All-drive heterogeneous multi-intelligent system preset time cooperative fault-tolerant method

Abstract

The application discloses a full-drive heterogeneous multi-intelligent system preset time cooperative fault-tolerant method, which comprises the following steps: S1, a virtual unmanned aerial vehicle is constructed as a virtual leader, and information interaction characteristics among the leader and followers and among the followers are established by using graph theory knowledge; S2, a point is randomly selected on the ground to establish a three-dimensional rectangular coordinate system, and unmanned ground vehicle full-drive system model and unmanned aerial vehicle full-drive system model are established; finally, a full-drive system model of the heterogeneous multi-intelligent system under fault is obtained; S3, based on the interaction characteristics of individuals in the heterogeneous multi-intelligent system, a distributed preset time observer is constructed; and S4, preset time cooperative formation control of the position of the unmanned ground vehicle and the unmanned aerial vehicle follower under the influence of the actuator fault is realized by means of a decentralized fault-tolerant formation control ware. The application improves the system's maneuvering response speed and the robustness and fault tolerance of the formation system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of fault-tolerant formation control of air-ground multi-agent system, and particularly relates to a preset time cooperative fault-tolerant method for full-drive heterogeneous multi-agent system. BACKGROUND

[0002] A multi-agent system is composed of multiple autonomous unit subsystems with communication, sensing, computing and execution capabilities, realizes information interaction based on a communication network and achieves cooperation through a distributed control unit. With the cross and integration development of biology, artificial intelligence, control science and computer science, the multi-agent system has attracted more and more attention and has been practically applied in many fields. Unmanned aerial vehicles and unmanned ground vehicles are the most representative two types of objects in the multi-agent system, and through the reasonable cooperation of the unmanned aerial vehicles and the unmanned ground vehicles, the deficiencies of a single type of object can be made up and the efficiency of cooperative operation can be effectively improved. For example, in reconnaissance under complex terrain conditions, the formation control of multiple unmanned aerial vehicles can be used to cover a large area to quickly search for targets. However, the speed, height and attitude uncertainty of the unmanned aerial vehicles limit the ability of the sensors carried on the unmanned aerial vehicles to distinguish and locate ground features. At this time, by introducing multiple unmanned ground vehicles for cooperative reconnaissance, the unmanned aerial vehicles can provide large-scale environmental information, the unmanned ground vehicles can plan the route in advance to avoid obstacles such as buildings or fences in front, accurately locate the ground target, and realize the complementary advantages and cooperative of the heterogeneous cluster system.

[0003] Since the unmanned aerial vehicles and the unmanned ground vehicles have completely different physical structures, their dynamic models are completely different, and the aerial vehicles move in three-dimensional space while the ground vehicles move in two-dimensional space, so the existing distributed cooperative formation control algorithm for homogeneous multi-agent systems cannot be directly applied. In the actual cooperative operation process, the multi-agent system will inevitably have various faults such as actuator faults, sensor faults and component faults due to sudden deterioration of the external environment, long-time high-load operation and other reasons. Since the multi-agent system has strong coupling, when some subsystems fail, the fault information will be transmitted to the neighbor agents through the communication network and then spread to the whole system. If the fault information of the system cannot be effectively processed in time, the expected cooperative operation task will be difficult to achieve, causing system paralysis, economic losses, and even casualties. The existing heterogeneous multi-agent control strategy does not well solve the problem of fault information propagation. Therefore, in the cooperative control problem of the multi-agent system, when a fault occurs, how to suppress the propagation of the fault information and design a corresponding fault-tolerant control method to ensure the stable operation and cooperation of the whole system has practical significance.

[0004] At present, the unmanned aerial vehicle and unmanned ground vehicle are mostly modeled as a first-order state space model. However, the unmanned aerial vehicle and unmanned ground vehicle system shall follow objective physical laws, such as Newton's law, Lagrange equation, and momentum theorem. The system model directly established based on the above physical laws is mostly a second-order or high-order differential equation. If the second-order or high-order system model is converted into a first-order state space model, the full drive characteristics of the original system are destroyed. The controller design based on the high-order full drive system model is more convenient and easy to implement, and the full drive characteristics allow to eliminate all open-loop dynamics to establish a new, desired, and constant linear closed-loop system. Therefore, the cooperative control strategy based on the full drive system method has application value.

[0005] In addition, with the continuous improvement of the complexity, refinement and efficiency of the cooperative task, the maneuvering responsiveness of the multi-agent system is also required to be more stringent. Under the premise of ensuring the realization of the expected cooperative task, the timeliness and rapidity of task execution are required to be further improved, which makes the existing fault-tolerant control algorithm of the multi-agent system with asymptotic convergence as the target no longer applicable. Although the existing fixed heterogeneous multi-agent system cooperative control strategy can realize the convergence of the system within a fixed time, the size of the convergence time still depends on the parameter value of the designed controller, and the introduction of the sign function in the controller leads to the shaking of the control input. Therefore, it is urgent to research a new control strategy to realize the convergence of the heterogeneous multi-agent system within any preset time. SUMMARY

[0006] The purpose of the present application is to provide a heterogeneous multi-agent system preset time cooperative fault-tolerant method which can realize the tracking of the expected motion trajectory information provided by the leader within a predetermined time, improve the maneuvering response speed of the system and the robustness and fault tolerance of the formation system.

[0007] Technical scheme: The full drive heterogeneous multi-agent system preset time cooperative fault-tolerant method comprises the following steps:

[0008] S1, a virtual unmanned aerial vehicle is constructed as a virtual leader, and the virtual leader provides expected motion trajectory information; the follower includes N1 unmanned ground vehicles and N2 unmanned aerial vehicles following the virtual leader, and the information interaction characteristics of the leader and the follower and the follower are established by using the knowledge of graph theory;

[0009] S2, a point on the ground is randomly selected to establish a three-dimensional rectangular coordinate system, the motion characteristics of the unmanned ground vehicle and the unmanned aerial vehicle are analyzed, the full drive system model of the unmanned ground vehicle and the full drive system model of the unmanned aerial vehicle are established, the fault model is constructed by analyzing the influence of the fault on the performance of the system, and finally the full drive system model of the heterogeneous multi-agent system under fault is obtained;

[0010] S3, based on the interaction characteristics of individuals in a heterogeneous multi-agent system, constructs a distributed preset time observer to track the expected movement trajectory information provided by the leader within a preset time.

[0011] S4 combines the theory of all-drive systems and the theory of preset time convergence. It uses the real-time observation information of the expected motion trajectory information provided by the leader and its own position information by the preset time observer to design a distributed fault-tolerant formation controller. The distributed fault-tolerant formation controller realizes the preset time coordinated formation control of the positions of unmanned ground vehicles and unmanned aerial vehicles under the influence of actuator failure.

[0012] Furthermore, in step S1, the motion trajectory information includes position information, velocity information, and acceleration information, which are respectively defined as follows: and x 01 x 02 and x 03 These represent the leader's position on the X, Y, and Z axes, respectively. Represents all real numbers, and the superscript T indicates matrix transpose;

[0013] The set of unmanned ground vehicles is defined as

[0014] An unmanned aerial vehicle (UAV) set is defined as

[0015] Heterogeneous multi-agent system set is defined as

[0016] The connections between all followers are represented by a directed graph. It means that, among them n i Let N represent the i-th follower, and N represent the total number of followers, where N = N1 + N2. Denotes the edge set, (n i ,n j ) represents the number of followers n j Able to acquire followers n i Information; The connection matrix has non-negative weights. For the real number field, when (n j ,n i )∈ε,a ij =1, when a ij =0;

[0017] The Laplace matrix is ​​defined as in and

[0018] Furthermore, the information exchange characteristics between leaders and followers are used... This means that s is a sequence of events where ... the i-th follower is able to receive information from the leader if and only if the i-th follower is able to receive information from the leader. i =1; otherwise s i =0;

[0019] The information exchange matrix of the entire heterogeneous multi-agent system is defined as follows:

[0020] There exists a diagonal matrix P = diag{p1,...,p} N} makes in 1 represents a column vector whose elements are all 1.

[0021] Furthermore, in step S2, the model of the unmanned ground vehicle all-wheel drive system is as follows:

[0022]

[0023] in, x i1 ′ and x i2 ′ represent the positions of unmanned ground vehicle i on the X and Y axes, respectively; u i1 ′ and u i2 ′ represent the control inputs of unmanned ground vehicle i on the X and Y axes, respectively; L i v represents the distance from the reference position to the inertial position of the unmanned ground vehicle i. i w i θ i Let represent the velocity, angular velocity, and direction of the unmanned ground vehicle i, respectively;

[0024] The unmanned aerial vehicle all-drive system model is as follows:

[0025]

[0026] in, x i1 "、x i2 "and x i3 "" represents the position of unmanned aerial vehicle i on the X, Y, and Z axes respectively; the air resistance vector is Define three new variables D i1 D i2 D i3 And let Drag coefficient K ij >0, j=1,2,3, the mass m of unmanned aerial vehicle i i >0, f i1 "=Di1 ,f i2 ″=D i2 ,f i3 ″=D i3 -g, g is the acceleration of gravity; b i ″=1 / m i ; u i1 ″, u i2 ″ and u i3 ″ represent the control input of the unmanned aerial vehicle i in the X-axis, Y-axis and Z-axis, respectively;

[0027] The fault model is:

[0028]

[0029] wherein, u ij represent the output and input of the jth actuator of the ith agent at time t, respectively, when j = 1, 2; when j = 1, 2, 3; p ij represents the performance factor of the actuator, which satisfies 0 < p p ij ≤ p ij ≤ 1, wherein p ij is a normal number;

[0030] The full-drive system model of the ith agent under fault is described as:

[0031]

[0032] wherein, when x i = x i ′, f i = f i ′, b i = 1, Λ(p i ) = diag(p i1 , p i2 ), u i = [u i1 , u i2 ] T , u i1 and u i2 represent the control input of the ith follower in the X-axis and Y-axis, respectively; when x i = x i ″, f i = f i ″, b i = 1 / m i , Λ(pi ) = diag(p i1 , p i2 , p i3 ), u i = [u i1 , u i2 , u i3 ] T , u i1 , u i2 and u i3 represent the control input of the i-th follower in X-axis, Y-axis and Z-axis, respectively.

[0033] Further, in step S3, define the estimation value of the i-th agent to the expected position information, velocity information and acceleration information provided by the leader as and

[0034] The distributed preset time observer is designed as follows:

[0035]

[0036]

[0037]

[0038] wherein k, c and δ are normal numbers, and δ≥x (3) , x0 (3) represents the third derivative of x0; T1, T2 and T3 are three different time constants, and satisfy T1

[0039]

[0040]

[0041]

[0042]

[0043] Select the parameter c so that it satisfies c≥c1λ max (P) / λ min (Q), wherein c1 is a normal number, then within the preset time T3

[0044] Define wherein and are the estimation of the i-th unmanned ground vehicle to the position, velocity and acceleration of the leader in X-axis, and are the i-th UGV's estimation of the leader's position, velocity and acceleration in Y-axis, respectively.

[0045] Further, in step S4, the formation error is defined as:

[0046]

[0047] where h i is the desired formation distance; since

[0048] The air-ground cooperative pre-set time formation problem is that there is a time constant T p that can be set in advance, so that the following formula is true:

[0049]

[0050]

[0051] where when x0=[x 01 ,x 02 ] T when x0=[x 01 ,x 02 ,x 03 ] T .

[0052] Further, in step S4, the decentralized fault-tolerant controller based on the full-drive system model of the intelligent agent under fault is designed as follows:

[0053]

[0054]

[0055] a i0 and a i1 are two normal numbers, when , is the estimation value of j=1,2; when , is the estimation value of j=1,2,3,

[0056]

[0057]

[0058] φ​i1 and φ i2 is determined by the equation:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] k is a constant, when a i = 2; when a i = 3;

[0065] when π i11 , π i12 , π i21 , π i22 are elements of the vector Π i , Π i = [π i11 , π i12 , π i21 , π i22 ] T ; when π i11 , π i12 , π i13 , π i21 , π i22 , π i23 are elements of the vector Π i , Π i = [π i11 , π i12 , π i13 , π i21 , π i22 , π i23 ] T ;

[0066] The adaptive update law for the estimated value of the actuator fault coefficient is:

[0067]

[0068] where,

[0069]

[0070]

[0071] p is a normal number small enough and satisfies p << p ij , β ij is a normal number, g 11 , g 12 , g 21 and g 22 are elements of a positive definite matrix G, G = [g 11 , g 12 ; g 21 , g 22 ].

[0072] Further, the control parameters a i0 and a i1 and the matrix G are obtained by the following steps:

[0073] SD1, select any negative definite matrix

[0074] SD2, select a matrix such that Δ(Z i , F i ) = [Z i ; Z i F i ] and det(Δ)≠0;

[0075] SD3, calculate [a i0 , a i1 ] = -Z i F i 2 Δ -1 (Z i , F i ), A ic = [0, 1; -a i0 , -a i1 ];

[0076] SD4, according to and get and

[0077] SD5, select any positive definite matrix get wherein

[0078] Compared with the prior art, the present application has the following remarkable effects:

[0079] The application proposes a hierarchical controller design method: in the upper layer structure, a distributed preset time observer is designed based on the interaction characteristics between agents, and the tracking of the expected motion trajectory information provided by the leader within the preset time is realized; in the lower layer structure, a decentralized fault-tolerant formation controller is designed based on the established full-drive system model, the real-time observation information of the expected motion trajectory information provided by the leader and the position information of the agent itself by using the distributed preset time observer, so that the preset time cooperative formation control of the unmanned ground vehicle and the unmanned aerial vehicle under the influence of the fault is ensured, and the maneuvering response speed of the system and the robustness and fault tolerance of the formation system are significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 for the flowchart of the application;

[0081] Figure 2 for the structure diagram of the air-ground heterogeneous multi-agent system;

[0082] Figure 3 for the communication topology structure diagram of the air-ground heterogeneous multi-agent system;

[0083] Figure 4 for the schematic diagram of the acceleration estimation of the virtual leader in the X axis;

[0084] Figure 5 for the schematic diagram of the acceleration estimation of the virtual leader in the Y axis;

[0085] Figure 6 for the schematic diagram of the acceleration estimation of the virtual leader in the Z axis;

[0086] Figure 7 for the schematic diagram of the speed estimation of the virtual leader in the X axis;

[0087] Figure 8 for the schematic diagram of the speed estimation of the virtual leader in the Y axis;

[0088] Figure 9 for the schematic diagram of the speed estimation of the virtual leader in the Z axis;

[0089] Figure 10 for the schematic diagram of the position estimation of the virtual leader in the X axis;

[0090] Figure 11 for the schematic diagram of the position estimation of the virtual leader in the Y axis;

[0091] Figure 12 for the schematic diagram of the position estimation of the virtual leader in the Z axis;

[0092] Figure 13 for the formation effect diagram of the heterogeneous multi-agent;

[0093] Figure 14 is a schematic diagram of the formation error situation on the X axis;

[0094] Figure 15 is a schematic diagram of the formation error situation on the Y axis;

[0095] Figure 16 is a schematic diagram of the formation error situation on the Z axis;

[0096] Figure 17 is a schematic diagram of the first unmanned ground vehicle fault coefficient estimation situation;

[0097] Figure 18 is a schematic diagram of the second unmanned ground vehicle fault coefficient estimation situation;

[0098] Figure 19 is a schematic diagram of the first unmanned aerial vehicle fault coefficient estimation situation;

[0099] Figure 20 is a schematic diagram of the second unmanned aerial vehicle fault coefficient estimation situation. DETAILED DESCRIPTION

[0100] The application will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

[0101] The embodiment first establishes a full-drive system model of the unmanned ground vehicle and the unmanned aerial vehicle under fault; the information interaction characteristics between the leader and the follower and the followers are established by using graph theory knowledge; under the influence of the multi-agent structure, fault information is easy to spread among the agents, in order to solve this problem, a hierarchical structure controller design method is proposed; in the upper layer structure, a distributed preset time observer is designed to realize the tracking of the expected motion trajectory information provided by the leader within the preset time. In the lower layer structure, based on the established full-drive system model, a decentralized fault-tolerant formation controller is designed by using the real-time observation information of the expected motion trajectory information provided by the leader and the self position information of the distributed preset time observer.

[0102] The application directly designs a preset time cooperative fault-tolerant controller based on the full-drive system model of the heterogeneous multi-agent system, the designed fault-tolerant controller does not need to introduce a virtual control variable, can avoid the problem of differential explosion, and the convergence time of the formation error has a performance that can be arbitrarily set in advance without depending on the initial state or the control parameter of the system, and the formation controller obtained accordingly has rapid convergence, good fault propagation suppression performance and fault-tolerant performance, and can meet the dual requirements of stability and maneuvering response speed of the heterogeneous multi-agent system.

[0103] Firstly, the related symbol definitions are given: and denote the set of all real numbers, non-negative numbers, positive numbers and natural numbers, respectively; denote the set of all n-dimensional real vectors, The index set of consecutive integers is denoted as I[n1,n2]={n1,n1+1,...,n2}, where 1 represents a column vector with all elements being 1; 0 represents a column vector with all elements being 0; the transpose operation of a vector or matrix is denoted by superscript ''T''; the inverse operation of a matrix is denoted by superscript ''-1''. denotes the Kronecker product operation; for a matrix P, λ max (P) is the maximum eigenvalue of matrix P, λ min (P) is the minimum eigenvalue of matrix P; sign(·) is the sign function. For variable col{a i}=[a1,a2,a3] T I n is an identity matrix of size n x n,

[0104] As shown in Figure 1 , the specific steps of the method for preset time cooperative fault-tolerant control of the heterogeneous multi-agent system of the application are as follows:

[0105] Step 1, a virtual unmanned aerial vehicle is constructed as a virtual leader, which provides expected motion trajectory information; the followers in the heterogeneous multi-agent system include N1 unmanned ground vehicles and N2 unmanned aerial vehicles following the virtual leader, and the information interaction characteristics between the leader and the followers and between the followers are established by using graph theory knowledge.

[0106] The expected position information, velocity information and acceleration information provided by the leader are defined as: and Wherein, x 01 , x 02 and x 03 represent the positions of the leader in the X-axis, Y-axis and Z-axis, respectively.

[0107] The virtual leader is marked as i=0, the N1 unmanned ground vehicle followers are marked as i=1,2,...,N1, and the N2 unmanned aerial vehicle followers are marked as i=N1+1,N1+2,...,N1+N2. Correspondingly, the unmanned ground vehicle set is defined as The unmanned aerial vehicle set is defined as The heterogeneous multi-agent system set is defined as

[0108] The connection relationship between all followers is represented by a directed graph , wherein n iLet N represent the i-th follower, and N represent the total number of followers, where N = N1 + N2. Denotes the edge set, (n i ,n j ) represents the number of followers n j Able to acquire followers n i Information. The connection matrix has non-negative weights. Let a be the field of real numbers, if a ij =1 then (n j ,n i )∈ε;a ij =0, The Laplace matrix is ​​defined as in,

[0109] The information exchange characteristics between leaders and followers This means that s is a sequence of events where ... the i-th follower is able to receive information from the leader if and only if the i-th follower is able to receive information from the leader. i =1; otherwise, s i =0. The information exchange matrix of the entire heterogeneous multi-agent system is defined as...

[0110] There exists a diagonal matrix P = diag{p1,…,p N} makes in

[0111] Step 2: Randomly select a point on the ground to establish a three-dimensional rectangular coordinate system, analyze the motion characteristics of unmanned ground vehicles and unmanned aerial vehicles, and establish an all-drive system model for unmanned ground vehicles and an all-drive system model for unmanned aerial vehicles; analyze the impact of faults on the system performance, and establish an all-drive system model for heterogeneous multi-agent systems under fault conditions.

[0112] The model of an all-wheel drive system for unmanned ground vehicles is as follows:

[0113]

[0114] in, x i1 ′ and x i2 ′ represent the positions of unmanned ground vehicle i on the X and Y axes, respectively;

[0115] u i1 ′ and u i2 ′ represent the control inputs of unmanned ground vehicle i on the X and Y axes, respectively; L i v represents the distance from the reference position to the inertial position of the unmanned ground vehicle i. i wi θ i Let i represent the velocity, angular velocity, and direction of the unmanned ground vehicle i, respectively.

[0116] The unmanned aerial vehicle all-drive system model is as follows:

[0117]

[0118] in, x i1 "、x i2 "and x i3 "" represents the position of unmanned aerial vehicle i on the X, Y, and Z axes respectively; the air resistance vector is and Drag coefficient K ij >0, the mass m of unmanned aerial vehicle i i >0, f i1 "=D i1 ,f i2 "=D i2 ,f i3 "=D i3 -g, where g is the acceleration due to gravity; b i "=1 / m i ; u i1 "、u i2 "and u i3 "" represents the control input of unmanned aerial vehicle i on the X-axis, Y-axis and Z-axis respectively.

[0119] The fault model under consideration is:

[0120]

[0121] in, u ij (t) represent the output and input of the j-th actuator of the i-th agent at time t, respectively; ρ ij Let be the performance factor of the actuator, which satisfies 0 < p ij ≤ρ ij ≤1, where p ij It is a positive constant.

[0122] Finally, the all-drive system model of the i-th follower under fault conditions can be obtained as follows:

[0123]

[0124] Among them, when At that time, x i =x i ′, fi = f i i = 1, A(p i ) = diag(p i1 , p i2 ), u i = [u i1 , u i2 ] T , u i1 and u i2 denote the control input of the ith follower in X-axis and Y-axis, respectively; when , x i = x i ", f i = f i ", b i = 1 / m i , A(p i ) = diag(p i1 , p i2 , p i3 ), u i = [u i1 , u i2 , u i3 ] T , u i1 , u i2 and u i3 denote the control input of the ith follower in X-axis, Y-axis and Z-axis, respectively.

[0125] Step 3, based on the interaction characteristics of the individuals in the heterogeneous multi-agent system established in step 1, a distributed preset time observer is constructed using the interaction information with the neighbor nodes, and accurate tracking of the expected motion trajectory information provided by the leader within the preset time is realized.

[0126] Define the estimation values of the ith agent for the expected position information, speed information and acceleration information provided by the leader as and

[0127] Then the distributed preset time observer is designed as follows:

[0128]

[0129] where k, c and δ are normal numbers, and δ ≥ x0 (3) , x0 (3) denotes the third derivative of x0, T1, T2 and T3 are three different time constants, and satisfy T1 < T2 < T3, and sign(·) is a sign function.

[0130] ​

[0131]

[0132]

[0133]

[0134] Definition e a = col{e ai} and ω a = col{ω ai}, col denotes column, we can get The Lyapunov function V o1 (t) of the observer acceleration term is selected as follows:

[0135]

[0136] V o1 is the abbreviation of V o1 (t).

[0137] The derivative of formula (6) is:

[0138]

[0139] Wherein, c≥c1λ max (P) / λ min (Q), c1 is a normal number, σ1=σ(t,T1); we can get, Further,

[0140]

[0141] For t∈[T1,∞), we can have:

[0142]

[0143] Further,

[0144] 0≤V o1 (t)≤V o1 (T1)=0,t∈[T1,∞) (10)

[0145] Finally we can get: V o1 ≡0 and That is

[0146] Definition e v = col{e vi} and ω v = col{ω vi}, we can get The Lyapunov function V for the observer velocity term is chosen as o2 (t):

[0147]

[0148] V o2 is a short hand for V o2 (t).

[0149] Taking the derivative of equation (11) gives

[0150]

[0151] where σ2= σ(t, T2).

[0152] It can be shown that

[0153] For t ∈ [T2, ∞), we have

[0154]

[0155] Finally, we have V o2 ≡ 0 and i.e.

[0156] Using the same method, we have and Finally, we have

[0157] In summary, if c is chosen such that it satisfies c ≥ clλ max (P) / λ min (Q), then within a predetermined time T3,

[0158] It is noted that the UGVs only move in a two-dimensional plane, so they do not need the leader's information in the Z-axis. Therefore, we define where and are the i-th UGV's estimate of the leader's position, velocity and acceleration in the X-axis, respectively, and are the i-th UGV's estimate of the leader's position, velocity and acceleration in the Y-axis, respectively.

[0159] Step 4: Based on the accurate estimation of the expected trajectory information provided by the leader within the preset time, and further combining the theory of all-drive systems and the theory of preset time convergence, and based on the all-drive system model of the heterogeneous multi-agent system under fault conditions established in Step 2, a distributed fault-tolerant formation controller is designed using the real-time observation information of the expected trajectory information provided by the leader and its own position information from the distributed preset time observer in Step 3. Adaptive technology is used to estimate the unknown actuator failure coefficient to compensate for the impact of the failure on the system. The designed distributed fault-tolerant formation controller realizes the preset time cooperative formation control of the positions of unmanned ground vehicles and unmanned aerial vehicles under the influence of actuator failure.

[0160] Based on the accurate estimation of the expected trajectory information provided by the leader using a distributed pre-set time observer, the formation error can be defined as:

[0161]

[0162] Among them, h i For the desired formation distance; due to so

[0163] The air-to-ground coordinated pre-setup time problem aims to achieve the following: there exists a time constant T that can be arbitrarily set in advance. p This makes the following equation true:

[0164]

[0165] Among them, when When, x0 = [x 01 ,x 02 ] T ;when When, x0 = [x 01 ,x 02 ,x 03 ] T .

[0166] Based on the fault-tolerant agent-driven all-drive system model, the distributed fault-tolerant controller can be designed as follows:

[0167]

[0168] Among them, a i0 and a i1 They are two positive numbers, when hour, yes Estimates for j = 1, 2; when hour, yes estimates of j = 1, 2, 3;

[0169]

[0170] φ i1 and φ i2 are determined by equations (17) - (21) :

[0171]

[0172]

[0173]

[0174]

[0175]

[0176] where k is a constant; when , a i = 2; when , a i = 3.

[0177] when , π i11 , π i12 , π i21 , π i22 are elements of the vector Π i , Π i = [π i11 , π i12 , π i21 , π i22 ] T ; when , π i11 , π i12 , π i13 , π i21 , π i22 , π i23 are elements of the vector Π i , Π i = [π i11 , π i12 , π i13 , π i21 , π i22 , π i23 ] T .

[0178] The adaptive update law for the estimates of the actuator failure coefficients is:

[0179]

[0180] wherein,

[0181]

[0182]

[0183] wherein, p is a sufficiently small positive number and satisfies p << p ij , β ij is a positive number, g 12 and g 22 are elements of a positive definite matrix G, G = [g 11 , g 12 ; g 21 , g 22 ].

[0184] The following provides a proof process that the designed decentralized fault-tolerant controller can achieve the preset time formation control of the heterogeneous multi-agent system.

[0185] According to the defined formation error, the agent formation error dynamics expression can be obtained as follows:

[0186]

[0187] When t ∈ [T3, T p ), the decentralized fault-tolerant controller (16) is substituted into the formation error dynamics expression (23) and the can be obtained

[0188]

[0189] wherein, A ic = [0, 1; -a i0 , -a i1 ], when , j = 1, 2; when , j = 1, 2, 3.

[0190] The Lyapunov function of the ith follower closed-loop system at t ∈ [T3, T p ) can be selected as:

[0191]

[0192] Taking the derivative of V i1 can be obtained:

[0193]

[0194] wherein, γi is a constant.

[0195] V i2 The derivative of Φ

[0196]

[0197] Considering the adaptive update law (22), we have

[0198]

[0199] Further,

[0200]

[0201] From (29), we have

[0202]

[0203] Since we have

[0204] When t∈[T p ,∞), substituting the decentralized fault-tolerant controller (16) into the platoon error dynamics (23), we have

[0205]

[0206] The Lyapunov function of the ith follower closed-loop system at t∈[T p ,∞) is We can choose

[0207]

[0208] is the short form of Similarly, is the short form of and is the short form of

[0209] The derivative of (31) is

[0210]

[0211] According to (19), we have p = 0, Therefore, i = 0. Further, and According to (32), we have

[0212] ​

[0213] Therefore,

[0214] In summary, under the action of the proposed decentralized fault-tolerant controller, the formation error of the system tends to zero within the preset time T p , and when the time is greater than the preset time T p , the formation error is always zero.

[0215] The above designed decentralized fault-tolerant controller (16) can realize that the heterogeneous multi-agent system converges to 0 within the preset time T p and the actuator fault estimation error is bounded.

[0216] The control parameters a i0 and a i1 and the matrix G can be obtained by the following steps:

[0217] D1, select any negative definite matrix

[0218] D2, select a matrix such that Δ(Z i ,F i )=[Z i ;Z i F i ] and det(Δ)≠0;

[0219] D3, calculate [a i0 ,a i1 ]=-Z i F i 2 Δ -1 (Z i ,F i ) and A ic =[0,1;-a i0 ,-a i1 ];

[0220] D4, according to and get and

[0221] D5, select any positive definite matrix can get where

[0222] In this embodiment, an unmanned aerial vehicle is taken as a virtual leader, two unmanned ground vehicles (i=1, 2) and two unmanned aerial vehicles (i=3, 4) are taken as followers to form an air-ground heterogeneous formation system, and the structure of the whole formation system is as follows Figure 2As shown, the communication topology between followers is as follows: Figure 3 As shown, the communication connection weights between the agents are 0 or 1.

[0223] Depend on Figure 2 We can obtain the matrix sum matrix as follows:

[0224]

[0225]

[0226] The initial state of each follower is: x1 = [1.3, 0] T , x2 = [1.6, 0] T , x3 = [1.8, 0, 0] T , x4 = [2.1, 0, 0] T , The leader's trajectory is x0 = [sin(0.5t), cos(0.5t), 0.5t] T The desired formation distance is set to: h i =col{0.5i}.

[0227] Consider the following fault scenarios:

[0228]

[0229]

[0230]

[0231]

[0232] Choose time parameters as T1 = 0.3s, T2 = 0.6s, T3 = 1s, T... p =6s, observer parameters are k=1, c=2.7, δ=0.5. Choosing matrices F=diag(-2,-1), Z=[-1,1], W=I2, the control parameter a can be obtained. i0 =2 and a i0 =3, A ic =[0,1;-2,-3] and G=[1.25,0.25;0.25,0.25]. The adaptive parameter is chosen as: β 11 =9.5, β 12 =12,β 21 =9.3, β 22 =2.9, β 31 =1.8, β32 = 0.7, β 33 = 4, β 41 = 10, β 42 = 2.6, β 43 = 2. The initial value of the fault estimation is set as:

[0233] To verify the effect of the air-ground cooperative fault-tolerant control strategy based on the full-drive system method of the application, a corresponding program is written in MATLAB for simulation verification:

[0234] Figures 4-12 The real-time observation of the expected motion trajectory information provided by the leader by the distributed preset time observer designed in the application is presented, and it can be seen that the acceleration, speed and position observation errors remain zero after preset times T1, T2 and T3, respectively.

[0235] Figures 13-16 The performance of the decentralized fault-tolerant controller designed in the application is presented.

[0236] Figures 17-20 The estimation of the actuator fault coefficient is presented.

[0237] From the simulation results, it can be seen that the preset time fault-tolerant formation control method based on the full-drive system model of the application can enable the air-ground full-drive heterogeneous formation system composed of multiple unmanned ground vehicles and multiple unmanned aerial vehicles to quickly form the expected formation and stably maintain under the condition of actuator failure, which confirms that the designed preset time observer plays a good role in estimating the expected motion trajectory information of the virtual leader, the designed adaptive update law can well estimate the system actuator fault coefficient, and the reconstructed controller enables the designed decentralized controller to have good robustness and fault tolerance, so it can be concluded that the air-ground cooperative formation system composed of multiple unmanned ground vehicles and multiple unmanned aerial vehicles can achieve the expected formation task by using the decentralized adaptive fault-tolerant formation controller designed based on the full-drive system model of the application under the condition of actuator failure.

[0238] The embodiments of the application are described in detail above in combination with the drawings, but the application is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the purpose of the application.

Claims

1. A full-drive heterogeneous multi-intelligent system preset time cooperative fault-tolerant method, characterized in that, The steps include the following: S1, a virtual unmanned aerial vehicle is constructed as a virtual leader, which provides expected motion trajectory information; the follower includes a unmanned ground vehicle and a unmanned aerial vehicle, which uses graph theory knowledge to establish information interaction characteristics between the leader and the follower and between the followers; a unmanned aerial vehicle, which uses graph theory knowledge to establish information interaction characteristics between the leader and the follower and between the followers; S2, a point is randomly selected on the ground to establish a three-dimensional rectangular coordinate system, the motion characteristics of the unmanned ground vehicle and the unmanned aerial vehicle are analyzed, the full-drive system model of the unmanned ground vehicle and the full-drive system model of the unmanned aerial vehicle are established; by analyzing the influence of the fault on the performance of the system, a fault model is constructed, and finally the full-drive system model of the heterogeneous multi-agent system under the fault is obtained; S3, based on the interaction characteristics of individuals in the heterogeneous multi-agent system, a distributed preset time observer is constructed to realize the tracking of the expected motion trajectory information provided by the leader within the preset time; the estimation values of the expected position information, speed information and acceleration information provided by the leader for the first agent are defined as , , and , respectively. The distributed preset time observer is designed as follows: wherein , and are normal numbers, and , denotes the third derivative of , and are three different time constants, and satisfy ; Selection parameter Such that it satisfies Where Is a constant, then in a predetermined time Within ; definition , , , ,in , and They are respectively the i-th unmanned ground vehicle to the leader in Estimation of the position, velocity, and acceleration of the shaft. , and They are respectively the i-th unmanned ground vehicle to the leader in Estimation of the position, velocity, and acceleration of the shaft; S4, combined with the full-drive system theory and the preset time convergence theory, the real-time observation information of the expected motion trajectory information provided by the leader and the position information of the self are used to design a decentralized fault-tolerant formation controller by using the distributed preset time observer; the preset time cooperative formation control of the follower positions of the unmanned ground vehicle and the unmanned aerial vehicle under the influence of the actuator fault is realized by the decentralized fault-tolerant formation controller.

2. The preset time cooperative fault-tolerant control method for the heterogeneous multi-intelligent system according to claim 1, characterized in that, In step S1, the motion trajectory information includes position information, velocity information and acceleration information, respectively defined as , and , , and represent the position of the leader on the axis, axis and axis, respectively, represents all real numbers, and the superscript T represents matrix transposition; The unmanned ground vehicle collection is defined as ; An unmanned vehicle collection is defined as ; A heterogeneous multi-agent system set is defined as ; The connections between all followers are represented by a directed graph. It means that, among them , Indicates the first One follower This indicates the total number of followers. , Represents an edge set. Indicates follower Able to acquire followers Information; The connection matrix has non-negative weights. For the real number field, when , ,when , ; The Laplacian matrix is defined as where and .

3. The preset time cooperative fault-tolerant control method for the heterogeneous multi-intelligent system according to claim 2, characterized in that, The information interaction characteristics between the leader and the follower are represented by , where the leader's information is received by the th follower if and only if ; otherwise ; The information exchange matrix of the whole heterogeneous multi-agent system is defined as ; There is a positive diagonal matrix such that where , is a column vector with all elements equal to 1.

4. The preset time cooperative fault-tolerant control method for the heterogeneous multi-intelligent system according to claim 1, characterized in that, In step S2, the full-drive system model of the unmanned ground vehicle is as follows: wherein, , and denote the position of the unmanned ground vehicle i in the axis and axis, respectively; , and denote the control input of the unmanned ground vehicle i in the axis and axis, respectively; , denotes the distance of the unmanned ground vehicle i from a reference position to an inertial position, denote the velocity, angular velocity and orientation of the unmanned ground vehicle i, respectively; The full-drive system model of the unmanned aerial vehicle is as follows: wherein, , , and denote the position of the unmanned vehicle i in axis, axis and axis respectively; the air resistance vector is , define three new variables and let , , the drag coefficient , the mass of the unmanned vehicle i , , , is the gravitational acceleration; ; , , and denote the control input of the unmanned vehicle i in axis, axis and axis respectively; The fault model is: wherein, , , and, respectively represent the output and input of the th actuator of the th agent at time t, when , , , ; when , ; represents the performance factor of the actuator, which satisfies wherein is a positive constant; Faulty under the first Intelligent agent full drive system model described as: wherein when , , , , , , and denote the control input of the i-th follower in the axis and the axis, respectively; when , , , , , , , and denote the control input of the i-th follower in the axis, axis and axis, respectively.

5. The preset time cooperative fault-tolerant control method for the heterogeneous multi-intelligent system according to claim 1, characterized in that, In step S4, based on the accurate estimation of the expected motion trajectory information provided by the leader by the preset time observer, the formation error is defined as: wherein is the desired platoon distance; since so ; The air-ground cooperative preset time formation problem is that there is a time constant that can be set in advance so that the following formula is established: wherein when , when , .

6. The preset time cooperative fault-tolerant control method of the heterogeneous multi-intelligent system according to claim 1, characterized in that, In step S4, the decentralized fault-tolerant controller designed based on the full-drive system model of the agent under the fault is as follows: and are two positive constants, when , , is an estimate of ; when , , is an estimate of , and is determined by the equation: is a positive constant, when , ; when , ; When , , , , is an element of the vector , ; when , , , , , , is an element of the vector , ; The adaptive update law of the estimated value of the actuator fault coefficient is: wherein, is a normal number sufficiently small and satisfies , is a normal number, , , and are the elements of the positive definite matrix , .

7. The preset time cooperative fault-tolerant control method of the heterogeneous multi-intelligent system according to claim 6, characterized in that, Control parameters and and matrix obtained from the following steps: SD1, select any negative definite matrix ; SD2, select a matrix such that and ; SD3, compute , ; SD4, according to and obtained and ; SD5, select any positive definite matrix , obtain wherein .

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