Multi-water-surface-robot system preset-time self-adaptive fuzzy cooperative formation control method

Abstract

The invention provides a preset time adaptive fuzzy cooperative formation control method for a multi-water-surface-robot system, and the method comprises the steps: building a motion model containing uncertainty and actuator faults based on a speed state vector, and approaching the uncertainty through a fuzzy logic system; constructing a fuzzy logic expansion state observer containing a time-varying gain function to estimate an unmeasurable speed and compensate interference and uncertainty; based on observer output, distributed errors are defined, a barrier Lyapunov function constraint boundary is introduced, and uncertainty and faults are compensated in combination with fuzzy and multiplicative fault adaptive laws. According to the method, the multiple water surface robots can form and keep the expected formation within the preset time, the tracking error is converged to the small neighborhood of the original point, the method does not depend on initial conditions, and the control precision and robustness are improved.

Description

Technical Field

[0001] This invention relates to the field of motion control technology, specifically providing a preset-time adaptive fuzzy cooperative formation control method for multi-surface robot systems. Background Technology

[0002] Currently, single-robot systems only consider the state and movement of a single robot, suitable for industrial automation and home services. However, in scenarios such as natural disaster relief and agriculture, multiple robots need to work collaboratively, making the research on robot formation control particularly significant. Robot formation control is highly complex, requiring the handling of communication between multiple robots to ensure information sharing and task coordination. Existing research shows that actuator failures only affect individual robots, while robot formation control needs stronger fault tolerance to ensure that the formation can still operate even when some robots fail.

[0003] In recent years, researchers have proposed various formation control methods, including consensus algorithms, distributed control methods, virtual structure methods, and rule-based methods. However, dynamic uncertainties, strong coupling interference, and communication delays in complex marine environments remain challenges for the formation control of multi-surface robot systems. Furthermore, most current cooperative formation control schemes are designed based on known velocity information. However, in real-world marine environments, velocity information is not always accurately measured due to environmental interference, sensor limitations, measurement costs, and the dynamic characteristics of the system. Therefore, researching cooperative formation control of multi-surface robot systems under conditions of unknown velocity information is of great significance.

[0004] Therefore, there is an urgent need for a preset time adaptive fuzzy cooperative formation control method for multi-surface robot systems to solve the above problems. Summary of the Invention

[0005] In order to overcome the above-mentioned defects, the present invention is proposed to provide a solution or partial solution to the aforementioned problems.

[0006] This invention provides a preset-time adaptive fuzzy cooperative formation control method for a multi-surface robot system, comprising: establishing a motion model based on velocity state vectors, incorporating uncertainties and actuator faults, and approximating the uncertainties using a fuzzy logic system to obtain the final motion model; constructing an extended state observer based on fuzzy logic, and introducing a time-varying gain function into the state observer; defining distributed errors based on the output of the state observer and introducing a barrier Lyapunov function to constrain the boundary; and combining fuzzy adaptive law and fault adaptive law to compensate for uncertainties and faults, thereby achieving the desired formation within a preset time.

[0007] In one technical solution of the aforementioned pre-set time adaptive fuzzy cooperative formation control method for multi-surface robot systems, before establishing a motion model based on velocity state vectors, incorporating uncertainties and actuator faults, and approximating the uncertainties using a fuzzy logic system to obtain the final motion model, the following steps are included: setting the initial motion model with control inputs containing actuator faults:

[0008]

[0009] Where, ρ i =diag[ρ 1i , ρ 2i , ρ 3i The ] represents a time-varying multiplicative actuator fault, which is a gain matrix. It is a time-varying additive actuator fault, τ i This refers to the actual controller to be designed.

[0010] In one technical solution of the pre-time adaptive fuzzy cooperative formation control method for the aforementioned multi-surface robot system, the process of establishing a motion model based on the velocity state vector, incorporating uncertainties and actuator faults, and approximating the uncertainties using a fuzzy logic system to obtain the final motion model includes:

[0011] Construct an initial motion model for the surface robot system, which includes the kinematic and dynamic models of the surface robot system:

[0012]

[0013] Where, χ i =[x i y i , ψ i ] T This represents the output of the surface robot system, while (x) i y i ) and ψ i H represents the position and heading angle of the i-th surface robot system in the geodetic coordinate system, respectively; i (ψ i Let ) denote the rotation matrix, and satisfy ? I is the identity matrix; ξ i =[u i v i r i ] T Let u represent the velocity vector of the i-th surface robot in volume coordinates. i v i and r i M represents the surge velocity, sway velocity, and yaw velocity of the i-th surface robot, respectively; i >0 is the inertia matrix; Ci (ξ i ) is the Coriolis and centripetal force matrix; D i (ξ i ) represents the nonlinear damping parameter matrix; Δ i Indicates unknown dynamics in the model; τ di =[τ du，i , τ dv，i , τ dr，i ] T These are external time-varying disturbances caused by wind, waves, and ocean currents; This indicates a control input with an actuator malfunction;

[0014] Define the velocity state vector η i =H i (ψ i )ξ i The kinematic and dynamic models of the i-th surface robot in the multi-surface robot formation system are as follows:

[0015]

[0016] in,

[0017] Using a fuzzy logic system to approximate and R(r) i )η i The uncertainties included are:

[0018]

[0019] Where, θ i =[θ 1i θ 2i θ 3i ] T It is an adaptive parameter vector. It is a fuzzy basis function, and has X i =η i δ i It is a fuzzy approximation error;

[0020] Will Substituting these values ​​into the motion model, we obtain the final motion model:

[0021]

[0022] The considered surface robot network consists of a virtual leader and N surface robot followers, as shown in the figure. For information exchange in this network, where It is a set of nodes, where node 0 represents the leader, and nodes 1, ..., N represent followers. Each node represents a surface robot. This represents an edge set where node i and node j share information, and each edge connects two different nodes. Is with the diagram The relevant adjacency matrix, when (i, j) ∈ ε, has its elements defined as a ij >0, otherwise, a ij =0, and the graph The associated Laplace matrix is ​​defined as in, and

[0023] In one technical solution of the aforementioned pre-set time-adaptive fuzzy cooperative formation control method for multi-surface robot systems, the process of constructing an extended state observer based on fuzzy logic and introducing a time-varying gain function into the observer includes:

[0024] The time-varying gain function:

[0025]

[0026] Where T > 0 is the preset time, and φ is a constant that satisfies 0 < φ < 1;

[0027] Using φ as a design parameter, the preset time convergence limit of the cooperative formation tracking system based on the preset time-extended state observer is adjusted based on φ, resulting in the following state observer:

[0028]

[0029] in, and They are χ i η i and τ di The estimated value, and B 1i B 2i and B 3i It is a positive definite diagonal matrix.

[0030] In one technical solution of the preset-time adaptive fuzzy cooperative formation control method for the aforementioned multi-surface robot system, the process of defining distributed errors and introducing Lyapunov function constraint boundaries based on the state observer output includes: Based on the communication topology, the cooperative formation tracking error is defined as follows:

[0031]

[0032] In the formula, (χ io χjo Let b be the desired formation of the i-th and j-th robots. i It is an adjustment function, χ d For virtual leader trajectories;

[0033] right Differentiating, we get:

[0034]

[0035] in, η i =[η 1，i η 2，i η 3，i ] T η j =[η 1，j η 2，j η 3，j ] T ;

[0036] To constrain formation tracking error Choose the following barrier Lyapunov functions:

[0037]

[0038] Among them, z 1l，i For tracking error vector The l-th element, p 1，i It is z 1l，i The constraint boundary satisfies |z 1l，i |<p 1，i ;

[0039] For V 1i Differentiating, we get:

[0040]

[0041] In one technical solution of the aforementioned pre-time adaptive fuzzy cooperative formation control method for multi-surface robot systems, the process of defining distributed errors and introducing obstacle Lyapunov function constraint boundaries based on the state observer output further includes:

[0042] Define the following dynamic error vector:

[0043]

[0044] Where, α i =[α 1，i α 2，i α 3,i ] T It is a virtual controller, according to and roll out

[0045] Therefore, the virtual controller is designed as follows:

[0046]

[0047] Among them, c 1，i =diag[c 11，i c 12，i c 13，i ], c 11，i c 12,i and c 13，i These are design parameters, and c 11，i >0, c 12，i >0 and c 13，i >0;

[0048] In one technical solution of the preset-time adaptive fuzzy cooperative formation control method for the aforementioned multi-surface robot system, the process of combining fuzzy adaptive law and fault adaptive law to compensate for uncertainties and faults and achieve the desired formation within the preset time includes:

[0049] right Differentiating, we get:

[0050] Choose the following obstacles and use Lyapunov functions to constrain the velocity:

[0051]

[0052] Where, p 2，i It is z 2l，i The constraint boundary, i.e., satisfying |z 2l，i |<p 2，i Λ l，i >0 and Γ l，i >0 is a design parameter;

[0053] For V 2i Differentiating, we get:

[0054]

[0055] in,

[0056] The collaborative formation controller is designed as follows:

[0057]

[0058] Among them, c 2，i =diag[c 21，i c 22，i c 23，i], c 21，i c 22，i and c 23，i These are design parameters, and c 21，i >0, c 22，i >0 and c 23，i >0;

[0059] In one technical solution of the preset time adaptive fuzzy cooperative formation control method for the aforementioned multi-surface robot system, the fuzzy adaptive law and the multiplicative fault adaptive law are designed as follows:

[0060]

[0061] Where, γ 1，i =diag[γ 11，i γ 12，i γ 13，i ], γ 2，i =diag[γ 21，i γ 22，i γ 23，i ], γ 1l，i and γ 2l，i It is a design parameter, and γ 1l，i >0, γ 2l，i >0, l=1, 2, 3.

[0062] The beneficial effects of the pre-set time adaptive fuzzy cooperative formation control method for a multi-surface robot system provided by this invention are as follows: First, this method proposes a pre-set time extended state observer based on fuzzy logic, which can not only estimate the unmeasurable velocity from the position information of the surface robots, but also compensate for unknown time-varying disturbances and uncertainties in the system model. Second, an adaptive cooperative formation control scheme is designed. By defining a distributed cooperative formation tracking error and introducing a barrier Lyapunov function, formation errors and velocities are prevented from violating predefined constraints. Furthermore, the designed fuzzy adaptive law and multiplicative fault adaptive law can compensate for the uncertainties in the model and the impact of unknown actuator faults on the system. This scheme enables multiple surface robots to form and maintain the desired formation within a pre-set time, with the tracking error converging to a small neighborhood of the origin within the pre-set time, and is independent of the initial conditions of the surface robot system. Attached Figure Description

[0063] The disclosure of this invention will become more readily understood with reference to the accompanying drawings. It will be readily understood by those skilled in the art that these drawings are for illustrative purposes only and are not intended to limit the scope of protection of this invention. Furthermore, similar numbers in the drawings are used to denote similar components, wherein:

[0064] Figure 1This is a schematic diagram of a preset time adaptive fuzzy cooperative formation control method for a multi-surface robot system according to an embodiment of the present invention;

[0065] Figure 2 This is a schematic diagram of the motion coordinate system of a surface robot according to an embodiment of the present invention;

[0066] Figure 3 This is a communication topology diagram according to an embodiment of the present invention;

[0067] Figure 4 This is a phase plane trajectory diagram for cooperative formation control according to an embodiment of the present invention;

[0068] Figure 5 The cooperative formation tracking error z of four surface robots according to an embodiment of the present invention 11，i Trajectory diagram;

[0069] Figure 6 The cooperative formation tracking error z of four surface robots according to an embodiment of the present invention 12，i Trajectory diagram;

[0070] Figure 7 The cooperative formation tracking error z of four surface robots according to an embodiment of the present invention 13，i Trajectory diagram;

[0071] Figure 8 This is a schematic diagram of the surge velocity trajectory of a cooperative formation of four surface robots according to an embodiment of the present invention;

[0072] Figure 9 This is a schematic diagram of the swaying velocity trajectory of a cooperative formation of four surface robots according to an embodiment of the present invention;

[0073] Figure 10 This is a schematic diagram of the yaw speed trajectory of a cooperative formation of four surface robots according to an embodiment of the present invention;

[0074] Figure 11 This is a surge velocity estimation error diagram of a cooperative formation of four surface robots according to an embodiment of the present invention;

[0075] Figure 12 This is a diagram showing the estimation error of the swaying velocity of a cooperative formation of four surface robots according to an embodiment of the present invention;

[0076] Figure 13 This is a diagram showing the yaw speed estimation error of a cooperative formation of four surface robots according to an embodiment of the present invention;

[0077] Figure 14The control input signal τ of a four-water surface robot system according to an embodiment of the present invention is 1i Trajectory graph;

[0078] Figure 15 The control input signal τ of a four-water surface robot system according to an embodiment of the present invention is 2i Trajectory graph;

[0079] Figure 16 The control input signal τ of a four-water surface robot system according to an embodiment of the present invention is 3i Trajectory graph;

[0080] Figure 17 This is a fuzzy adaptive law trajectory curve diagram according to an embodiment of the present invention;

[0081] Figure 18 This is a trajectory curve of the multiplicative fault adaptive law according to an embodiment of the present invention. Detailed Implementation

[0082] Some embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0083] like Figure 1-18 As shown, this invention discloses a preset-time adaptive fuzzy cooperative formation control method for a multi-surface robot system, comprising the following steps:

[0084] Step S1: Consider a formation of N surface robots with unmeasurable velocity and unknown actuator failures. The kinematic and dynamic model of the i-th surface robot system, i = 1, 2, ..., N (i = 1, 2, ..., N), is described as follows:

[0085]

[0086] Where, χ i =[x i y i , ψ i ] T This represents the output of the surface robot system, while (x) i y i ) and ψ i H represents the position and heading angle of the i-th surface robot system in the geodetic coordinate system, respectively; i (ψ i Let ) denote the rotation matrix, and satisfy ? I is the identity matrix; ξ i =[u i v i ri ] T Let u represent the velocity vector of the i-th surface robot in volume coordinates. i v i and r i M represents the surge velocity, sway velocity, and yaw velocity of the i-th surface robot, respectively; i >0 is the inertia matrix; C i (ξ i ) is the Coriolis and centripetal force matrix; D i (ξ i ) represents the nonlinear damping parameter matrix; Δ i Indicates unknown dynamics in the model; τ di =[τ du，i , τ dv，i , τ dr，i ] T These are external time-varying disturbances caused by wind, waves, and ocean currents; This indicates a control input with an actuator malfunction.

[0087] Consider the following unknown time-varying multiplicative and additive actuator fault model:

[0088]

[0089] Where, ρ i =diag[ρ 1i , ρ 2i , ρ 3i ] represents a time-varying multiplicative actuator fault, which is a gain matrix. It is a time-varying additive actuator fault, τ i This represents the actual controller to be designed. The motion coordinate system of the surface robot is as follows: Figure 2 As shown.

[0090] The matrix description in the model of the surface robot system is as follows:

[0091]

[0092] in, c 13i =-m 22i v, m i It's about the quality of the surface robot. and I represents the hydrodynamic added mass. zi This represents the moment of inertia of the surface robot in the heading direction; and It is the damping coefficient in the surge direction; and It is the damping coefficient in the direction of swaying; and It is the damping coefficient in the heading direction.

[0093] To facilitate controller design and analysis, a velocity state vector η is defined. i =H i (ψ i )ξ i The system model (1) of the i-th surface robot is redescribed as follows:

[0094]

[0095] in,

[0096] In the dynamic model of the surface robot (5), due to the inaccuracy of measurement in practical applications, it is difficult to accurately obtain the model parameters. and R(r) i )η i It includes uncertain parameters and unknown dynamics. These uncertainties have a significant impact on the design of the surface robot controller; therefore, a fuzzy logic system is used to approximate these uncertainties.

[0097]

[0098] Where, θ i =[θ 1i θ 2i θ 3i ] T It is an adaptive parameter vector. It is a fuzzy basis function, and has X i =η i δ i It is the fuzzy approximation error.

[0099] Substituting formula (7) into formula (5) yields

[0100]

[0101] The considered surface robot network consists of a virtual leader and N surface robot followers, as shown in the figure. For information exchange in this network, where It is a set of nodes, where node 0 represents the leader, and nodes 1, ..., N represent followers. Each node represents a surface robot. Let represent an edge set, where node i and node j share information, and each edge connects two different nodes. Is with the diagram The relevant adjacency matrix, when (i, j) ∈ ε, has its elements defined as aij >0, otherwise, a ij =0. (Compared to the graph) The associated Laplace matrix is ​​defined as in and

[0102] To facilitate controller design, the following necessary assumptions are made:

[0103] Assumption 1: The unknown external disturbances in model (1) are bounded, and their first derivatives are also bounded. That is... in and It is a normal number.

[0104] Assumption 2: Diagram It contains a spanning tree whose root node is the leader node "0".

[0105] Assumption 3: For a communication network structure consisting of N surface robots and a virtual leader, there is at least one directed path from the leader to each surface robot in the communication graph.

[0106] Assumption 4: Expected trajectory χ d It is bounded and smooth, and its first derivative is... and second derivative It is bounded.

[0107] Cooperative formation control objective: Under the conditions of satisfying assumptions 1 to 4, for a surface robot system (5) with unmeasurable velocity and unknown actuator failure, the control objective under the guidance of a virtual leader is as follows:

[0108] ① Ensure that the trajectory of each surface robot system follows the trajectory of the virtual leader with high precision. d And form the desired formation χ within a preset time. io ,Right now

[0109]

[0110] Where, χ io =[χ 1，io , χ 2，io , χ 3，io ] T , χ d =[x d y d , ψ d ] T ; It is a positive constant, determined by the design parameters, and can be made small enough.

[0111] ② The formation tracking error converges to a smaller compact set at the origin within a preset time, and the formation error and velocity do not exceed the predetermined constraint boundaries.

[0112] Step S2: Design an adaptive cooperative formation controller for multiple surface robot systems. First, a preset time-extended state observer is designed to estimate the unknown velocity. Second, a log-type obstacle Lyapunov function is introduced to constrain formation error and velocity. Finally, a cooperative formation controller is designed for each surface robot. Specifically:

[0113] Step S21: Construct an extended state observer based on fuzzy logic to estimate unmeasurable velocity, unknown disturbances, and model uncertainties. To achieve the preset time convergence of the cooperative formation tracking system, the following time-varying gain function is introduced into the observer:

[0114]

[0115] Where T > 0 is the preset time, and φ is a constant that satisfies 0 < φ < 1.

[0116] Here, φ serves as a design parameter used to adjust the preset time convergence limit of the cooperative formation tracking system based on a preset time-extended state observer. The preset time can be given by the user in advance, and only one parameter needs to be adjusted to reach the preset time convergence limit.

[0117] The pre-defined time-extended state observer based on fuzzy logic is designed as follows:

[0118]

[0119] in, and They are χ i η i and τ di The estimated value, and B 1i B 2i and B 3i It is a positive definite diagonal matrix.

[0120] Define the observer error Based on the dynamics of formulas (8) and (13), the observer error dynamics can be derived as follows:

[0121]

[0122] in, and It is the estimation error.

[0123] To simplify controller design and analysis, define Therefore, the observer error dynamics (14) can be written in the following form:

[0124]

[0125] in, E i and A i The definition is as follows:

[0126]

[0127] Select parameter B 1i B 2i and B 3i Make matrix E i If it is Hurwitz's, then we can conclude that there exists P = P. T >0, making Where Q is a given positive definite symmetric matrix.

[0128] Step S22: Based on the designed preset time-extended state observer, further design an adaptive fuzzy cooperative formation controller for the multi-surface robot system. A log-type obstacle Lyapunov function is used to handle formation tracking errors and velocity constraints. An adaptive method is designed to compensate for the impact of time-varying multiplicative actuator failures on the system. The cooperative formation controller design mainly consists of two steps.

[0129] Step S221: Design the virtual controller

[0130] Based on the communication topology, the cooperative formation tracking error is defined as follows:

[0131]

[0132] In the formula, z 1，i =[z 11i , z 12i , z 13i ] T , (χ io χ jo Let b be the desired formation of the i-th and j-th robots. i It is an adjustment function, χ d For virtual leader trajectories;

[0133] right Differentiation yields:

[0134]

[0135] in, η i =[η 1，i η 2，i η3，i ] T η j =[η 1，j η 2，j η 3，j ] T .

[0136] To constrain formation tracking error Choose the following barrier Lyapunov functions:

[0137]

[0138] Among them, z 1l，i For tracking error vector The l-th element, p 1，i It is z 1l，i The constraint boundary satisfies |z 1l，i |<p 1，i .

[0139] For V 1i Differentiating, we get:

[0140]

[0141] Define the following dynamic error vector:

[0142]

[0143] Where, α i =[α 1，i α 2，i α 3，i ] T It is a virtual controller, according to and Can be launched

[0144] Therefore, the virtual controller is designed as follows:

[0145]

[0146] Among them, c 1，i =diag[c 11，i c 12，i c 13，i ], c 11，i c 12，i and c 13，i These are design parameters, and c 11，i >0, c 12，i >0 and c 13，i >0;

[0147] Step S222: Design a collaborative formation controller

[0148] For formula (21) Differentiation yields

[0149]

[0150] To solve the velocity constraint problem, the following obstacle Lyapunov function is chosen.

[0151]

[0152] Where, p 2，i It is z 2l，i The constraint boundary, i.e., satisfying |z 2l，i |<p 2，i Λ l，i >0 and Γ l，i >0 is a design parameter.

[0153] For V in formula (24) 2i Differentiation yields

[0154]

[0155] in,

[0156] The collaborative formation controller is designed as follows:

[0157]

[0158] Among them, c 2，i =diag[c 21，i c 22，i c 23，i ], c 21，i c 22，i and c 23，i These are design parameters, and c 21，i >0, c 22，i >0 and c 23，i >0;

[0159] The fuzzy adaptive law and multiplicative fault adaptive law in formula (25) are designed as follows:

[0160]

[0161] Where, γ 1，i =diag[γ 11，i γ 12，i γ 13，i ], γ 2，i =diag[γ 21，i γ 22，i γ23，i ], γ 1l，i and γ 2l，i It is a design parameter, and γ 1l，i >0, γ 2l，i >0, l=1, 2, 3.

[0162] To demonstrate the effectiveness of the proposed adaptive fuzzy cooperative formation control scheme, it was applied to a communication network consisting of four (N=4) surface robots and a virtual leader, and simulation experiments were conducted using Matlab software. The model parameters of the surface robots are shown in Table 1.

[0163] Table 1 Parameters of the Surface Robot Model

[0164]

[0165] In real-world environments, disturbances and unknown model dynamics may differ due to water flow factors. To avoid loss of generality, the following unknown time-varying disturbances and unknown model dynamics are introduced to verify the robustness of the proposed adaptive fuzzy cooperative formation controller. The unknown external time-varying disturbance in the system model is assumed to be: τ di =[τ du，i , τ dv，i , τ dr，i ] T =[0.2sin(0.5t)+0.6cos(0.5t), 0.2cos(08y), 0.2sin(0.6t)+0.1cos(0.6t)] T The virtual leader's trajectory is: χ d =[2cos(0.1t)+3sin(0.1t), 2sin(0.1t)-3cos(0.1t),0.1t] T The unknown dynamics of the system model are chosen as follows: The system's unknown time-varying actuator fault assumption is: ρ i =diag[0.7+0.3sin(0.02t), 0.6+0.2sin(0.02t), 0.4+0.1sin(0.02t)], The constraint boundary is chosen as: p 1，i =1, p ξ，i =2.5.

[0166] The communication topology between the four surface robots and a virtual leader is as follows: Figure 3 As shown. The desired formation is defined as: χ 1o = [0, -0.5, 0] T , χ 2o = [-0.5, 0, 0] T , χ 3o=[0.5, 0, 0] T , χ 4o =[0, 0.5, 0] T The robot's initial position is chosen as: χ1(0) = [2, -3.6, 0] T , χ2(0)=[1.4,-3,0] T , χ3(0)=[2.6,-3,0] T , χ4(0)=[2,-2.4,0] T The controller design parameters are selected as: c 1，i =diag[80, 80, 80], c 2，i =diag[12, 12, 12]; Λ i = diag[0.2, 0.2, 0.2], Γ i =diag[0.1, 0.1, 0.1]; T=3, T=3, φ=0.9; γ 1，i =diag[20, 20, 20], γ 2，i =diag[0.1, 0.1, 0.1]. The initial velocity of the water surface robot formation is selected as: ξ i (0) = [0, 0, 0] T The initial values ​​of the adaptive law parameters in formula (37) are chosen as follows:

[0167] Using the above simulation parameters, the virtual controller (22), adaptive fuzzy cooperative controller (26), and adaptive law (27) were applied to the simulation study of four surface robots. All data were obtained in the Matlab simulation environment. The four surface robots can form the desired formation along the virtual leader's trajectory within a preset time. The specific simulation results are as follows: Figures 4 to 18 As shown.

[0168] Figure 4 This figure shows the phase plane formation motion trajectory of four surface robots and a virtual leader. The four surface robots track the virtual leader from different initial positions, forming a desired formation. The figures also show their positions and formations at times 0 seconds, 25 seconds, 36 seconds, and 50 seconds, where 0 seconds represents the initial formation of the four surface robots. The figure demonstrates that after forming the desired formation, the formation maintains its motion and tracks the virtual leader. The tracking errors in position and heading angle of the four surface robots in cooperative formation are shown below. Figure 5-7 As shown, p 1，i The corresponding solid line represents the formation error constraint boundary, from Figure 5-7As can be seen, the formation error is small and meets the preset constraints. The magnified view shows that within the preset time T = 3 seconds, the formation error converges to a small neighborhood of the origin.

[0169] Figure 8-10 The diagram represents the velocity trajectories of four surface robots in a coordinated formation, specifically their surge velocity, yaw velocity, and roll velocity. The formation velocity stabilizes at t = 1 second and maintains this stable velocity throughout the formation. ξ，i The corresponding solid line represents the velocity constraint boundary, and the formation speed meets the preset constraint conditions.

[0170] Figure 11-13 The formation velocity estimation error converges to a smaller set near the origin, proving that the designed extended state observer can estimate the unknown velocity of the system well. Figure 14-16 The control input signal characteristics of four surface robot systems are shown. As can be seen from the figure, the control input signals of the robots are all bounded.

[0171] The trajectory curves of fuzzy adaptive law and multiplicative fault adaptive law are as follows: Figure 17 and Figure 18 As shown. Observation Figure 17 The initial fluctuations represent a rapid learning process of the fuzzy logic system on its initial parameters. After 2 seconds, the fuzzy membership function is optimized through an adaptive law, effectively compensating for the uncertainties in the system. (Observation) Figure 18 It can be seen that the estimated value of the multiplicative actuator fault converges smoothly and there is no chattering.

[0172] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the original technical features, and the technical solutions resulting from these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A preset-time adaptive fuzzy cooperative formation control method for a multi-surface robot system, characterized in that, include: A motion model is established based on the velocity state vector, incorporating uncertainties and actuator failures, and the uncertainty is approximated using a fuzzy logic system to obtain the final motion model. Construct an extended state observer based on fuzzy logic, and introduce a time-varying gain function into the state observer; Based on the output of the state observer, a distributed error is defined and a barrier Lyapunov function is introduced to constrain the boundary. By combining fuzzy adaptive law and fault adaptive law, uncertainties and faults are compensated for, and the desired formation within a preset time is achieved.

2. The method according to claim 1, characterized in that, Before establishing a motion model based on velocity state vectors, incorporating uncertainties and actuator faults, and approximating the uncertainties using a fuzzy logic system to obtain the final motion model, the following steps are included: setting up a model with control inputs containing actuator faults in the initial motion model: Where, ρ i =diag[ρ 1i , ρ 2i , ρ 3i The ] represents a time-varying multiplicative actuator fault, which is a gain matrix. It is a time-varying additive actuator fault, τ i This refers to the actual controller to be designed.

3. The method according to claim 2, characterized in that, The process of establishing a motion model based on the velocity state vector, incorporating uncertainties and actuator failures, and approximating the uncertainties using a fuzzy logic system to obtain the final motion model includes: Construct an initial motion model for the surface robot system, which includes the kinematic and dynamic models of the surface robot system: Where, χ i =[x i y i , ψ i ] T This represents the output of the surface robot system, while (x) i y i ) and ψ i H represents the position and heading angle of the i-th surface robot system in the geodetic coordinate system, respectively; i (ψ i Let ) denote the rotation matrix, and satisfy ? I is the identity matrix; ξ i =[u i v i r i ] T Let u represent the velocity vector of the i-th surface robot in volume coordinates. i v i and r i M represents the surge velocity, sway velocity, and yaw velocity of the i-th surface robot, respectively; i >0 is the inertia matrix; C i (ξ i ) is the Coriolis and centripetal force matrix; D i (ξ i ) represents the nonlinear damping parameter matrix; Δ i Indicates unknown dynamics in the model; τ di =[τ du，i , τ dv，i , τ dr，i ] T These are external time-varying disturbances caused by wind, waves, and ocean currents; This indicates a control input with an actuator malfunction; Define the velocity state vector η i =H i (ψ i )ξ i The kinematic and dynamic models of the i-th surface robot in the multi-surface robot formation system are as follows: in, Using a fuzzy logic system to approximate and R(r) i )η i The uncertainties included are: Where, θ=[θ 1i ,θ 2i ,θ 3i ] T It is an adaptive parameter vector. It is a fuzzy basis function, and has X i =η i δ i It is a fuzzy approximation error; Will Substituting these values ​​into the motion model, we obtain the final motion model: The considered surface robot network consists of a virtual leader and N surface robot followers, as shown in the figure. For information exchange in this network, where It is a set of nodes, where node 0 represents the leader, and nodes 1, ..., N represent followers. Each node represents a surface robot. This represents an edge set where node i and node j share information, and each edge connects two different nodes. Is with the diagram The relevant adjacency matrix, when (i, j) ∈ ε, has its elements defined as a ij >0, otherwise, a ij =0, and the graph The associated Laplace matrix is ​​defined as in, and 4. The method according to claim 1, characterized in that, The process of constructing an extended state observer based on fuzzy logic and introducing a time-varying gain function into the observer includes: The time-varying gain function: Where T>0 is the preset time, and φ is a constant that satisfies 0<φ<1; Using φ as a design parameter, the preset time convergence limit of the cooperative formation tracking system based on the preset time-extended state observer is adjusted based on φ, resulting in the following state observer: in, and They are χ i η i and τ di The estimated value, and B 1i B 2i and B 3i It is a positive definite diagonal matrix.

5. The method according to claim 3, characterized in that, Based on the output of the state observer, the process of defining the distributed error and introducing a barrier Lyapunov function to constrain the boundary includes: Based on the communication topology, the cooperative formation tracking error is defined as follows: In the formula, z 1，i =[z 11，i , z 12，i , z 13i ] T , (χ io χ jo Let b be the desired formation of the i-th and j-th robots. i It is an adjustment function, χ d For virtual leader trajectories; For z 1，i Differentiating, we get: Among them, or i =[the 1，i ,or 2，i ,or 3，i ] T ,or j =[the 1，j ,or 2，j ,or 3，j ] T ; To constrain the formation tracking error z 1i Choose the following barrier Lyapunov function: Among them, z 1l，i To track the error vector z 1i The l-th element, p 1，i It is z 1l，i The constraint boundary satisfies |z 1l，i |<p 1，i ; For V 1i Differentiating, we get:

6. The method according to claim 5, characterized in that, The process of defining distributed error and introducing barrier Lyapunov function constraints based on the state observer output also includes: Define the following dynamic error vector: Where, α i =[α 1，i α 2，i α 3，i ] T It is a virtual controller, according to and roll out Therefore, the virtual controller is designed as follows: Among them, c 1，i =diag[c 11，i c 12，i c 13，i ], c 11，i c 12，i and c 13，i These are design parameters, and c 11，i >0, c 12，i >0 and c 13，i >0; 7. The method according to claim 6, characterized in that, The process of combining fuzzy adaptive law and fault adaptive law to compensate for uncertainties and faults and achieve the desired formation within a preset time includes: For z 2，i Differentiating, we get: Choose the following obstacles and use Lyapunov functions to constrain the velocity: Where, p 2，i It is z 2l，i The constraint boundary, i.e., satisfying |z 2l，i |<p 2，i Λ l，i >0 and Γ l，i >0 is a design parameter; For V 2i Differentiating, we get: in, The collaborative formation controller is designed as follows: Among them, c 2，i =diag[c 21，i c 22，i c 23，i ], c 21，i c 22，i and c 23，i These are design parameters, and c 21，i >0, c 22，i >0 and c 23，i >0; 8. The method according to claim 7, characterized in that, The fuzzy adaptive law and the multiplicative fault adaptive law are designed as follows: where, γ 1，i = diag[γ 11，i , γ 12，i , γ 13，i , γ 2，i = diag[γ 21，i , γ 22，i , γ 23，i , γ 1l，i and γ 2l，i are design parameters, and γ 1l，i > 0, γ 2l，i > 0, l = 1, 2, 3.

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