the position system can be described as follows:

[0047]

[0048] Where i = 1, ..., n, m i Let i, x, y, and y represent the mass of the i-th drone. v represents the aerodynamic damping coefficients in three directions. i,x ,v i,y and v i,z Let g be the velocity in three directions, and g be the acceleration due to gravity. Indicates the control thrust, R i The translation matrix can be represented as:

[0049]

[0050] (2) The dynamic model of the UAV attitude system can be expressed as:

[0051]

[0052] Among them, I i,x ,I i,y and I i,z For the moment of inertia, I i,r Let i be the moment of inertia of the horizontal rotor., φ,i , θ and w is the aerodynamic damping coefficient. i It can be represented by the rotational speed of the four horizontal rotors: w i =-r i,1 -r i,2 +r i,3 +r i,4 , where r i,1 ,r i,2 ,r i,3 ,r i,4 This indicates the rotational speed of the four rotors. as well as This indicates the control torque in three directions.

[0053] Furthermore, based on the nonlinear dynamic model of the above position and attitude systems, using the dynamic equation (1), the dynamic position equation of the system can be obtained as follows:

[0054]

[0055] in:

[0056] q i,1 =[q i,11 ,q i,12 ,q i,13 ] T Let q represent the position vector of the system, where q i,11 =x i ,q i,12 =y i ,q i,13 =z i ;

[0057] q i,2 =[q i,21 ,q i,22 ,q i,23 ] T Let q represent the velocity vector of the system, where q i,21 =v i,x ,q i,22 =v i,y ,q i,23 =v i,z ;

[0058] m i Let the mass of the i-th agent be denoted as 'i'. External disturbances y i,1 =[y i,11 ,y i,12 ,y i,13 ] T For output, u iThe input to the unmanned aerial vehicle (UAV) system can be represented as:

[0059]

[0060] Similarly, using dynamic equation (2), the dynamic equation of the attitude system can be obtained as follows:

[0061]

[0062] in:

[0063] p i,1 =[p i,11 ,p i,12 ,p i,13 ] T Let p represent the system's attitude vector, where p i,11 =φ i ,p i,12 =θ i ,p i,13 =ψ i ;

[0064] p i,2 =[p i,21 ,p i,22 ,p i,23 ] T The derivative vector represents the system attitude, where

[0065] I i =diag(1 / I i,x ,1 / I i,y ,1 / I i,z ), External disturbances For output, The input consists of three control torques, h i,2 (p i,2 ) is represented as:

[0066]

[0067] Based on this, the control objective of this embodiment is to achieve tracking control of multiple UAVs with uncertain disturbances and sensor failures, and the following assumptions and lemmas are given:

[0068] Assumption 2: The disturbance and closed-loop system of the drone are bounded.

[0069] Assumption 3: The leader's positional trajectory y L,1 and attitude trajectory p i,d Its second derivative is bounded.

[0070] Assumption 4: Based on Fourier transform, an unknown time-varying external disturbance can be expressed as: The superposition of sinusoidal components can be expressed as: Where a i,n To represent an unknown amplitude, ω i,n ξ represents an unknown frequency. i,n Indicates an unknown phase.

[0071] Lemma 1: Based on FLS (Fuzzy Logic System), for an unknown continuous function f(ξ): ξ∈R h →R can be approximated as:

[0072]

[0073] Where ε(ξ)>0 represents the optimal approximation error. It is a constant. Let s(ξ) represent the ideal weight vector. 1 (ξ),...,s h (ξ)] T Let be a basis function vector, then The optimal value can be expressed as:

[0074]

[0075] Lemma 2: Let the adaptive law be:

[0076] like Then the estimation error Similarly, if Then the estimation error

[0077] Lemma 3: For The inequality is then:

[0078]

[0079] in, For matrix The smallest singular value.

[0080] The following explanations are provided for the above assumptions and lemmas: Assumption 1 states that all followers can directly or indirectly access the leader's output through directed paths, which is a prerequisite for distributed control; Assumption 2 guarantees the boundedness of disturbances because, in real-world physical phenomena, drones are subject to external environmental disturbances during flight, such as changes in wind speed and air density. These disturbances are usually bounded and do not grow indefinitely; Assumption 3 is also based on real-world physical phenomena, stating that the drone's position trajectory and attitude are continuous, ensuring flight stability; In Assumption 4, wind disturbances, oscillations in the disk-torsion system, etc., can be approximated as a superposition of sinusoidal forms based on Fourier transform. In this way, the disturbance can be converted into the output vector of the unknown exogenous system (11). Since the UAV system has nonlinear terms, Lemma 1 introduces the method of approximating nonlinear terms in fuzzy logic system, which aims to eliminate the influence of nonlinear terms. On this basis, the fault adaptive rate can be designed in the form of equations (32) and (65), requiring the adaptive rate estimation error to be positive. Lemma 2 gives a sufficient condition for the adaptive rate estimation error to be positive. Finally, in order to obtain the two tracking error results of equations (56) and (85), Lemma 3 is also introduced, so as to extend the convergence of the synchronization error equation (20) to the tracking error equation (56).

[0081] Step S2: Based on the above assumptions and lemmas, in order to facilitate the subsequent estimation of sensor faults and external disturbances, in this embodiment, sensor fault parameters characterizing the state loss of the UAV are first constructed based on the dynamic model, and the unknown time-varying external disturbances in the model are modeled as the output of a finite-dimensional linear generator to construct disturbance parameters characterizing the external disturbances.

[0082] Based on the dynamic model considering external disturbances and sensor failures constructed in step S1 above, firstly, in step S2.1, for sensor failures, according to the actual position state and expected position state of the UAV after the failure, a sensor failure model is constructed in the UAV position system to obtain sensor failure parameters characterizing the state loss of the UAV.

[0083] Specifically, when a fault occurs, the actual state of the i-th UAV is inconsistent with the expected state, exhibiting a certain degree of state loss. The sensor fault in the position system can then be represented as:

[0084]

[0085] in, and λ represents the actual state after the fault. i,1 =diag(λ i,11 ,λ i,12 ,λ i,13 ) and λ i,2 =diag(λ i,21,λ i,22 ,λ i,23 ) is a diagonal matrix, and the parameters of this matrix are the sensor fault parameters that characterize the state loss of the UAV.

[0086] Similarly, sensor faults in an attitude system can be represented as:

[0087]

[0088] in, and μ represents the actual state after the fault. i,1 =diag(μ i,11 ,μ i,12 ,μ i,13 ) and μ i,2 =diag(μ i,21 ,μ i,22 ,μ i,23 Let be a diagonal matrix, and its parameters are the sensor fault parameters characterizing the state loss of the UAV. The i-th UAV in In case of a fault,

[0089] when There is λ i,11 ,λ i,12 ,...,λ i,23 ,μ i,11 ,μ i,12 ,...,μ i,23 =1;

[0090] when have

[0091] in, and It is a positive number.

[0092] Step S2.2: Model the unknown time-varying external disturbance in the model as the output of a finite-dimensional linear generator, and construct disturbance parameters characterizing the external disturbance by combining the Sylvester equation.

[0093] Specifically, to facilitate the estimation of unknown disturbances, equation (3) is transformed into:

[0094]

[0095] in, With κ i It is a vector containing unknown parameters, i = [i1, i2, i3]. T =[-i,x / m i ,-i,y / m i ,-i,z / m i ] Tκ i =[κ i1 ,κ i2 ,κ i1 ] T =[1 / m i λ i,21 ,1 / m i λ i,22 ,1 / m i λ i,23 ] T , with U i (u i ) is a diagonal matrix, which can be represented as:

[0096]

[0097] External disturbances It can be viewed as the output of a finite-dimensional linear generator, and can be expressed as:

[0098]

[0099] in, It is a state variable. and Unknown constant coefficient matrix; (W) i N i ) is observable, and W i The eigenvalues ​​lie on the imaginary axis to ensure that the system (11) remains in a critically stable state, which makes the external disturbance Δ i It can be represented in sine form.

[0100] To further simplify the characterization of the aforementioned external disturbances, a Sylvester equation is defined as follows:

[0101] F i W i -S i F i =T i N i (12)

[0102] In the above formula, This is the solution we want to obtain. It is a Herwitz matrix whose eigenvalues ​​lie in the left half-plane. It is a constant matrix. Where, if F i W i ,S i And T i N i If they are matrices of the same size, then F i The necessary and sufficient condition for this equation to have a unique solution is W. i With S iThey do not share common eigenvalues.

[0103] At the same time, define a new vector σ i =F i G i Differentiating both sides and substituting them into equation (11), we get Combining this with Sylvester's equation (12), equation (11) is transformed into a special canonical form as follows:

[0104]

[0105] By introducing the Sylvester equation as described above, equation (11) can be transformed into a special gauge form, which facilitates the subsequent simplification of the characterization of external disturbances.

[0106] In the special canonical form obtained from the above transformation, the second equation characterizes the external disturbance. Due to σ i It is unknown, therefore it is necessary to estimate the vector σ. i The value of the external disturbance is thus obtained, which can be expressed as:

[0107]

[0108] in, and Let the state variables of the filter satisfy:

[0109]

[0110] To determine whether the design of equation (14) is reasonable, substitute equations (14) to (17) into equation (13) to obtain the following Herwitz stability matrix:

[0111]

[0112] The above results indicate that, due to S i It is a Herwitz matrix, and the estimation error is... It is asymptotically stable, therefore, substituting equation (14) into (13) to replace the external disturbance, it can be expressed as:

[0113]

[0114] In the above formula, The decay exponent, It is a perturbation matrix containing unknown parameters. The vector in has been solved in (15)-(17), let but:

[0115]

[0116] Based on the above equation (19), the external disturbance can be converted into an unknown parameter ρ. i This parameter is used as a disturbance parameter to characterize external disturbances. In this way, the disturbance suppression problem can be transformed into an adaptive control problem, which facilitates the subsequent adaptive control design.

[0117] Step S3: For the inner and outer loop control of the UAV system, the estimation of sensor fault parameters is introduced, and the estimation of synchronization error and speed error is constructed. Based on the error estimation, the virtual controller, the actual controller and their corresponding adaptive laws, fault adaptive laws and disturbance adaptive laws for disturbance parameters are designed.

[0118] In this embodiment, an adaptive fuzzy tracking control strategy based on adaptive fault compensation technology is used to achieve the tracking task of multiple UAVs under conditions of disturbance and sensor failure. The inner and outer loop control of the UAV system correspond to the attitude control and position control of the UAV system, respectively. Corresponding controllers and adaptive laws are designed for the inner and outer loop control to control the UAV system.

[0119] (1) For outer-loop control, i.e., position control of the UAV system:

[0120] First, the synchronization error and velocity error are constructed, including:

[0121] (1.1) Based on the relative positions among followers and the relative positions between followers and the leader, the synchronization error is constructed as follows:

[0122]

[0123] in, Let represent the relative positions between the i-th and j-th drones in three-dimensional space. Let b be the relative position between the i-th drone and the leader in three-dimensional space. i ≥0 is a fixed gain. Indicates the position of a leader.

[0124] (1.2) The velocity error is constructed as follows:

[0125]

[0126] Where, ζ i,1 It is a virtual controller.

[0127] Furthermore, since the system contains unknown fault parameters, and therefore the synchronization error and speed error are also unknown, this embodiment introduces sensor fault parameters into the synchronization error and speed error to estimate them. The estimate, and satisfy in This is for estimating the error.

[0128] The synchronization error is then estimated as follows:

[0129]

[0130] The speed error is estimated as follows:

[0131]

[0132] According to (20)-(23), we have:

[0133]

[0134] Based on this, and considering the synchronization error, combined with the nonlinear dynamic model of the position system, according to (3), (20), and (21), Z is obtained. i,1 The time derivative can be expressed as:

[0135]

[0136] in, Ideal weight vector Best approximation error The basis function matrix is ​​represented as:

[0137]

[0138] Based on Lyapunov stability theory, the Lyapunov function is defined as:

[0139]

[0140] Where, η i,1k It is a positive real number. It is a positively defined matrix; It is the estimation error of the ideal weight vector and satisfies This is an estimate of the ideal weight vector. The Lyapunov function is set for the synchronization error and includes the synchronization error Z. i,1 .

[0141] To verify stability, the Lyapunov function V was tested. i,1 Differentiating, we have:

[0142]

[0143] The derivative of the Lyapunov function mentioned above (27) includes The problem consists of three parts, each of which needs to be solved separately, including:

[0144] For the first part, design a virtual controller. for:

[0145]

[0146] Among them, C i,1 It is a normal number.

[0147] Combine (24) and substitute the virtual controller into (25), The following formula can be derived:

[0148]

[0149] According to Young's inequality, we can further obtain:

[0150]

[0151] Based on (29) and (30), we can conclude that:

[0152]

[0153] For the second part, the fault adaptive law is designed as follows:

[0154]

[0155] in:

[0156]

[0157] And τ i,1k It is a normal number.

[0158] According to Young's inequality and Lemma 2, we can conclude that:

[0159]

[0160] From (32) and (33), we can conclude that:

[0161]

[0162] For the third part, design an adaptive law. for:

[0163]

[0164] Where, m i,1k It is a normal number.

[0165] According to (35), we can conclude that:

[0166]

[0167] Substituting (31), (34), and (36) into (27), we obtain the following time derivative inequality:

[0168]

[0169] Furthermore, in the backstepping method, the number of Lyapunov functions is the same as the order of the system. In this embodiment, the order of the dynamic position equation of the system, i.e., equation (3), is 2. Therefore, two Lyapunov functions are defined here. Specifically, for the velocity error, according to (1), (19), and (21), the first derivative of the velocity error can be expressed as:

[0170]

[0171] in, Ideal weight vector Best approximation error The basis function matrix is ​​represented as:

[0172]

[0173] Since the first derivative of the velocity error (38) uses the nonlinear term of the fuzzy logic system estimation, and the nonlinear term includes the time derivative of the virtual controller, it is necessary to express the time derivative of the virtual controller, that is, to express the time derivative of the virtual controller. Taking the time derivative, we get:

[0174]

[0175] Based on Lyapunov stability theory, the Lyapunov function is defined as:

[0176]

[0177] Where, η i,2k It is a positive constant. and All are positively defined matrices; It is the estimation error of the ideal weight vector and satisfies This is an estimate of the ideal weight vector. The Lyapunov function is set for the velocity error and includes the velocity error Z. i,2 .

[0178] To verify stability, the Lyapunov function V was tested. i,2 Taking the first derivative, we get:

[0179]

[0180] The derivative of the Lyapunov function (41) includes The problem has four parts, and each part needs to be solved separately, including:

[0181] For the first part, design the actual controller u. i for:

[0182]

[0183] Among them, C i,2 It is a positive control constant.

[0184] Based on (24), and substituting the control law into (41), The following formula can be derived:

[0185]

[0186] According to Young's inequality, we can further calculate:

[0187]

[0188] Substituting (44) into (43) yields:

[0189]

[0190] For the second part, design a fault adaptive law. for:

[0191]

[0192] in, And τ i,2k It is a positive constant. Based on (46), we have:

[0193]

[0194] For the third part, design an adaptive law. for:

[0195]

[0196] Where, m i,2k It is a normal number that can be designed.

[0197] According to (48), it can be calculated that:

[0198]

[0199] For Part 4, design an adaptive law for the perturbation. for:

[0200]

[0201] Where, mi,3k It is a normal number.

[0202] The external disturbance determined according to step S2 above is given by equation (19), where the unknown matrix ρ i As a parameter representation of external disturbances, the aforementioned disturbance adaptive law is designed based on the adaptive control method. Used to estimate the unknown matrix ρ i This allows us to obtain an estimate of the external disturbance.

[0203] According to (50), we can obtain:

[0204]

[0205] From (37), (41), (45), (47), (49), and (51), the following time derivative inequality can be obtained:

[0206]

[0207] in:

[0208]

[0209] Furthermore, Theorem 1 is given here: Under assumptions 1-4, considering the position dynamic equation (3) of the UAV with unknown sensor faults and disturbances, a virtual controller (28), an actual controller (42), and adaptive laws (32), (35), (46), (48), and (50) are designed to ensure the following control objectives are achieved:

[0210] All signals in a closed-loop system are bounded;

[0211] The consistent tracking error between leaders and followers is semi-globally consistent and eventually bounded.

[0212] Furthermore, based on the semi-globally consistent eventually bounded correlation theory, if the above Lyapunov function V is positive definite, and in and If the function is bounded, it can be proven that the Lyapunov function is convergent, meaning that the synchronization error, velocity error, and adaptive estimation error are convergent. Specifically, based on the stability analysis results of Lyapunov stability theory, the calculation methods for the controller and control law are proven. Consider the following Lyapunov function:

[0213]

[0214] According to (53), we can conclude that:

[0215]

[0216] in, i = 1, 2, ..., n, k = 1, 2, 3,

[0217] Then, by integrating both sides of (54) over [0,t], we can obtain the following relation:

[0218]

[0219] From (55), we can see that signal Z i,1 Z i,2 , It is uniform and ultimately bounded, which means and It is bounded; based on a virtual controller. and the actual controller u i The fact that it is bounded, according to (53), Furthermore, according to Lemma 3, for By selecting a sufficiently large design parameter C i,1 C i,2 ,m i,1k ,m i,2k ,m i,3k ,τ i,1k ,τ i,2k We can obtain:

[0220] ||yy L ||≤∈. (56)

[0221] This means that the follower trajectory tracking error converges to a small neighborhood of the origin, and the proof is complete. It should be noted that the design parameters in (54) need to be large enough so that the error coefficient remains negative. Excessively increasing the error coefficient will lead to an increase in control energy, thereby deteriorating the tracking performance.

[0222] (2) For inner-loop control, i.e. attitude control of the UAV system:

[0223] Similar to the outer-loop control described above, in order to estimate the synchronization error and angular velocity error, estimated values ​​of sensor fault parameters are introduced into the synchronization error and velocity error. and satisfy in To estimate the error, the synchronization error can be rewritten as follows:

[0224]

[0225] in, and p represents the synchronization error and acceleration error estimates. i,d It indicates the leader's stance. It is a virtual controller.

[0226] For synchronization error The derivative can be expressed as:

[0227]

[0228] Define the Lyapunov candidate function as:

[0229]

[0230] Where, π i,1k If >0 is a positive constant to be determined, then the Lyapunov function... The time derivative can be expressed as:

[0231]

[0232] The derivative of the Lyapunov function (60) includes The problem has two parts, and each part needs to be solved separately, including:

[0233] For the first part, define the virtual controller. for:

[0234]

[0235] in, It is a normal number.

[0236] Combining equations (58) and (61), the following equation holds for synchronization error:

[0237]

[0238] According to Young's inequality, we can further obtain:

[0239]

[0240] but (62) can be rewritten as:

[0241]

[0242] For the second part, design a fault adaptive law. for:

[0243]

[0244] In the above formula, Among them, ι i,1k For the positive constants to be designed.

[0245] Based on equation (65), the following formula can be further derived:

[0246]

[0247] Substituting equations (64) and (66) into equation (60), then The time derivative can be expressed as:

[0248]

[0249] For angular velocity errors, FLS (fuzzy logic system) is used to approximate unknown parameters, including:

[0250]

[0251] in, Ideal weight vector Optimal approximation error The basis function matrix can be represented as:

[0252]

[0253] but The time derivative can be expressed as:

[0254]

[0255] Define the Lyapunov candidate function as:

[0256]

[0257] Where, π i,2k >0 is a positive integer. This is a positively defined matrix.

[0258] Differentiating the Lyapunov function above, we get:

[0259]

[0260] The derivative of the Lyapunov function (72) includes The problem consists of three parts, each of which needs to be solved separately, including:

[0261] For the first part, design the control law. for:

[0262]

[0263] in, It is a positive control constant.

[0264] According to equations (68) and (73), we can calculate:

[0265]

[0266] According to Young's inequality, the following inequalities hold:

[0267]

[0268] Combining equations (74) and (75), the following equation holds:

[0269]

[0270] For the second part, design a fault adaptive law. for:

[0271]

[0272] In the above formula, Among them, ι i,2k It is a positive number.

[0273] Based on (77), the following formula can be further derived:

[0274]

[0275] For the third part, design an adaptive law. for:

[0276]

[0277] Where, m i,4k It is a normal number.

[0278] Then we have:

[0279]

[0280] From equations (67), (71), (76), (78), and (80), the time derivative inequality can be obtained as follows:

[0281]

[0282] in,

[0283] Theorem 2 is given here: Considering the attitude dynamics equation (4) of a UAV with unknown sensor failure under assumptions 1-3, a virtual controller (62), an actual controller (73), and adaptive laws (66), (77), and (79) are designed to ensure the following control objectives:

[0284] All signals in a closed-loop system are bounded;

[0285] The consensus tracking error between leaders and followers is a semi-global consensus that is eventually bounded.

[0286] Furthermore, similarly, the above method is proven based on stability analysis results from Lyapunov stability theory. Consider the following Lyapunov function:

[0287]

[0288] According to equation (82), we have:

[0289]

[0290] in, For i = 1, 2, ..., n and k = 1, 2, 3,

[0291] Then, integrating both sides of equation (83) over [0,t], we obtain the following relation:

[0292]

[0293] From equation (84), it can be seen that signal Z i,1 , It is uniformly bounded, which means that... and It is bounded; based on a virtual controller. and actual controller It is bounded, starting from (82), with restrictions. Furthermore, according to Lemma 3, when At that time, by design parameters ι i,1k ,ι i,2k ,m i,4k By selecting a sufficiently large value, we can obtain:

[0294]

[0295] in, Equation (85) shows that the tracking error of the tracker converges to a small neighborhood of the origin, thus completing the proof. In addition, it should be noted that the design parameters in Equation (81) need to be large enough to keep the error coefficient negative. An excessively large error coefficient will lead to an increase in control energy and a deterioration in tracking performance.

[0296] Step S4: Collect the status information of each UAV in real time, and use the designed controller and adaptive law to realize the tracking control of the multi-quadrotor UAV system.

[0297] Preferably, the effectiveness of the method proposed in this embodiment is verified through the following UAV simulation examples. For example... Figure 3As shown, any one drone is selected as the leader, and four drones are selected as followers. The edges of the directed topology represent the information transmission between the leader and followers. Furthermore, the adjacency matrix P is defined as:

[0298]

[0299] Based on the above definition, the following execution... Figure 4 The multi-drone formation tracking trajectory shown below uses the following reference trajectory selection:

[0300]

[0301] To complete the tracking task, the design parameters are determined as follows:

[0302] C i,1 =18,C i,2 =18, τ 1,11 =11880,τ 2,11 =2055,τ 3,11 =10130,τ 4,11 =6521,τ i,21 =10000,τ 1,12 =3530,τ 2,12 =876,τ 3,12 =3570,τ 4,12 =3506,τ i,22 =10000,τ i,13 =30000,τ i,23 =20000,ι i,1k =ι i,2k =20000,m i,1k =20,m i,2k =10,m i,31 =2,m i,32 =3.2,m i,33 =3,m i,4k =10,η i,1k =η i,2k =0.01,π i,1k =π i,2k =0.01,Γ i,1k =Γ i,2k =0.001×I 5×5 N i,2k =0.001×I 5×5 ,Λ i1 =0.003×I 12×12 ,Λ i2 =0.008×I 12×12 ,Λ i3 =10×I 12×12 ,S i=-0.01×I 3×3 ,T i =10×I 3×3 i = 1, 2, 3, 4, k = 1, 2, 3.

[0303] The initial conditions are set as follows:

[0304] q 1,11 (0) = -0.5, q 2,11 (0) = -1.5, q 3,11 (0)=-1,q 4,11 (0)=-2,q i,21 (0)=0,q i,12 (0)=q i,22 (0)=0,q i,13 (0)=0,q i,23 (0)=0.1,p i,1k (0)=p i,2k (0) = 0, α i (0)=0 3×1 ,β ik (0)=0 3×1 ,γ ik (0)=0 3×1 , i = 1, 2, 3, 4, k = 1, 2, 3.

[0305] External disturbances can be represented as:

[0306]

[0307] when At that time, λ i,12 =1.2; when At that time, λ i,11 =1.2; the fault parameters of other sensors become 1.

[0308] The position trajectory tracking and reference signals of the four follower drones are as follows: Figure 4 As shown, the trajectory of the sensor fault parameters is as follows: Figure 5 As shown, from Figure 5 It can be seen that the adaptive parameters and The system converges rapidly to 1.2 after the fault occurs. The simulation results of the position system are as follows: Figure 6 and Figure 7 As shown, by Figure 6 (a) It can be seen that the fault caused the x-direction tracking task to be impaired, resulting in a collision; after handling the fault, from Figure 6 (b) It can be seen that the tracking curve has recovered to the specified tracking state. Figure 7This describes the tracking situation in the y-direction. Within 3 seconds of the fault occurring, the status curve showed a significant shift. After the fault was resolved, the tracking error gradually converged again. Figure 8 (a)-(d) Figure 9 (a)-(d) Figure 10 Figures (a)-(d) show the reliability of the disturbance tracking scheme. It is worth noting that although sensor failure affected the tracking performance of the disturbance, the tracking error quickly reached asymptotic stability. Figure 11 (a)-(d) Figure 12 (a)-(d) and Figure 13 In the diagram (a)-(d), the input signals of the four slaves are shown in three different directions. At the moment of the fault, the input curve shows a certain degree of abrupt change, but after the fault is handled, the input curve returns to a stable state.

[0309] Using the methods described above, the influence of unknown disturbances is eliminated through disturbance suppression, and an adaptive law is designed to estimate the fault parameters of the UAV system with uncertain disturbances and sensor failures. Based on this, stability analysis proves that the tracking error is bounded. Finally, simulation results demonstrate that the control strategy proposed in this embodiment can guarantee the tracking task under unknown disturbances. Simultaneously, the comparison results of fault handling also prove the effectiveness of the proposed method. The UAV's position trajectory also demonstrates that the algorithm can effectively achieve leader-following tracking tasks.

[0310] Example 2

[0311] This embodiment provides a multi-UAV tracking and control system that considers disturbances and sensor malfunctions, including:

[0312] The model building module is used to build dynamic models of each UAV for a multi-quadrotor UAV system, taking into account external disturbances and sensor failures.

[0313] The fault and disturbance characterization module is used to construct sensor fault parameters that characterize the state loss of UAVs based on the dynamic model, and to model unknown time-varying external disturbances in the model as the output of a finite-dimensional linear generator to construct disturbance parameters that characterize external disturbances.

[0314] The controller design module is used for the inner and outer loop control of the UAV system. It introduces the estimation of sensor fault parameters, constructs the estimation of synchronization error and speed error, and designs the virtual controller, the actual controller and their corresponding adaptive laws, fault adaptive laws and disturbance adaptive laws for disturbance parameters based on the error estimation.

[0315] The tracking and control module is used to collect the status information of each UAV in real time and realize the tracking and control of the multi-quadrotor UAV system using the designed controller and adaptive law.

[0316] Example 3

[0317] This embodiment provides an electronic device, including: a memory for storing executable instructions; and a processor for executing the executable instructions stored in the memory to implement the method provided in this embodiment.

[0318] Example 4

[0319] This embodiment also provides a computer-readable storage medium storing executable instructions, which, when executed by a processor, will cause the processor to execute the method described above in this embodiment.

[0320] Example 5

[0321] This embodiment provides a computer program product including executable instructions, which are computer instructions; the executable instructions are stored in a computer-readable storage medium. When the processor of an electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, the electronic device performs the method described in this embodiment.

[0322] The steps and methods involved in Embodiments 2 to 5 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0323] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0324] The above description is only a preferred embodiment of the present invention. Although the specific implementation of the present invention has been described in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative effort are still within the scope of protection of the present invention.

Claims

1. A multi-UAV tracking control method considering disturbances and sensor failures, characterized in that, include: For a multi-quadrotor unmanned aerial vehicle (UAV) system, a dynamic model of each UAV is constructed, taking into account external disturbances and sensor failures. Based on the dynamic model, sensor fault parameters characterizing the state loss of the UAV are constructed, and the unknown time-varying external disturbances in the model are modeled as the output of a finite-dimensional linear generator to construct disturbance parameters characterizing the external disturbances. Based on the actual and expected position of the UAV after the malfunction, a sensor malfunction model is constructed in the UAV positioning system, represented as follows: ； In the formula, and This represents the actual state after the fault. as well as It is a diagonal matrix, and the parameters of this matrix are sensor fault parameters that characterize the state loss of the UAV; Based on the actual and desired attitude states of the UAV after a malfunction, a sensor malfunction model is constructed in the UAV attitude system, represented as follows: ； in, and This represents the actual state after the fault. as well as It is a diagonal matrix, and the parameters of this matrix are the sensor fault parameters that characterize the state loss of the UAV; No. A drone in In case of a fault, when have ; when have ; in, and It is a positive number; For the inner and outer loop control of the UAV system, the estimation of sensor fault parameters is introduced, and the estimation of synchronization error and speed error is constructed. Based on the error estimation, a virtual controller, a real controller and their corresponding adaptive laws, fault adaptive laws and disturbance adaptive laws for disturbance parameters are designed. The inner and outer loop control of the UAV system corresponds to the attitude control and position control of the UAV system, respectively; among them, for the position control of the UAV system, the virtual controller is designed as follows: ； in, It is a positive constant; The fault adaptive law for virtual controllers is designed as follows: ； in, , It is a positive constant; The adaptive law for virtual controllers is designed as follows: ； in, It is a positive constant; The actual controller is designed as follows: ； in, It is a positive control constant; The fault adaptive law designed for practical controllers is as follows: ； in, ,and It is a positive constant; The adaptive law designed for practical controllers is as follows: ； in, It is a positive constant that can be designed; The disturbance adaptive law designed for practical controllers is as follows: ； in, It is a positive constant; For attitude control of the unmanned aerial vehicle (UAV) system, a virtual controller is designed as follows: ； in, It is a positive constant; The fault adaptive law for virtual controllers is designed as follows: in, , For the positive constants to be designed; The actual controller is designed as follows: in, It is a positive control constant; The fault adaptive law designed for practical controllers is as follows: in, , It is a positive number; The adaptive law designed for practical controllers is as follows: in, It is a positive constant; The system collects real-time status information of each UAV and uses the designed controller and adaptive law to achieve tracking and control of the multi-quadrotor UAV system.

2. The multi-UAV tracking and control method considering disturbances and sensor failures as described in claim 1, characterized in that, The dynamic model of the UAV includes the dynamic model of the UAV position system and the dynamic model of the UAV attitude system; The dynamic model of the UAV position system is as follows: ； In the formula, , They represent the first i The position of the UAV in the geocentric coordinate system E, including its origin, horizontal, vertical, and longitudinal coordinates. Indicates the first The quality of the drone , The aerodynamic damping coefficient is... , For velocities in three directions, It is the acceleration due to gravity. Indicates control of thrust, The translation matrix is ​​represented as: ； Where, vector Indicates in The attitude vectors of roll, pitch, and yaw are represented by the force generated by each horizontal rotor. ,and ; The dynamic model of the UAV attitude system is as follows: ； In the formula, , For rotational inertia, Let be the moment of inertia of the horizontal rotor. , The aerodynamic damping coefficient is... It is represented by the rotational speed of the four horizontal rotors: , , This represents three control torques.

3. The multi-UAV tracking and control method considering disturbances and sensor failures as described in claim 1, characterized in that, Design a virtual controller, a real controller, and their corresponding adaptive laws, fault adaptive laws, and disturbance adaptive laws oriented towards disturbance parameters to satisfy the control objective: All signals in a closed-loop system are bounded; The consistent tracking error between the leader and follower drones is a cooperative semi-global uniform end boundary.

4. A multi-UAV tracking and control system that considers disturbances and sensor failures, characterized in that, The multi-UAV tracking and control method considering disturbances and sensor failures as described in any one of claims 1-3 includes: The model building module is used to build dynamic models of each UAV for a multi-quadrotor UAV system, taking into account external disturbances and sensor failures. The fault and disturbance characterization module is used to construct sensor fault parameters that characterize the state loss of UAVs based on the dynamic model, and to model unknown time-varying external disturbances in the model as the output of a finite-dimensional linear generator to construct disturbance parameters that characterize external disturbances. The controller design module is used for the inner and outer loop control of the UAV system. It introduces the estimation of sensor fault parameters, constructs the estimation of synchronization error and speed error, and designs the virtual controller, the actual controller and their corresponding adaptive laws, fault adaptive laws and disturbance adaptive laws for disturbance parameters based on the error estimation. The tracking and control module is used to collect the status information of each UAV in real time and realize the tracking and control of the multi-quadrotor UAV system using the designed controller and adaptive law.

5. An electronic device, characterized in that, include: Memory, used to store executable instructions; The processor, when executing executable instructions stored in the memory, implements the multi-UAV tracking control method considering disturbances and sensor failures as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The system stores executable instructions that, when executed by a processor, implement the multi-UAV tracking and control method according to any one of claims 1-3, taking into account disturbances and sensor failures.

7. A computer program product, characterized in that, The computer program product includes executable instructions stored in a computer-readable storage medium; When the processor of the electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, it implements the multi-UAV tracking and control method considering disturbances and sensor failures as described in any one of claims 1-3.

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