Multi-unmanned aerial vehicle tracking control method and system considering disturbance and sensor faults

Abstract

The invention discloses a multi-unmanned aerial vehicle tracking control method and system considering disturbance and sensor faults, and relates to the technical field of unmanned aerial vehicle tracking control, and the method comprises the steps: constructing a kinetic model of each unmanned aerial vehicle considering external disturbance and sensor faults for a multi-quadrotor unmanned aerial vehicle system; based on the kinetic model, constructing sensor fault parameters representing the state loss of the unmanned aerial vehicle, modeling unknown time-varying external disturbance in the model as output of a finite-dimensional linear generator, and constructing disturbance parameters representing the external disturbance; for inner and outer ring control of an unmanned aerial vehicle system, estimation of sensor fault parameters is introduced, estimation of synchronization errors and speed errors is constructed, and a virtual controller, an actual controller and corresponding adaptive laws, fault adaptive laws and disturbance adaptive laws facing disturbance parameters are designed according to error estimation; state information of each unmanned aerial vehicle is collected in real time, and tracking control of the multi-quad-rotor unmanned aerial vehicle system is realized by using a designed controller and an adaptive law.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) tracking control, and in particular to a multi-UAV tracking control method and system taking disturbances and sensor failures into consideration. Background Art

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

[0003] With the widespread application of quadrotor unmanned aerial vehicles (UAVs) in rescue, detection, surveillance, and military applications, as well as 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 each other to perform larger and more complex tasks, such as formation flying. Among these challenges, the nonlinearity, high coupling, underactuated structure, and uncertainty of multi-UAV dynamic models are currently challenging. Traditionally, backstepping, sliding mode control, and PID control have been used to minimize the impact of these characteristics. Adaptive fuzzy control strategies have also been proposed to address these challenges by approximating continuous nonlinear functions with unknown parameters and unknown boundaries in strict feedback switching nonlinear systems.

[0004] In practical applications, failure is an inevitable problem in the control field. Sensor aging and signal processing problems may cause collisions between drones or even cause the entire system to crash. Currently, there are two commonly used fault handling methods, namely fault diagnosis technology and fault-tolerant control technology. For example, the existing technology proposes an observer-based fault detection filter for fault diagnosis, an observer-based controller for systems with actuator failures, and a fuzzy adaptive formation control strategy and a fixed-time controller combined with the above-mentioned adaptive fuzzy control strategy to address actuator failures. Among them, the control process involves actuator failures and sensor failures, but the existing technology mostly only considers actuator failures. For multiple drones, sensor failures may lead to more serious consequences due to information transmission in the topology. Therefore, mitigating the impact of unknown sensor failures is crucial.

[0005] In addition, the actual operating environment may also impose unknown interference on the drone, such as wind disturbance, which prevents the closed-loop system from achieving the desired stability. In order to stabilize the quadrotor, the existing technology proposes to use the traditional PID method to adjust the speed of the four rotors, but it is only applicable to the local analysis of nonlinear systems. Based on the above PID method, PID is combined with fuzzy control methods to study the attitude stability problem and accurate trajectory tracking problem at the same time. For example, based on the three-dimensional fuzzy control method and the traditional PD control method, the corresponding attitude controller and position controller are designed respectively to obtain better dynamic response. However, the above linearization method is used to deal with the strong nonlinear dynamics in multiple drones. Its approximation accuracy is low, and it is difficult to accurately and effectively estimate external disturbances, resulting in the tracking control of multiple drones unable to achieve the desired stability of the closed-loop system. Summary of the Invention

[0006] To address the deficiencies of the above-mentioned prior art, the present invention provides a multi-UAV tracking control method and system that takes disturbances and sensor failures into consideration. By using adaptive fault compensation and adaptive fuzzy disturbance suppression, the problem of UAV trajectory tracking under the influence of sensor failures and disturbances is solved.

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

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

[0009] For a multi-quadrotor UAV system, a dynamic model of each UAV is constructed that takes into account external disturbances and sensor failures;

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

[0011] For the inner and outer loop control of UAV systems, we introduce the estimation of sensor fault parameters, construct the estimation of synchronization error and speed error, and design the virtual controller, actual controller and its corresponding adaptive law, fault adaptive law, and disturbance adaptive law for disturbance parameters based on the error estimation.

[0012] The status information of each UAV is collected in real time, and the designed controller and adaptive law are used to achieve tracking control of the multi-quadrotor UAV system.

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

[0014] A multi-UAV tracking control system considering disturbances and sensor failures includes:

[0015] A model building module is used to build a dynamic model of each drone in a multi-quadrotor drone 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 UAV's state loss based on the dynamic model, and to model the unknown time-varying external disturbance in the model as the output of a finite-dimensional linear generator to construct disturbance parameters that characterize the external disturbance;

[0017] The controller design module is used to estimate sensor fault parameters for the inner and outer loop control of the UAV system, construct estimates of synchronization error and speed error, and design virtual controllers, actual controllers, and their corresponding adaptive laws, fault adaptive laws, and disturbance adaptive laws for disturbance parameters based on the error estimates.

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

[0019] In a third aspect, the present invention also provides an electronic device comprising: a memory for storing executable instructions; and a processor for implementing the above-mentioned multi-UAV tracking control method considering disturbances and sensor failures when executing the executable instructions stored in the memory.

[0020] In a fourth aspect, 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-mentioned multi-UAV tracking control method considering disturbances and sensor failures.

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

[0022] One or more of the above technical solutions have the following beneficial effects:

[0023] The present 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, the problem of UAV trajectory tracking under the influence of sensor failures and disturbances is solved. The present invention first proposes a dynamic estimator for a nonlinear multi-UAV system based on an adaptive law to compensate for loss failures. This estimator is applicable to both the inner and outer loop systems of UAVs. Compared with traditional methods, the present invention reconstructs the ideal state during the actuator design process and directly compensates for the state loss interval, eliminating the need to design an observer. Secondly, for multi-UAV systems with unknown time-varying disturbances, the present invention proposes an adaptive anti-interference strategy. This strategy first performs a coordinate transformation on the power system to make the system model non-a priori, overcoming the system model conversion problem caused by state reconstruction. Finally, an adaptive anti-interference strategy is used to achieve stable tracking of UAV trajectories under the influence of disturbances.

[0024] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0026] Figure 1 This is an overall flow chart of the multi-UAV tracking control method considering disturbances and sensor failures according to an embodiment of the present invention;

[0027] Figure 2 Schematic diagram of a quadrotor drone according to an embodiment of the present invention;

[0028] Figure 3 The communication topology of the multi-UAV system in an embodiment of the present invention;

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

[0030] Figure 5 is the estimated value of the sensor fault parameter in the embodiment of the present invention; where (a) is The trajectory of (b) is , i=1,2,3,4.

[0031] Figure 6 In the embodiment of the present invention, x d and q i,11 trajectories; (a) is compensation without fault, (b) is compensation with fault, i=1,2,3,4.

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

[0033] Figure 8 are the disturbance and estimation in the x direction in the embodiment of the present invention; wherein (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 is the disturbance and estimation in the y direction in the embodiment of the present invention; wherein (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 The disturbance and estimation in the z direction in the embodiment of the present invention are shown in FIG. 1 , 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 is the control input signal in the x direction in the embodiment of the present invention; wherein (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 is the control input signal in the y direction in the embodiment of the present invention; wherein (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 is the control input signal in the z direction in the embodiment of the present invention; wherein (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 DESCRIPTION

[0039] It should be noted that the following detailed descriptions are exemplary only and are intended to describe specific embodiments and provide further explanation of the present invention, and are not intended to limit the exemplary embodiments according to the present invention. Unless otherwise indicated, all technical and scientific terms used herein have the same meanings as those commonly understood by those of ordinary skill in the art to which the present invention belongs. In addition, it should be understood that when the terms "comprise" and / or "include" 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 control method considering disturbances and sensor failures. Figure 1 As shown, the specific steps include:

[0042] Step S1: For a multi-quadrotor UAV system, a dynamic model of each UAV is constructed taking into account external disturbances and sensor failures.

[0043] For a multi-quadcopter drone system, in order to represent the information exchange between each drone, this embodiment first describes the directed graph of the system. Specifically, consider the directed graph G = (Z, H, P), where represents the set of edges, Z=(1,…,n) represents the set of points, is the adjacency matrix, (Z i ,Z j )∈H represents the path of agent information from i to j; the set of neighbors is defined as E i ={Z j ∣(Z j ,Z i ∈H,i≠j)}, a ij >0 means agent i receives information from agent j, otherwise a ij =0; is the in-degree matrix, where is the Laplace matrix; represents the augmented graph, where and definition b i > 0 means agent i can directly obtain information from agent j, otherwise b i =0.

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

[0045] Secondly, based on the directed graph of the multi-UAV system mentioned above, consider Figure 2 The quadrotor UAV shown in the figure constructs a nonlinear dynamic model of a multi-quadrotor UAV system, which includes a dynamic model of the UAV position system and a dynamic model of the UAV 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 They represent the origin, horizontal, vertical and vertical positions of the i-th UAV in the geocentric coordinate system E, and its posture is defined as the posture structure G 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 Respectively represent the origin, horizontal, vertical and vertical positions of the i-th UAV in the attitude coordinate system B, as shown in the following example: Figure 2 As shown, the vector [x i ,y i ,z i ] T Described in O i,e The horizontal, vertical and vertical position vectors, vector [φ i ,θ i ,ψ i ] T Indicates that in O i,b The roll, pitch, and yaw attitude vectors, and the force generated by each horizontal rotor are expressed as And k=1,2,3,4, then the dynamic model of the position system is described as:

[0047]

[0048] Where i = 1,...,n,m i represents the mass of the i-th drone, i,x,i,y and is the aerodynamic damping coefficient in three directions, v i,x ,v i,y and v i,z are the velocities in three directions, g is the acceleration due to gravity, Indicates control thrust, R i is the translation matrix, which can be expressed 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 is the moment of inertia, I i,r is the moment of inertia of the horizontal rotor, i, φ,i , θ and is the aerodynamic damping coefficient, w i It can be expressed by the rotation 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 Indicates the rotation speed of the four rotors, as well as Indicates the control torque in three directions.

[0053] Furthermore, based on the nonlinear dynamic model of the above position system and attitude system, using the dynamic formula (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 represents 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 represents 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 is the mass of the i-th agent; is an external disturbance, y i,1 =[y i,11 ,y i,12 ,y i,13 ] T is the output, u iis the input of the UAV system and can be expressed as:

[0059]

[0060] Similarly, using the dynamics formula (2), the dynamics equation of the posture system can be obtained as follows:

[0061]

[0062] in:

[0063] p i,1 =[p i,11 ,p i,12 ,p i,13 ] T represents the posture vector of the system, 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 represents the derivative vector of the system attitude, where

[0065] I i =diag(1 / I i,x ,1 / I i,y ,1 / I i,z ), is an external disturbance, For output, is an input composed of three control torques, h i,2 (p i,2 ) is expressed as:

[0066]

[0067] On this basis, it is clear that the control objective of this embodiment is to achieve tracking control of multiple UAVs with uncertain disturbances and sensor failures. The following assumptions and lemmas are given:

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

[0069] Hypothesis 3: Leader's position trajectory y L,1 and posture trajectory p i,d and its second-order derivative is bounded.

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

[0071] Lemma 1: Based on FLS (fuzzy logic system), the unknown continuous function f(ξ):ξ∈R h →R can be approximated as:

[0072]

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

[0074]

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

[0076] like The estimated error Similarly, if The estimated error

[0077] Lemma 3: For Then the inequality is:

[0078]

[0079] in, is a matrix The smallest singular value of .

[0080] Explain the above assumptions and lemmas: Assumption 1 shows that all followers can directly or indirectly access the leader's output through a directed path, which is a prerequisite for achieving distributed control; Assumption 2 ensures the boundedness of disturbances, because in real physical phenomena, drones will be disturbed by the external environment during flight, such as changes in wind speed and air density. These disturbances are usually bounded and will not grow infinitely; Assumption 3 is also based on real physical phenomena. The position trajectory and attitude of the drone are continuous, ensuring the stability of the flight; In Assumption 4, wind disturbances, oscillation disturbances on the torsion system, etc. can all be approximated as sine superposition forms based on Fourier transform. Formula, so that 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 fuzzy logic system approximation of nonlinear terms, aiming to eliminate the influence of nonlinear terms. On this basis, the fault adaptation rate can be designed in the form of Formula (32) and Formula (65), requiring the adaptation rate estimation error to be positive, and Lemma 2 gives the sufficient conditions for the adaptation rate estimation error to be positive; Finally, in order to obtain the two tracking error results of Formula (56) and Formula (85), Lemma 3 is also introduced, thereby extending the convergence of the synchronization error Formula (20) to the tracking error Formula (56).

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

[0082] Based on the dynamic model considering external disturbances and sensor failures constructed in the above step S1, first, in step S2.1, for sensor failures, a sensor failure model of the drone position system is constructed according to the actual position state and expected position state of the drone after the failure, and the sensor failure parameters that characterize the drone state loss are obtained.

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

[0084]

[0085] in, and is the actual state after the fault, λ 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 matrix parameters are the sensor fault parameters that characterize the UAV state loss.

[0086] Similarly, a sensor failure in the attitude system can be expressed as:

[0087]

[0088] in, and is the actual state after the fault, μ 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 ) is a diagonal matrix, and the matrix parameters are the sensor fault parameters that characterize the UAV state loss. When the time fails,

[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 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 that characterize the external disturbance by combining the Sylvester equation.

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

[0094]

[0095] in, and κ i is a vector containing unknown parameters, i=[i1,i2,i3] T =[-i,x / m i ,-i,y / m i ,-i,z / m i ] T, κ 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 expressed as:

[0096]

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

[0098]

[0099] in, is a state variable, and Unknown constant coefficient matrix; (W i ,N i ) is observable, and W i The eigenvalue of is located on the imaginary axis to ensure that the system (11) remains in the critical stable state, which makes the external disturbance Δ i It can be expressed in sinusoidal form.

[0100] In order to further simplify the representation of the above external disturbance, a Sylvester equation is defined as:

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

[0102] In the above formula, is the desired solution, is a Hurwitz matrix with eigenvalues ​​in the left half plane, Is a constant matrix. If F i ,W i ,S i and T i N i 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 iThere are no common eigenvalues.

[0103] At the same time, define a new vector σ i =F i G i , and then derive both sides and insert them into formula (11), we get Combined with the Sylvester equation (12), equation (11) is transformed into a special canonical form:

[0104]

[0105] By introducing the Sylvester equation as mentioned above, Equation (11) can be transformed into a special canonical form, so as to simplify the representation of external disturbances in the subsequent process.

[0106] In the special canonical form obtained by the above transformation, the second equation represents the external perturbation Due to σ i is unknown, so we need to estimate the vector σ i The value of the external disturbance can be expressed as:

[0107]

[0108] in, and is the state variable of the filter, satisfying:

[0109]

[0110] In order to judge whether the design of formula (14) is reasonable, substitute formula (14)-formula (17) into (13) to obtain the following Hurwitz stability matrix:

[0111]

[0112] The above results show that due to S i is a Hurwitz matrix, estimating the error It is asymptotically stable, so we substitute Equation (14) into (13) to replace the external disturbance, which can be expressed as:

[0113]

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

[0115]

[0116] Based on the above formula (19), the external disturbance can be converted into the unknown parameter ρ i , that is, this parameter is used as a disturbance parameter to characterize the external disturbance. In this way, the disturbance suppression problem can be transformed into an adaptive control problem, which is convenient for 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, the estimation of synchronization error and speed error is constructed, and the virtual controller, actual controller and its corresponding adaptive law, fault adaptive law and disturbance adaptive law for disturbance parameters are designed based on the error estimation.

[0118] In this embodiment, an adaptive fuzzy tracking control strategy based on adaptive fault compensation technology is used to achieve multi-UAV tracking tasks in the presence of disturbances and sensor failures. The inner and outer control loops of the UAV system correspond to the attitude and position control of the UAV system, respectively. For these inner and outer control loops, corresponding controllers and adaptive laws are designed to control the UAV system.

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

[0120] First, construct the synchronization error and speed error, including:

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

[0122]

[0123] in, is the relative position between the i-th UAV and the j-th UAV in three-dimensional space, is the relative position between the i-th UAV and the leader in three-dimensional space, b i ≥0 is fixed gain, Indicates the leader position.

[0124] (1.2) Construct the velocity error, which is:

[0125]

[0126] Among them, i,1 For virtual controllers.

[0127] Furthermore, since the system contains unknown fault parameters, the synchronization error and speed error are unknown. Therefore, in order to estimate the synchronization error and speed error, this embodiment introduces the sensor fault parameter into the synchronization error and speed error. estimates and meet in is the estimation error.

[0128] The estimation of synchronization error is then:

[0129]

[0130] The velocity error is estimated as:

[0131]

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

[0133]

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

[0135]

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

[0137]

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

[0139]

[0140] Among them, η i,1k is a positive real number, is a positive definition matrix; is the estimation error of the ideal weight vector and satisfies is the estimated value of the ideal weight vector. The Lyapunov function is set for the synchronization error, which includes the synchronization error Z i,1 .

[0141] To verify the stability, the Lyapunov function V i,1 Taking the derivative, we have:

[0142]

[0143] The derivatives of the above Lyapunov function (27) include Three parts need to be solved separately, including:

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

[0145]

[0146] Among them, C i,1 is a positive constant.

[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] According to (29) and (30), we can conclude that:

[0152]

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

[0154]

[0155] in:

[0156]

[0157] And τ i,1k is a positive constant.

[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] Among them, m i,1k is a positive constant.

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

[0166]

[0167] Substituting (31), (34) and (36) into (27), we can 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 system's dynamic position equation, equation (3), is 2. Therefore, a Lyapunov function is defined twice. Specifically, for the velocity error, according to (1), (19), and (21), the first-order derivative of the velocity error can be expressed as:

[0170]

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

[0172]

[0173] Since the first-order derivative of the speed error (38) uses a fuzzy logic system to estimate the nonlinear term, 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, Taking the time derivative we get:

[0174]

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

[0176]

[0177] Among them, η i,2k is a positive constant, and All are positively defined matrices; is the estimation error of the ideal weight vector and satisfies is the estimated value of the ideal weight vector. The Lyapunov function is set for the velocity error, which contains the velocity error Z i,2 .

[0178] To verify the stability, the Lyapunov function V i,2 Taking the first-order derivative, we get:

[0179]

[0180] The derivatives of the above Lyapunov function (41) include Four parts need to be solved separately, including:

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

[0182]

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

[0184] According to (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) we can obtain:

[0189]

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

[0191]

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

[0193]

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

[0195]

[0196] Among them, m i,2k It is a positive constant that can be designed.

[0197] According to (48), we can calculate:

[0198]

[0199] For the fourth part, design the perturbation adaptive law for:

[0200]

[0201] Among them, mi,3k is a positive constant.

[0202] The external disturbance determined according to step S2 above is formula (19), where the unknown matrix ρ i As a parameter representation of the external disturbance, based on the adaptive control method, the above disturbance adaptive law is designed To estimate the unknown matrix ρ i , and thus obtain the estimated value of the external disturbance.

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

[0204]

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

[0206]

[0207] in:

[0208]

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

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

[0211] The consistent tracking error between the leader and followers is eventually bounded by semi-global consistency.

[0212] Furthermore, based on the semiglobally consistent ultimately bounded correlation theory, if the above Lyapunov function V is positive definite, and in and If it is bounded, it can be proved that the above Lyapunov function is convergent, that is, the synchronization error, speed error and adaptive estimation error are convergent. Specifically, the stability analysis results based on the Lyapunov stability theory prove the calculation method of the above controller and control law. 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 relationship:

[0218]

[0219] From (55), we can see that the signal Z i,1 ,Z i,2 , is uniformly ultimately bounded, which means and is bounded; based on a virtual controller and the actual controller u i The fact that is bounded, according to (53), In addition, according to Lemma 3, for By choosing 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 get:

[0220] ||yy L ||≤∈. (56)

[0221] This means that the tracking error of the follower trajectory converges to a small neighborhood of the origin, and the proof is complete. It should be pointed out that the design parameters in (54) are required to be large enough so that the error coefficient remains negative. Excessive increase in 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 mentioned above, in order to estimate the synchronization error and angular velocity error, the estimated value of the sensor fault parameter is introduced into the synchronization error and velocity error. and satisfy in is the estimation error. Then the synchronization error can be rewritten as the following equation:

[0224]

[0225] in, and represents the synchronization error and acceleration error estimation, p i,d Shows the leader's attitude, For virtual controllers.

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

[0227]

[0228] Define the Lyapunov candidate function as:

[0229]

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

[0231]

[0232] The derivatives of the above Lyapunov function (60) include There are two parts, which need to be solved separately, including:

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

[0234]

[0235] in, is a positive constant.

[0236] Combining equations (58) and (61), the following equation holds for the 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 is the positive constant to be designed.

[0245] According to formula (65), we can further derive the formula:

[0246]

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

[0248]

[0249] For the angular velocity error, FLS (fuzzy logic system) is used to approximate the unknown parameters, which are:

[0250]

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

[0252]

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

[0254]

[0255] Define the Lyapunov candidate function as:

[0256]

[0257] Among them, π i,2k >0 is a normal number, Define the matrix for positive.

[0258] By taking the derivative of the above Lyapunov function, we can get:

[0259]

[0260] The derivatives of the above Lyapunov function (72) include Three parts need to be solved separately, including:

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

[0262]

[0263] in, is the positive control constant.

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

[0265]

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

[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 Is a positive number.

[0273] According to (77), we can further derive the formula:

[0274]

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

[0276]

[0277] Among them, m i,4k is a positive constant.

[0278] Then we have:

[0279]

[0280] From equations (67), (71), (76), (78) and (80), we can get the time derivative inequality:

[0281]

[0282] in,

[0283] Theorem 2 is given here: Considering the attitude dynamics equation (4) of the 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 of a closed-loop system are bounded;

[0285] The consensus tracking error between the leader and followers is cooperatively semi-globally consistent and eventually bounded.

[0286] Furthermore, the above method is also proved based on the stability analysis results of Lyapunov stability theory. Consider the following Lyapunov function:

[0287]

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

[0289]

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

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

[0292]

[0293] From formula (84), we can see that the signal Z i,1 , is uniformly eventually bounded, which means and is bounded; based on a virtual controller and the actual controller is bounded, starting from (82), the limit In addition, from Lemma 3, we can see that when By setting the design parameters ι i,1k ,ι i,2k ,m i,4k Choosing it large enough gives:

[0294]

[0295] in, Equation (85) shows that the tracking error of the tracker's trajectory converges to a small neighborhood of the origin, and the proof is complete. In addition, it should be pointed out that the design parameters in Equation (81) are required to be large enough to keep the error coefficient negative. Excessively large error coefficients will lead to an increase in control energy and deteriorate tracking performance.

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

[0297] Preferably, the effectiveness of the above method proposed in this embodiment is verified by the following UAV simulation example. Figure 3As shown, any UAV is selected as the leader and four UAVs are selected as followers. The edges of the directed topology represent the information transfer between the leader and followers. In addition, the adjacency matrix P is defined as:

[0298]

[0299] Based on the above definition, the execution Figure 4 The multi-UAV formation tracking trajectory shown, the reference trajectory is selected as follows:

[0300]

[0301] In order 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:

[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] The external disturbance can be expressed as:

[0306]

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

[0308] The position trajectory tracking and reference signals of the four following 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 After the fault occurs, it quickly converges to 1.2. The simulation results of the position system are as follows Figure 6 and Figure 7 As shown by Figure 6 (a) shows that the fault causes the x-direction tracking task to be damaged and a collision occurs; after the fault is handled, Figure 6 (b) It can be seen that the tracking curve returns to the specified tracking state. Figure 7The tracking situation in the y direction is shown in Figure 3. Within 3 seconds after the fault occurred, the state curve shifted significantly. After the fault was resolved, the tracking error gradually converged. Figure 8 (a)-(d) Figure 9 (a)-(d) Figure 10 (a)-(d) show the reliability of the disturbance tracking scheme. It is worth noting that although the sensor failure affects the tracking performance of the disturbance, the tracking error quickly reaches asymptotic stability. Figure 11 (a)-(d) Figure 12 (a)-(d) and Figure 13 Figures (a)-(d) show the input signals of the four followers in three different directions. When the fault occurs, the input curves show a certain degree of mutation, but after the fault is processed, the input curves return to stability.

[0309] Through the above method, a disturbance suppression method is used to eliminate the effects of unknown disturbances. An adaptive law is designed to estimate the fault parameters of a UAV system with uncertain disturbances and sensor failures. Based on this, a 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. Furthermore, comparative fault handling results demonstrate the effectiveness of this method. The UAV's position trajectory also demonstrates that the algorithm can effectively implement leader-following tracking tasks.

[0310] Example 2

[0311] This embodiment provides a multi-UAV tracking and control system that takes disturbances and sensor failures into account, including:

[0312] A model building module is used to build a dynamic model of each drone in a multi-quadrotor drone 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 UAV's state loss based on the dynamic model, and to model the unknown time-varying external disturbance in the model as the output of a finite-dimensional linear generator to construct disturbance parameters that characterize the external disturbance;

[0314] The controller design module is used to estimate sensor fault parameters for the inner and outer loop control of the UAV system, construct estimates of synchronization error and speed error, and design virtual controllers, actual controllers, and their corresponding adaptive laws, fault adaptive laws, and disturbance adaptive laws for disturbance parameters based on the error estimates.

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

[0316] Example 3

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

[0318] Example 4

[0319] This embodiment further provides a computer-readable storage medium storing executable instructions. When the executable instructions are executed by a processor, the processor will be caused to execute the above method provided in this embodiment.

[0320] Example 5

[0321] This embodiment provides a computer program product including executable instructions, which are computer instructions stored in a computer-readable storage medium. When a 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 provided in this embodiment.

[0322] The steps involved in the above embodiments 2 to 5 correspond to those in embodiment 1. For detailed implementation, please refer to the relevant description of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media that includes one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and cause the processor to perform any method of the present invention.

[0323] Those skilled in the art will appreciate that the modules or steps of the present invention described above can be implemented using a general-purpose computer device. Alternatively, they can be implemented using program code executable by a computing device, which can then be stored in a storage device and executed by the computing device. Alternatively, they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific 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 is described in conjunction with the accompanying drawings, it does not limit the scope of protection of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative work 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 UAV system, a dynamic model of each UAV is constructed that takes into account external disturbances and sensor failures; Based on the dynamic model, the sensor fault parameters that characterize the UAV state loss are constructed. The unknown time-varying external disturbance in the model is modeled as the output of a finite-dimensional linear generator to construct the disturbance parameters that characterize the external disturbance. For the inner and outer loop control of UAV systems, we introduce the estimation of sensor fault parameters, construct the estimation of synchronization error and speed error, and design the virtual controller, actual controller and its corresponding adaptive law, fault adaptive law, and disturbance adaptive law for disturbance parameters based on the error estimation. The status information of each UAV is collected in real time, and the designed controller and adaptive law are used to achieve tracking control of the multi-quadrotor UAV system.

2. The multi-UAV tracking control method considering disturbances and sensor failures according to claim 1 is characterized in that: The dynamic model of the UAV includes a dynamic model of the UAV position system and a dynamic model of the UAV attitude system; Among them, the dynamic model of the UAV position system is: In the formula, i=1,...,n,O i,e ,x i,e ,y i,e ,z i,e They represent the origin, horizontal, vertical and vertical positions of the i-th UAV in the Earth-centered Earth-fixed coordinate system E, respectively. i Indicates the mass of the i-th drone, i,x,i,y, is the aerodynamic damping coefficient, v i,x ,v i,y ,v i,z are the velocities in three directions, g is the acceleration due to gravity, Indicates control thrust, R i is the translation matrix, expressed as: Among them, the vector [φ i ,θ i ,ψ i ] T Indicates that in O i,b The roll, pitch, and yaw attitude vectors, and the force generated by each horizontal rotor are expressed as And k=1,2,3,4; The dynamic model of the UAV attitude system is: Where, I i,x ,I i,y ,I i,z is the moment of inertia, I i,r is the moment of inertia of the horizontal rotor, i,φ,i,θ, is the aerodynamic damping coefficient, w i It is expressed by the rotation speed of the four horizontal rotors: w i =-r i,1 -r i,2 +r i,3 +r i,4 , Indicates three control torques.

3. The multi-UAV tracking control method considering disturbances and sensor failures according to claim 1 is characterized in that: According to the actual position state and expected position state of the UAV after the failure, a sensor failure model in the UAV position system is constructed, which is expressed as: Where, and is the actual state after the fault, λ 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 whose parameters are the sensor fault parameters that characterize the UAV state loss; According to the actual attitude state and expected attitude state of the UAV after the failure, a sensor failure model in the UAV attitude system is constructed, which is expressed as: in, and is the actual state after the fault, μ 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 ) is a diagonal matrix, and the matrix parameters are the sensor fault parameters that characterize the UAV state loss; The i-th drone is When the time fails, When there are λ i,11 , λ i,12 ,..., λ i,23 , μ i,11 , μ i,12 ,..., μ i,23 = 1; when have in, and Is a positive number.

4. The multi-UAV tracking control method considering disturbances and sensor failures according to claim 1, characterized in that: Design virtual controllers, actual controllers, and their corresponding adaptive laws, fault adaptive laws, and disturbance adaptive laws for disturbance parameters to meet the control objectives: All signals of a closed-loop system are bounded; The consistent tracking error between the leader and follower UAVs is cooperatively semi-globally uniformly bounded.

5. The multi-UAV tracking control method considering disturbances and sensor failures according to claim 1, characterized in that: The inner and outer loop controls of the UAV system correspond to the attitude control and position control of the UAV system respectively. For the position control of the UAV system, the virtual controller is designed as follows: Among them, C i,1 is a positive constant; The fault adaptive law designed for the virtual controller is: in, τ i,1k is a positive constant; The adaptive law designed for the virtual controller is: Among them, m i,1k is a positive constant; The actual controller is designed as: Among them, C i,2 is the positive control constant; The fault adaptive law designed for the actual controller is: in, And τ i,2k is a positive constant; The adaptive law designed for the actual controller is: Among them, m i,2k is a positive constant; The disturbance adaptive law designed for the actual controller is: Among them, m i,3k is a positive constant.

6. The multi-UAV tracking control method considering disturbances and sensor failures according to claim 5, characterized in that: For the attitude control of the UAV system, the virtual controller is designed as follows: in, is a positive constant; The fault adaptive law designed for the virtual controller is: in, ι i,1k is the positive constant to be designed; The actual controller is designed as: in, is the positive control constant; The fault adaptive law designed for the actual controller is: in, ι i,2k is a positive constant; The adaptive law designed for the actual controller is: Among them, m i,4k is a positive constant.

7. A multi-UAV tracking control system considering disturbances and sensor failures, characterized in that: include: A model building module is used to build a dynamic model of each drone in a multi-quadrotor drone 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 UAV's state loss based on the dynamic model, and to model the unknown time-varying external disturbance in the model as the output of a finite-dimensional linear generator to construct disturbance parameters that characterize the external disturbance; The controller design module is used to estimate sensor fault parameters for the inner and outer loop control of the UAV system, construct estimates of synchronization error and speed error, and design virtual controllers, actual controllers, and their corresponding adaptive laws, fault adaptive laws, and disturbance adaptive laws for disturbance parameters based on the error estimates. The tracking control module is used to collect the status information of each UAV in real time, and use the designed controller and adaptive law to achieve tracking control of the multi-quadrotor UAV system.

8. An electronic device, characterized in that: include: a memory for storing executable instructions; The processor is configured to implement the multi-UAV tracking control method considering disturbances and sensor failures as described in any one of claims 1 to 6 when executing the executable instructions stored in the memory.

9. A computer-readable storage medium, characterized in that Executable instructions are stored, which are used to cause the processor to execute the executable instructions to implement the multi-UAV tracking control method considering disturbances and sensor failures as described in any one of claims 1 to 6.

10. 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, the multi-UAV tracking control method considering disturbances and sensor failures described in any one of claims 1 to 6 is implemented.

Images