A collaborative fault-tolerant control method for underwater robots

Abstract

The present invention discloses a collaborative fault-tolerant control method for an underwater robot, comprising the following steps: S1. Establishing the kinematic equations for the i-th underwater robot; S2. Based on the established kinematic equations for the underwater robot, setting five interrelated and influential primary indicators and establishing an indicator system, wherein the five primary indicators each contain a number of secondary indicators; S3. Using the DEMATEL method to obtain a direct influence matrix and the influence strength between the indicators, a comprehensive influence matrix is ​​calculated; S4. Based on the obtained comprehensive influence matrix, the local and overall weights of each indicator are determined using the ANP network analysis method; S5. Establishing a fault model with fault distribution characteristics based on the weights; S6. Designing an underwater robot controller based on the fault model. This method is applied to a multi-underwater robot system with topology switching, time-varying delays, and actuator failures. Using historical fault information combined with the DEMATEL-ANP method, the fault distribution characteristics are traced, resulting in a more realistic random fault model.

Description

Technical Field

[0001] The present invention relates to the technical field of fault-tolerant control, and in particular to a collaborative fault-tolerant control method for an underwater robot. Background Art

[0002] In recent decades, underwater robotics (AUVs) have rapidly developed, making significant progress in fields such as ocean exploration and underwater surveillance. Compared to single-robot systems, multi-robot systems offer irreplaceable advantages in terms of collaboration, distribution, intelligence, and safety. Multi-robot systems emphasize collaborative cooperation and interactive communication between robots. These characteristics enable them to improve efficiency and accuracy in dynamic underwater environments, conserve resources, and demonstrate exceptional adaptability to complex and challenging conditions. Research on the collaborative control of multi-robot systems provides a more practical and effective tool for exploring underwater environments. It is an inevitable trend in the development of underwater vehicles and holds significant scientific and application value.

[0003] As multiple underwater robots are applied in various fields, their complexity and control precision requirements are increasing. In real underwater environments, time delays in the controllers, actuators, and communication systems of multi-underwater robot control systems are common and can even occur when system components fail. In complex underwater environments, the transmission of status information such as the position and speed of each underwater robot may be restricted or even interrupted. The introduction of topology switching technology alleviates communication connectivity issues between underwater robots.

[0004] As the number of underwater robots increases, the probability of control system failure increases significantly. A single component failure can impact the performance of the entire system, even leading to system crashes. In real-world operating environments, actuators can suffer from damage, displacement, or partial failure.

[0005] In actual projects, it can be found that the occurrence of faults does not simply follow a uniform distribution. In many cases, the probability of minor faults is much higher. Therefore, the currently commonly used fault-tolerant systems are still unable to achieve true fault tolerance. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this paper presents a retrospective fault-tolerant control method for a multi-underwater robot system subject to topology switching, time-varying delays, and actuator failures. By combining historical fault information with the DEMAEL-ANP method, the distributed characteristics of the faults are traced, and a more realistic random fault model is established. By constructing a Lyapunov-Krasovskii function based on the model, a design method for a retrospective fault-tolerant controller is derived, and the system's convergence and stability are demonstrated.

[0007] In order to solve the above technical problems, the technical solution of the present invention is:

[0008] A collaborative fault-tolerant control method for an underwater robot comprises the following steps:

[0009] S1. Establish the kinematic equation of the i-th underwater robot, which is described as follows:

[0010]

[0011] S2. Based on the established underwater robot, set five interrelated and influential first-level indicators of "control-communication-emergency-navigation-energy supply" and establish an indicator system, in which the five first-level indicators each include several second-level indicators;

[0012] S3. Use the DEMATEL method to obtain the direct impact matrix and the impact intensity between indicators, and calculate the comprehensive impact matrix;

[0013] S4. Determine the local and overall weights of each indicator through the ANP network analysis method based on the obtained comprehensive impact matrix;

[0014] S5. Establishing a fault model with fault distribution characteristics according to the weights;

[0015] S6. Design the underwater robot controller based on the fault model.

[0016] Preferably, the control of the first-level indicators includes five second-level indicators: stern thruster, bow thruster, auxiliary thruster horizontal rudder, and rudder; communication includes three second-level indicators: digital radio, wireless network, and positioning sonar; emergency includes four second-level indicators: buoyancy adjustment device, high air pressure device, load jettisoning device, and protective pressure device; navigation includes six second-level indicators: GPS receiver, motion sensor, Doppler speed meter, temperature and salt probe, altimeter sonar, and navigator; energy supply includes three second-level indicators: current monitoring, instrument battery pack, and power battery pack.

[0017] Preferably, the method for obtaining the comprehensive impact matrix in step S3 is:

[0018] Establish direct impact matrix B:

[0019]

[0020] The normalized direct impact matrix B is obtained by normalizing the direct impact matrix X

[0021] X=s·B (3)

[0022] in, It means taking the maximum value of the sum of each row and column values, and taking the minimum value of the reciprocal;

[0023] The relationship matrix T can be calculated from X:

[0024]

[0025] Take r i , c j are the sums of the rows and columns in T respectively:

[0026]

[0027] r i The influence degree refers to the sum of the influence of the corresponding indicators of each row on other indicators, c j The degree of influence refers to the sum of the influence of other indicators on the j-column indicators. When i=j, r i -c j is the centrality, r i +c j is the cause degree, r i -c j The larger the value, the more important the indicator i is in the system. i +c j It refers to the degree of causal logical relationship between indicator i and other indicators. If it is greater than 0, it means that the indicator affects other indicators, and if it is less than zero, it means that the indicator is affected by other indicators. Set a threshold as μ, and the comprehensive influence matrix after setting is recorded as T μ .

[0028] Preferably, the method for analyzing the weights by the ANP network analysis method in step S4 is as follows:

[0029] Comprehensive impact matrix T μ The unweighted supermatrix Z is as follows:

[0030]

[0031] in, For the nth element group, if If it is not affected by other element groups, there is no need to establish a pairwise comparison matrix, and there is no direct influence between indicators, that is, b ij =0;

[0032] Calculate the weight matrix T s , for T μ Perform normalization and multiply the jth column by α i , get T s :

[0033]

[0034] The unweighted matrix Z and the normalized T s Multiply them together to get the weighted super matrix W a :

[0035]

[0036] Taking whether the weighted matrix is ​​a random irreducible matrix and a prime matrix as the iteration condition, a Iterate and finally get the steady-state matrix, that is, the limiting supermatrix W * :

[0037]

[0038] Take the column where the global variable is located as a column vector The mixed weight l can be obtained from formula (8):

[0039]

[0040] Preferably, in step S5, a fault model with fault distribution characteristics is established, and the expression is as follows:

[0041]

[0042] m ij (t) represents the partial function failure rate of the jth subsystem of the i-th robot.

[0043] As an advantage, in the fault model, m ij When (t)=1, it indicates that the robot is working normally. It indicates that some functions of the jth subsystem of the i-th robot have failed. and Indicates m ij (t) Upper and lower bounds; By defining a series of variables, the fault model with fault distribution characteristics can be restated as:

[0044]

[0045] Preferably, in step S6, the controller of the i-th robot is designed as follows:

[0046]

[0047] in is the controller gain matrix, Δa ij (t) is a bounded function, which represents the communication uncertainty between the i-th robot and the j-th robot. The corresponding Laplace transform form is: τ(t) is a time-varying function that satisfies:

[0048] Preferably, if any initial position and velocity state of the underwater robot system of the controller satisfies the following formula, the multi-underwater robot system achieves consistency, which is expressed as follows:

[0049]

[0050] Define the motion state vector of the i-th robot at time t as The motion state equation of the i-th robot is:

[0051]

[0052] The average state vector of the i-th robot is defined as but:

[0053]

[0054] The error state vector is defined as:

[0055]

[0056] The state error equation of the multi-underwater robot system is:

[0057]

[0058] in

[0059]

[0060] Preferably, step S7 is also included, which provides proof of fault-tolerant consistency:

[0061] Consider the nominal system situation ΔB=0, Δa ij (t)=0,Δl ij (t) = 0, the kinematic equations of the multi-underwater robot with error state vectors are fault-tolerant and consistent;

[0062] For the uncertain topology Δa ij ≠0, the kinematic equations of the multi-underwater robot proposed in the controller have fault-tolerant consistency.

[0063] The present invention has the following characteristics and beneficial effects:

[0064] The above technical solution, using historical fault information combined with the DEMATEL-ANP method, traces the distribution characteristics of faults and establishes a more realistic random fault model. By constructing the Lyapunov-Krasovskii function from the model, a design method for a backtracking fault-tolerant controller is derived, which exhibits excellent fault tolerance. When a complex underwater robot is operating underwater, if some components fail, or when a large number of underwater robots are working together underwater, if individual robots fail, the entire system can still maintain normal underwater operations. The introduction of fault-tolerant control ensures system stability and preserves some of its performance in the event of a fault. Fault-tolerant control also enhances system robustness and prevents minor faults from escalating into larger ones. Furthermore, since faults do not follow a uniform distribution, and in many cases, minor faults are much more likely to occur, the DEMATEL-ANP method introduces the concept of failure factors, enabling a more realistic and accurate partial failure model for underwater robot actuators. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0066] Figure 1 , safety and reliability index system of underwater robots according to embodiments of the present invention.

[0067] Figure 2 , four topological structures in the embodiments of the present invention.

[0068] Figure 3 , topology switching in the embodiments of the present invention.

[0069] Figure 4 , the lateral posture of the multi-underwater robot system in the embodiment of the present invention.

[0070] Figure 5 , the longitudinal posture of the multi-underwater robot system in the embodiment of the present invention.

[0071] Figure 6 , the depth posture of the multi-underwater robot system in the embodiment of the present invention.

[0072] Figure 7 , the pitch and roll posture of the multi-underwater robot system in the embodiment of the present invention.

[0073] Figure 8 , the yaw posture of the multi-underwater robot system in the embodiment of the present invention.

[0074] Figure 9 , the lateral speed of the multi-underwater robot system in the embodiment of the present invention.

[0075] Figure 10 , the longitudinal speed of the multi-underwater robot system in the embodiment of the present invention.

[0076] Figure 11 , vertical speed of the multi-underwater robot system in the embodiment of the present invention.

[0077] Figure 12 , the pitch angular velocity of the multi-underwater robot system in the embodiment of the present invention.

[0078] Figure 13 , the yaw angular velocity of the multi-underwater robot system in the embodiment of the present invention.

[0079] Figure 14 , three-dimensional trajectory of the multi-underwater robot system in an embodiment of the present invention. DETAILED DESCRIPTION

[0080] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other.

[0081] This embodiment provides a collaborative fault-tolerant control method for an underwater robot, comprising the following steps:

[0082] Step (1) Take the kinematic equation of the i-th underwater robot as follows:

[0083]

[0084] Step (2) establishes an indicator system with the first-level indicators of “control-communication-emergency-navigation-energy supply” which are interrelated and have an impact on each other, such as Figure 1 As shown;

[0085] First-level indicators are established in five aspects: robot control (C), communication (M), emergency (T), navigation (E), and energy supply (O). Among them, control includes five second-level indicators: stern thruster, bow thruster, auxiliary thruster horizontal rudder, and rudder; communication includes three second-level indicators: digital radio, wireless network, and positioning sonar; emergency includes four second-level indicators: buoyancy adjustment device, high air pressure device, load jettisoning device, and protective pressure device; navigation includes six second-level indicators: GPS receiver, motion sensor, Doppler speedometer, temperature and salt probe, altimeter sonar, and navigator; energy supply includes three second-level indicators: current monitoring, instrument battery pack, and power battery pack.

[0086] Step (3) obtain the direct impact matrix and the impact intensity between indicators through the DEMATEL method, and calculate the comprehensive impact matrix;

[0087] After processing the expert survey data, the direct impact matrix B is established:

[0088]

[0089] Among them, b ij Indicates the influence of index i on index j. When i=j, b ij = 0. The direct influence matrix B is normalized to obtain the normalized direct influence matrix X.

[0090] X=s·B (3)

[0091] in, It means taking the maximum value of the sum of each row and column value, and taking the minimum value of the reciprocal. The relationship matrix T can be calculated by X:

[0092]

[0093] Take r i , c j are the sums of the rows and columns in T respectively:

[0094]

[0095] r i The influence degree refers to the sum of the influence of the corresponding indicators of each row on other indicators, c j is the degree of influence, which refers to the sum of the influence of other indicators on the j-column indicators. When i=j, r i -c j is the centrality, r i +c j For the reason degree. i -c j The larger the value, the more important the indicator i is in the system. i +c j It refers to the degree of causal logical relationship between indicator i and other indicators. If it is greater than 0, it means that the indicator affects other indicators, and if it is less than zero, it means that the indicator is affected by other indicators. A threshold is set as μ to eliminate the smaller values ​​in the total influence matrix and simplify the network. The comprehensive influence matrix after setting is recorded as T μ .

[0096] Step (4) ANP network analysis method is used to determine the weights of the local and overall components;

[0097] The indicators are compared pairwise, and the importance levels are shown in Table 1. The unweighted supermatrix Z is as follows:

[0098]

[0099] Table 1 ANP evaluation scale

[0100]

[0101]

[0102] in, For the nth element group, if If it is not affected by other element groups, there is no need to establish a pairwise comparison matrix, and there is no direct influence between indicators, that is, b ij =0.

[0103] Calculate the weight matrix T s . μ Perform normalization and multiply the jth column by α i , get T s :

[0104]

[0105] The unweighted matrix Z and the normalized T s Multiply them together to get the weighted super matrix W a :

[0106]

[0107] Taking whether the weighted matrix is ​​a random irreducible matrix and a prime matrix as the iteration condition, a Iterate and finally get the steady-state matrix, that is, the limiting supermatrix W * :

[0108]

[0109] Take the column where the global variable is located as a column vector The mixed weight l can be obtained from formula (8):

[0110]

[0111] Establish through steps (3) and (4) Figure 1 The mutual influence relationship between the 5 first-level indicators and 21 second-level indicators is used to construct a network structure. Based on the data provided by deep-sea base experts, the comprehensive influence matrix between the first-level and second-level indicators can be obtained by combining equations (2)-(4), as shown in Tables 2 and 3:

[0112] Table 2 Mutual influence matrix among first-level indicators

[0113]

[0114]

[0115] Table 3 Mutual influence matrix among secondary indicators

[0116]

[0117]

[0118] The mixed weights of all indicators can be obtained from formula (12) as shown in Table 4:

[0119] Table 4 Mixed weights of indicators

[0120]

[0121]

[0122] From the normalized mixed weights in Table 4, it can be seen that the proportion of the control system in the underwater robot system is 0.30104, which shows that the control system is very important for the normal operation of the underwater robot system.

[0123] Step (5) establishing a fault model of fault distribution characteristics;

[0124]

[0125] m ij (t) represents the partial function failure rate of the jth subsystem of the i-th robot, m ij When (t)=1, it indicates that the robot is working normally. It indicates that some functions of the jth subsystem of the i-th robot have failed. and Indicates m ij (t) Upper and lower bounds.

[0126] According to the characteristics of the fault, set the scalar The faults can be differentiated. Indicates a serious malfunction. Indicates a minor malfunction. It can be restated as:

[0127]

[0128] When no fault occurs or a subsystem fails, it is considered a minor fault. ij (t) is the failure factor, and but:

[0129]

[0130] Define the following variables:

[0131]

[0132]

[0133] Θ i (t) = diag{θ i1 (t),…,θ is (t)}

[0134] ρ i (t) = diag{ρ i1 (t),…,ρ is (t)}

[0135]

[0136] but

[0137]

[0138] Among them, ρ i (t) with For unknown variables, define:

[0139]

[0140] but

[0141]

[0142] definition

[0143] D0=diag{ρ 10 ,ρ 20 ,…,ρ n0}

[0144]

[0145] G(t)=diag{g1(t),g2(t),…,g n (t)}

[0146]

[0147] G(t)|=diag{g1(t)|,|g2(t)|,…,|g n (t)|}

[0148]

[0149] Θ(t)=diag{Θ1(t),Θ2(t),…,Θ n (t)}

[0150] H=diag{h1,h2,…,hn}

[0151]

[0152] Then the fault model can be restated by the above variables as:

[0153]

[0154] Step (6) designing an underwater robot controller;

[0155] The controller design of the i-th robot is as follows:

[0156]

[0157] in is the controller gain matrix, Δa ij (t) is a bounded function, which represents the communication uncertainty between the i-th robot and the j-th robot. The corresponding Laplace transform form is: τ(t) is a time-varying function that satisfies:

[0158] If any initial position and velocity state of the underwater robot system satisfies the following equation, the multi-underwater robot system achieves consistency.

[0159]

[0160] Define the motion state vector of the i-th robot at time t as The motion state equation of the i-th robot is:

[0161]

[0162] The average state vector of the i-th robot is defined as but:

[0163]

[0164] The error state vector is defined as:

[0165]

[0166] The state error equation of the multi-underwater robot system is:

[0167]

[0168] in

[0169]

[0170] Step (7) considers the nominal system case (ΔB=0, Δaij (t)=0,Δl ij (t)=0), a multi-underwater robot system (1) with a fault-tolerant controller (15) is proposed to have fault-tolerant consistency;

[0171] Theorem 1: Assume that the graph G is a directed graph and consider the multi-underwater vehicle system (1) with a fault-tolerant controller (15). Given the failure matrix If there is a matrix And the positive scalar ò>0, so that the following linear matrix inequality (LMI) holds true, then the multi-underwater robot system composed of (1) can achieve fault-tolerant consistency.

[0172]

[0173] in

[0174]

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181]

[0182] Step (8) prove Theorem 1;

[0183] Consider the following Lyapunov function

[0184]

[0185] Where P, Q, and R are positive definite symmetric matrices, and the derivative of V(t) is:

[0186]

[0187]

[0188]

[0189]

[0190] in

[0191]

[0192] The matrix M1 is multiplied on the left and right by diag(X1,X1,X1), according to the inequality -R -1 ≤R-2I, let have to:

[0193]

[0194] in Y=BX1. ρ is an unknown variable, and using formula (14) we can get:

[0195]

[0196] in

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206] The gain K can be obtained by (27).

[0207] Step (9) for the uncertain topology (Δa ij ≠0), a multi-underwater robot system (1) with a fault-tolerant controller (15) is proposed to have fault-tolerant consistency;

[0208] Theorem 2: For uncertain topology (Δa ij ≠0), and the Laplace matrix form is represented by ΔL. Assuming that the graph G is a directed graph, consider a multi-underwater vehicle system (1) with a fault-tolerant controller (15) and time-varying delays and uncertain topology. Given the failure matrix If there is a matrix And the positive scalar 1tad,2>0, so that the following linear matrix inequality (LMI) holds true, then the multi-underwater robot system composed of (1) can achieve fault-tolerant consistency.

[0209]

[0210] in

[0211]

[0212]

[0213]

[0214]

[0215]

[0216]

[0217]

[0218]

[0219]

[0220] Step (10) proves Theorem 2;

[0221] The conclusion drawn in Theorem 1 is based on the premise that ΔL = 0, that is:

[0222]

[0223] in

[0224]

[0225]

[0226]

[0227]

[0228] When ΔL≠0, Δa in formula (15) ij Corresponding to ΔL, ΔL=E1Σ(t)E2, where represent constant matrices, It is a diagonal matrix whose diagonal elements represent the uncertainty of the edge, that is, the non-zero matrix Δa ij . Define the kth diagonal element of Σ(t) as Δa ikjk (k=1,…,|ε|) and i k ,j k ∈1,…,n.|Δa ikjk |≤Ψ ikjk ,|Δa ikjk | / Ψ ikjk≤1,Σ(t) can be written as Among them, Δ and are diagonal matrices, whose k-th diagonal elements are equal to Ψ ikjk and |Δa ikjk | / Ψ ikjk .but And ΔL=E1Ψ Δ Σ(t)E2. Therefore, to simplify the analysis, assume that Ψ ikjk =1,

[0229] By the Schur-procedure lemma: for matrices Γ, Λ and matrices Υ of appropriate dimensions, Υ=Υ T , then for any matrix F that satisfies F T (k)F(k)≤I, so that the inequality:

[0230] Υ+ΓF(k)Λ+Λ T F T (k)Γ T <0

[0231] If and only if there exists a positive scalar σ>0 such that Υ+σΓΓ T +σ -1 Λ T Λ<0 or

[0232]

[0233] Available

[0234]

[0235] Established.

[0236] in

[0237]

[0238]

[0239]

[0240]

[0241]

[0242]

[0243]

[0244]

[0245]

[0246]

[0247]

[0248]

[0249] The gain K can be obtained by (31).

[0250] Assumptions It is possible to obtain F2≤I.

[0251] Based on the above information, it can be concluded that when t→∞, all underwater robots have fault-tolerant consistency. The following simulation example verifies the effectiveness of the fault-tolerant control design method;

[0252] Five underwater robots were used as the experimental group. Their speeds were randomly distributed in the interval [0, 50]. The pitch and yaw angles were randomly distributed in the interval (-π / 3, π / 3). The initial value of all speeds was 0.5 m / s. The time-varying delay function was τ(t) = 10(1 + sin(2t)). The robot failure distribution is:

[0253]

[0254] E{θ 12 (t)=1}=0.27,E{θ 35 (t) = 1} = 0.34

[0255] E{θ 42 (t)=1}=0.46,E{θ 43 (t) = 1} = 0.62

[0256]

[0257]

[0258] Four topologies of the multi-underwater robot system and the corresponding Laplace matrices L1, L2, L3, and L4. Assuming that the weight of each edge is 1, the Laplace matrix L i , i=1,2,3,4 is described as Figure 2 shown.

[0259] The Laplace matrix of L1 is:

[0260]

[0261] According to Theorem 2, the controller gain matrix K is:

[0262] K=diag(0.7102,1.0059,0.7871,0.4219,0.3412).

[0263] Figure 3 It is a topology switching diagram, indicating that the system is in an uncertain topology situation.

[0264] according to Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 It is the posture change of each member of the experimental group during the convergence process. It can be seen that when some functions of the actuator are reduced, the posture state can still achieve consistency, proving that the controller (15) is effective.

[0265] Figure 9 、 Figure 10 、 Figure 11 、 Figure 12 、 Figure 13 It is the speed change of each member of the experimental group during the convergence process. It can be seen that when the function of some actuators decreases, the speed state can still achieve consistency, proving that the controller (15) is effective.

[0266] Figure 14 This is the three-dimensional trajectory of the experimental group under uncertain transformation topology conditions. It can be seen that in the case of partial failure of the actuator and time-varying delay, the system has good fault tolerance and maintains the same state and continues to move after convergence.

[0267] It can be seen from the simulation experiment diagram that the controller gain obtained by Theorem 2 can still achieve fault-tolerant consistency in the case of actuator failure and time-varying delay in the multi-underwater human system. The robot state converges quickly within 60-80 seconds and maintains the same state for continuous movement.

[0268] This example presents a backtracking fault-tolerant control method for a multi-AUV system with topology switching, time-varying delays, and actuator failures. First, the fault characteristics are derived using the AUV fault history information and the DEMATEL-ANP method. Then, based on the fault characteristics, a fault model for the multi-AUV system is established, and the topology switching problem is transformed into a graph uncertainty problem. A backtracking fault-tolerant controller is designed using the Lyapunov-Krasovskii function, and the fault-tolerant consistency of the controller for the AUV system with topology switching is demonstrated. Finally, simulation experiments verify the effectiveness of the proposed method.

[0269] While the embodiments of the present invention have been described in detail above with reference to the accompanying drawings, the present invention is not limited to the described embodiments. It will be apparent to those skilled in the art that various changes, modifications, substitutions, and variations of these embodiments, including components, may be made without departing from the principles and spirit of the present invention and still fall within the scope of protection of the present invention.

Claims

1. A collaborative fault-tolerant control method for an underwater robot, characterized in that: The following steps are involved: S1. Establish the kinematic equation of the i-th underwater robot, which is described as follows: S2. Based on the established underwater robot, set five interrelated and influential first-level indicators: "control - communication - emergency response - navigation - energy supply", and establish an indicator system, where the five first-level indicators each include several second-level indicators; S3. Use the DEMATEL method to obtain the direct impact matrix and the impact intensity between indicators, and calculate the comprehensive impact matrix; S4. Determine the local and overall weights of each indicator through the ANP network analysis method based on the obtained comprehensive impact matrix; S5. Establishing a fault model with fault distribution characteristics according to the weights; Establish a fault model with fault distribution characteristics, the expression is as follows: m ij (t) represents the partial function failure rate of the jth subsystem of the i-th robot; In the fault model, m ij When (t)=1, it indicates that the robot is working normally. It indicates that some functions of the jth subsystem of the i-th robot have failed. and Indicates m ij (t) Upper and lower bounds; By defining a series of variables, the fault model with fault distribution characteristics can be restated as: S6. Design the underwater robot controller based on the fault model.

2. The collaborative fault-tolerant control method of an underwater robot according to claim 1, characterized in that: Among the first-level indicators, control includes five second-level indicators: stern thruster, bow thruster, auxiliary thruster horizontal rudder, and rudder; communication includes three second-level indicators: digital radio, wireless network, and positioning sonar; emergency includes four second-level indicators: buoyancy adjustment device, high air pressure device, load jettisoning device, and protective pressure device; navigation includes six second-level indicators: GPS receiver, motion sensor, Doppler speedometer, temperature and salt detector, altimeter sonar, and navigator; energy supply includes three second-level indicators: current monitoring, instrument battery pack, and power battery pack.

3. The collaborative fault-tolerant control method of an underwater robot according to claim 2, characterized in that: The method for obtaining the comprehensive impact matrix in step S3 is as follows: Establish direct impact matrix B: The normalized direct impact matrix B is obtained by normalizing the direct impact matrix X X=s·B (4) in, It means taking the maximum value of the sum of each row and column values, and taking the minimum value of the reciprocal; The relationship matrix T can be calculated from X: Take r i , c j are the sums of the rows and columns in T respectively: r i The influence degree refers to the sum of the influence of the corresponding indicators of each row on other indicators, c j The degree of influence refers to the sum of the influence of other indicators on the j-column indicators. When i=j, r i -c j is the centrality, r i +c j is the cause degree, r i -c j The larger the value, the more important the indicator i is in the system. i +c j It refers to the degree of causal logical relationship between indicator i and other indicators. If it is greater than 0, it means that the indicator affects other indicators. If it is less than zero, it means that the indicator is affected by other indicators. Set a threshold as μ, and the comprehensive influence matrix after setting is recorded as T μ .

4. The collaborative fault-tolerant control method of an underwater robot according to claim 3, characterized in that: The method for analyzing the weights by the ANP network analysis method in step S4 is as follows: Comprehensive impact matrix T μ The unweighted supermatrix Z is as follows: in, For the nth element group, if If it is not affected by other element groups, there is no need to establish a pairwise comparison matrix, and there is no direct influence between indicators, that is, b ij =0; Calculate the weight matrix T s , for T μ Perform normalization and multiply the jth column by α i , get T s : The unweighted matrix Z and the normalized T s Multiply them together to get the weighted super matrix W a : Taking whether the weighted matrix is ​​a random irreducible matrix and a prime matrix as the iteration condition, a Iterate and finally get the steady-state matrix, that is, the limit supermatrix W * : Take the column where the global variable is located as a column vector The mixed weight can be obtained from formula (10):

5. The collaborative fault-tolerant control method of an underwater robot according to claim 4, characterized in that: In step S6, the controller of the i-th robot is designed as follows: in is the controller gain matrix, Δa ij (t) is a bounded function, which represents the communication uncertainty between the i-th robot and the j-th robot. The corresponding Laplace transform form is: τ(t) is a time-varying function that satisfies: 0≤τ(t)≤τ, 6. The cooperative fault-tolerant control method of an underwater robot according to claim 5, characterized in that: If any initial position and velocity state of the underwater robot system satisfies the following equation, the multi-underwater robot system achieves consistency, which is expressed as follows: Define the motion state vector of the i-th robot at time t as The motion state equation of the i-th robot is: Define the average state vector of the i-th robot as but: The error state vector is defined as: The state error equation of the multi-underwater robot system is: in 7. The cooperative fault-tolerant control method of an underwater robot according to claim 6, characterized in that: Also included is step S7, which provides proof of fault-tolerant consistency: Consider the nominal system situation ΔB=0, Δa ij (t)=0,Δl ij (t) = 0, the kinematic equations of the multi-underwater robot with error state vectors are fault-tolerant and consistent; For the uncertain topology Δa ij ≠0, the kinematic equations of the multi-underwater robot proposed in the controller have fault-tolerant consistency.

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