Anti-current trajectory tracking control method and system of jet arm seabed cable laying robot

Abstract

The application discloses a kind of anti-ocean current trajectory tracking control method and system of jet arm seabed cable laying robot, including constructing the anti-ocean current motion model of jet arm seabed cable laying robot;Based on anti-ocean current motion model, according to the given reference trajectory, obtain position error and heading tracking error, construct predetermined time controller;According to the virtual controller of jet arm seabed cable laying robot of predetermined time controller, to define longitudinal velocity error and angular velocity error;According to longitudinal velocity error and angular velocity error, construct parameter adaptive law;Based on virtual controller and parameter adaptive law, construct disturbance observer, to obtain actual controller for the anti-ocean current trajectory tracking of jet arm seabed cable laying robot.For the problem that existing seabed cable laying robot cannot realize accurate trajectory tracking in complex seabed environment, more perfect anti-ocean current motion model is established, and disturbance observer is introduced to estimate disturbance in real time, to realize accurate control;Using predetermined time theory can make the system converge to pre-set time, with better robustness;The use of disturbance observer will more accurately compensate the disturbance of ocean current in seabed, improve the anti-interference ability of seabed cable laying robot.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of seabed cable laying robots, and particularly relates to an anti-ocean current trajectory tracking control method and system for a jet arm seabed cable laying robot. BACKGROUND

[0002] In recent years, tracked robots have shown great application potential in crop transportation, open-pit mining, oil exploration and seabed cable laying and other fields. In particular, with the deepening of China's marine exploration, seabed cable laying robots with tracked characteristics play an important role in marine operations. At the same time, seabed cable laying robots have high uncertainty in complex marine operating environments and are difficult to model. Under such circumstances, the dynamic and nonlinear interaction between the seabed cable laying robot and its surrounding environment makes it a challenge to ensure accurate trajectory tracking.

[0003] At present, although the seabed cable laying robot has many advantages in completing actual marine tasks, the prior art still has the following problems: in the existing research on seabed cable laying robots, the motion of the seabed cable laying robot is subject to many uncertain factors, making it difficult to accurately model the motion characteristics of the seabed cable laying robot, especially the special state of trenching motion; at the same time, due to the difficulty in obtaining information about the actual seabed operating environment, the existing control methods mostly ignore environmental disturbance factors, resulting in unsatisfactory trajectory tracking control effect of the seabed cable laying robot in actual application. To solve these problems, a more perfect kinematic and dynamic model needs to be established, and a disturbance observer needs to be introduced to compensate for the influence of ocean currents on the seabed cable laying robot in real time, so as to achieve accurate control. In addition, the existing trajectory tracking control methods mostly do not consider forming the expected effect within a predetermined time, while the predetermined time control can improve the convergence speed and robustness of the system, enabling the seabed cable laying robot to achieve accurate trajectory tracking in complex seabed environments. SUMMARY

[0004] The present application provides an anti-ocean current trajectory tracking control method and system for a jet arm seabed cable laying robot to overcome the above technical problems.

[0005] To achieve the above purpose, the technical solution of the present application is as follows:

[0006] An anti-ocean current trajectory tracking control method for a jet arm seabed cable laying robot, specifically comprising the following steps:

[0007] S1: constructing an anti-ocean current motion model of the jet arm seabed cable laying robot;

[0008] S2: based on the anti-ocean current motion model, obtaining position error and heading tracking error according to a given reference trajectory, and based on the position error and the heading tracking error, constructing a predetermined time controller;

[0009] S3: Obtain the virtual controller of the jetting arm undersea cable laying robot according to the predetermined time controller;

[0010] And the virtual controller comprises a longitudinal velocity virtual controller and an angular velocity virtual controller;

[0011] And define longitudinal velocity error and angular velocity error according to the virtual controller;

[0012] S4: Construct parameter adaptive law according to the longitudinal velocity error and the angular velocity error;

[0013] The parameter adaptive law comprises a longitudinal velocity adaptive law and an angular velocity adaptive law;

[0014] S5: Construct a disturbance observer based on the virtual controller and the parameter adaptive law to obtain an actual controller for the jetting arm undersea cable laying robot for anti-ocean current trajectory tracking.

[0015] Further, the anti-ocean current motion model of the jetting arm undersea cable laying robot constructed in S1 is

[0016]

[0017] In the formula, η = [x, y, θ] T represents the position-deflection angle vector of the jetting arm undersea cable laying robot; x and y represent the horizontal and vertical coordinates of the two-dimensional coordinate position of the undersea cable laying robot; θ represents the deflection angle; v = [v, ω] Τ represents the velocity vector of the jetting arm undersea cable laying robot in the coordinate system; v represents the longitudinal velocity; ω represents the angular velocity; τ = [τ v , τ ω ] T , and τ v and τ ω are actual control signals in the longitudinal and rotational directions of the jetting arm undersea cable laying robot; F = [F v , F ω ] T , and f L and f R represent the resistance of the left and right tracks of the jetting arm undersea cable laying robot; F d represents the suspension rope force acting on the robot; represents the included angle between the suspension rope of the robot and the motion direction; Fcos(α1+α2) represents the component of the reaction force of the nozzle on the robot in the motion direction of the robot; α1 represents the included angle between the nozzle and the jetting arm; α2 represents the included angle between the jetting arm and the motion direction; F D represents the drag resistance; F ω = -f R b + f L b - Mμ , and b represents the distance from the track center to the robot’s geometric center; M μ Indicates the steering resistance torque; D = [D v D ω ] T , and D v With D ω Indicates the disturbance of the seabed current, and satisfies and Respectively represent D v With D ω The upper bound of J(θ), A, B, C represents the parameter matrix; m, I ω They represent the total mass and the moment of inertia of the submarine cable-laying robot underwater; μ L Indicates the positive friction coefficient between the left track and the soil; μ R Indicates the positive friction coefficient between the right track and the soil; L and R represent the left and right tracks respectively; I r represents the track moment of inertia; k r represents the traction coefficient; r represents the rotation radius of the track drive wheel, and -Av+BF represents the uncertainty term in the anti-ocean current motion model.

[0018] Furthermore, the S2 specifically includes the following steps:

[0019] S21: Based on the anti-ocean current motion model, according to the given reference trajectory η d Get the position error, where η d =[x d ,y d ,θ d ] T ;

[0020] And the position error is

[0021]

[0022] e x =xx d , e y =yy d

[0023] Where: e x Indicates the horizontal coordinate error of the position; x d Indicates the horizontal coordinate of the expected position; e y Indicates the position ordinate error; y d Indicates the desired position ordinate; e z Indicates position error;

[0024] And obtain the heading tracking error based on the position error, its expression is:

[0025] eθ = θ - θ d

[0026] where θ d denotes the ideal heading angle related to the position horizontal error e x and the position vertical error e y ; and θ d = atan2(e y , e x ); atan2 denotes the arctangent function;

[0027] S22: Construct the error constraint condition according to the position error and the heading tracking error, which is expressed as

[0028]

[0029] where Ω j (t) and denote the boundary function to be set, and j = z, θ;

[0030] S23: Construct the predetermined time performance function based on the error constraint condition, and design the boundary function as

[0031]

[0032] where ρ j (t) denotes the predetermined time performance function; ρ j∞ denotes the convergence precision; n denotes the order of the system; and σ σ ej , ρ j0 , ρ j∞ denote the design parameters according to the actual requirements, and σ ej > 0, ρ j0 > ρ j∞ > 0;

[0033] S24: Construct the logarithmic barrier function according to the designed boundary function, which is expressed as

[0034]

[0035] where γ z denotes an intermediate variable and γ θ denotes an intermediate variable and ln(·) denotes the natural logarithm function; and s z denotes the barrier function related to the position error; s θ denotes the barrier function related to the heading tracking error;

[0036] S25: Derivation of the logarithmic barrier function to obtain a predetermined time controller, whose expression is

[0037]

[0038] wherein φ q and χ q represent the predetermined time control signal; φ z , χ z represent the distance predetermined time signal; φ θ , χ θ represent the angle predetermined time signal.

[0039] Further, the S3 specifically comprises the following steps:

[0040] S31: Based on the anti-current motion model of the jet arm seabed cable laying robot, a virtual controller of the jet arm seabed cable laying robot is constructed according to the logarithmic barrier function and the predetermined time controller;

[0041] And the virtual controller comprises a longitudinal velocity virtual controller and an angular velocity virtual controller;

[0042] The expression of the longitudinal velocity virtual controller is

[0043]

[0044] The expression of the angular velocity virtual controller is

[0045]

[0046] wherein: and represent the virtual control signal; represent the first derivative of x d , y d ;

[0047] S32: The virtual controller is subjected to first-order low-pass filtering processing to obtain a first-order filter output error; and the longitudinal velocity error and the angular velocity error of the jet arm seabed cable laying robot are defined according to the first-order filter output error, whose expression is

[0048]

[0049] s v = v - α fv

[0050] s ω = ω - α fω

[0051] wherein s fv and s fωRepresents the output error of the first-order filter; α fv With α fω represents the filtered signal; and Indicates virtual control signal; s v ,s ω represent the longitudinal velocity error and angular velocity error respectively;

[0052] And the expression for first-order low-pass filtering of the virtual controller is:

[0053]

[0054] Where: α cv ,α cω Respectively represent the input of the first-order low-pass filter in the longitudinal velocity direction and the angular velocity direction; α fω (0),α cω (0) represents α cv ,α cω The initial value of κ1 represents α cv The filtering time constant; κ2 represents α cω The filter time constant; Represents α fv The first derivative of Represents α fω The first derivative of .

[0055] Furthermore, the S4 specifically includes the following steps:

[0056] Based on the fuzzy logic system approximation of the uncertainty term λ in the anti-ocean current motion model and λ=-Av+BF,λ=[λ v λ ω ] T , where λ v represents the unknown function term about the longitudinal velocity; λ ω Represents the unknown function term about angular velocity;

[0057] The expression of the unknown function term in the anti-ocean current motion model approximated by the fuzzy logic system is:

[0058]

[0059] Where: W v * represents the adaptive parameter W v The optimal parameter vector of ω * represents the adaptive parameter W ω The optimal parameter vector of ; Indicates is a continuous function of a variable; Indicates a continuous function of the variable; denotes a variable related to the longitudinal velocity v and the angular velocity ω; ε v ω denotes the approximation error and satisfies denotes a positive constant; denotes the basis function of the fuzzy logic system;

[0060] S42: constructing a parameter adaptive law according to the longitudinal velocity error and the angular velocity error in combination with step S41; the parameter adaptive law comprises a longitudinal velocity adaptive law and an angular velocity adaptive law;

[0061] the expression of the longitudinal velocity adaptive law is

[0062]

[0063] the expression of the angular velocity adaptive law is

[0064]

[0065] wherein: denotes the parameter adaptive law and i = v, ω; δ v , δ ω denotes a design parameter and δ v > 0, δ ω > 0; Γ v , Γ ω denotes a designed control gain matrix; denotes the estimated value of W v * ; and denotes the estimated value of W ω * .

[0066] Further, the S5 specifically comprises the following steps:

[0067] S51: constructing a disturbance observer based on the virtual controller and the parameter adaptive law;

[0068] the expression of the disturbance observer is

[0069]

[0070] wherein: ξ v and ξ ω denote the observed state; r v and r ω respectively denote unknown disturbances in the longitudinal velocity direction and the angular velocity direction. ​​​​​with respectively denote the estimate of unknown disturbance r v with r ω denoting the estimate of unknown disturbance r rv with k rω denoting positive design constants; with denoting the first derivative of ξ v with ξ ω denoting the first derivative of ξ

[0071] S52: constructing an actual controller for the current-resistant trajectory tracking of the jetting-arm seabed cable-laying robot based on the disturbance observer, which is expressed as

[0072]

[0073] wherein τ v ,τ ω denote the actual control signal for the current-resistant trajectory tracking; k v ,k ω denote design parameters.

[0074] A current-resistant trajectory tracking control system of a jetting-arm seabed cable-laying robot, comprising a model creation module, a virtual controller module, an adaptive law module, a disturbance observer module and a predetermined time module;

[0075] The model creation module is configured to construct a current-resistant motion model of the jetting-arm seabed cable-laying robot.

[0076] The predetermined time module is configured to obtain position error and heading tracking error based on the current-resistant motion model according to a given reference trajectory, and to construct a predetermined time controller based on the position error and the heading tracking error.

[0077] The virtual controller module is configured to obtain a virtual controller of the jetting-arm seabed cable-laying robot based on the current-resistant motion model according to the predetermined time controller.

[0078] The virtual controller comprises a longitudinal velocity virtual controller and an angular velocity virtual controller.

[0079] The longitudinal velocity error and the angular velocity error are defined according to the virtual controller.

[0080] The adaptive law module is configured to construct a parameter adaptive law based on the current-resistant motion model according to the longitudinal velocity error and the angular velocity error.

[0081] The parameter adaptive law comprises a longitudinal velocity adaptive law and an angular velocity adaptive law.

[0082] The disturbance observer module is used to construct a disturbance observer according to a virtual controller and a parameter adaptive law, and construct an actual controller for trajectory tracking of the jet arm seabed cable laying robot against ocean currents based on the disturbance observer.

[0083] Compared with the prior art, the anti-ocean current trajectory tracking control method and system of the jet arm seabed cable laying robot has the following beneficial effects:

[0084] Firstly, in the existing seabed cable laying robot research method, the modeling of the seabed cable laying robot is not perfect, and the modeling of the anti-ocean current motion model of the jet arm seabed cable laying robot is completed by combining the characteristics of the seabed cable laying robot trenching and the characteristics of the tracked mobile robot, so that the trajectory tracking control of the seabed cable laying robot is more easily realized.

[0085] Secondly, the influence of the seabed ocean current and other interference factors on the seabed cable laying robot is considered, and the disturbance observer is designed, so that the disturbance observer can more accurately compensate the disturbance of the seabed ocean current, improve the anti-interference ability of the seabed cable laying robot, and improve the practical application value of the seabed cable laying robot.

[0086] Thirdly, most of the control algorithms of the seabed cable laying robot can achieve the expected control target, but cannot completely guarantee completion within the pre-set time range. Therefore, the predetermined time theory is used in the present application, so that the system can converge within the pre-set time, has better robustness, and makes the trajectory tracking of the seabed cable laying robot achieve the expected control effect within the pre-set time. DETAILED DESCRIPTION

[0087] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0088] Figure 1 The flow chart of the anti-ocean current trajectory tracking control method of the jet arm seabed cable laying robot of the present application;

[0089] Figure 2 The two-dimensional plane graph of the trajectory tracking of the seabed cable laying robot in the actual task in the present embodiment;

[0090] Figure 3 The relative distance error curve graph between the seabed cable laying robot and the tracking trajectory in the present embodiment;

[0091] Figure 4A relative angle error curve between the submarine cable laying robot and the tracking trajectory in the embodiment;

[0092] Figure 5 A curve of a longitudinal input signal τ of the submarine cable laying robot in the embodiment; v

[0093] Figure 6 A curve of a rotational direction input signal τ of the submarine cable laying robot in the embodiment; ω

[0094] Figure 7 A block diagram of an anti-ocean current trajectory tracking control system of the jet arm submarine cable laying robot in the embodiment. DETAILED DESCRIPTION

[0095] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0096] The embodiment provides an anti-ocean current trajectory tracking control method of a jet arm submarine cable laying robot, as shown in the formula (1), and specifically includes the following steps: Figure 1

[0097] S1: constructing an anti-ocean current motion model of the jet arm submarine cable laying robot;

[0098] Specifically, the input signal of the submarine cable laying robot is set as an actual control signal τ, and the output signal is position information η and longitudinal velocity information v of the submarine cable laying robot, and the constructed anti-ocean current motion model of the jet arm submarine cable laying robot is

[0099]

[0100] In the formula, η=[x, y, θ] T represents a position-deflection angle vector of the jet arm submarine cable laying robot; x and y represent horizontal and vertical coordinates of a two-dimensional coordinate position of the submarine cable laying robot; θ represents a deflection angle; v=[v, ω] Τ represents a velocity vector in a coordinate system of the jet arm submarine cable laying robot; v represents a longitudinal velocity; ω represents an angular velocity; τ=[τ v , τ ω ] T , and τ v and τ ω respectively represent actual control signals of the jet arm submarine cable laying robot in a longitudinal direction and a rotational direction; F=[F​​​v ,F ω ] T , and f L and f R represent the resistance of the left and right tracks of the jetting arm seabed cable-laying robot respectively; F d represents the suspension rope force on the robot; represents the included angle between the suspension rope of the robot and the motion direction; Fcos(α1+α2) represents the component of the reaction force of the nozzle on the robot in the motion direction of the robot; α1 represents the included angle between the nozzle and the jetting arm; α2 represents the included angle between the jetting arm and the motion direction; F D represents the drag resistance; F ω =-f R b+f L b-M μ , and b represents the distance from the center of the track to the geometric center of the robot; M μ represents the steering resistance torque; D=[D v D ω ] T , and D v and D ω represent seabed current disturbance, and satisfy and represent the upper bounds of D v and D ω ; J(θ), A, B, C represent parameter matrices; m, I ω represent the total mass and the body moment of inertia of the seabed cable-laying robot under water respectively; μ L represents the positive friction coefficient of the left track with soil; μ R represents the positive friction coefficient of the right track with soil; L and R represent the left and right tracks respectively; I r represents the track moment of inertia; k r represents the traction coefficient; r represents the driving wheel radius of the track, and -Av+BF represents the uncertain term in the anti-current motion model;

[0101] S2: based on the anti-current motion model, obtaining position error and heading tracking error according to a given reference trajectory, and based on the position error and the heading tracking error, constructing a predetermined time controller;

[0102] Specifically comprising the following steps:

[0103] S21: based on the anti-current motion model, obtaining position error according to a given reference trajectory η d , wherein η d =[x d ,y d ,θ d ] T ;

[0104] and the position error is

[0105]

[0106] e x = x - x d , e y = y - y d

[0107] wherein e x represents the position horizontal coordinate error; x d represents the expected position horizontal coordinate; e y represents the position vertical coordinate error; y d represents the expected position vertical coordinate; e z represents the position error;

[0108] and the heading tracking error is obtained according to the position error, and the expression is

[0109] e θ = θ - θ d

[0110] wherein θ d represents the ideal heading angle related to the position horizontal coordinate error e x and the position vertical coordinate error e y ; and θ d = atan2(e y , e x ); atan2 represents the inverse tangent function;

[0111] S22: the error constraint condition is constructed according to the position error and the heading tracking error, and the expression is

[0112]

[0113] wherein Ω j (t) and represent the boundary function to be set, and j = z, θ;

[0114] S23: the predetermined time performance function is constructed based on the error constraint condition, and the boundary function is designed as

[0115]

[0116] wherein ρ j (t) represents the predetermined time performance function; ρ j∞ represents the convergence precision; n represents the order of the system; and σ ej , ρ j0 , ρ j∞represents the design parameters required according to actual needs, and σ ej >0, ρ j0 >ρ j∞ >0;

[0117] S24: Construct a logarithmic barrier function based on the designed boundary function, and its expression is:

[0118]

[0119] Where: γ z represents an intermediate variable and γ θ represents an intermediate variable and ln(·) represents the natural logarithm function; s θ For example, if and only if e θ = 0, s θ =0; when s θ →-∞, When s θ →-∞,e θ →- Ω θ (t); therefore, the azimuth angle tracking error e θ will converge to a compact set containing the origin inside; and s z represents the obstacle function with respect to the position error; s θ represents the obstacle function with respect to the heading tracking error;

[0120] S25: Derivative the logarithmic barrier function to obtain the scheduled time controller, which is expressed as

[0121]

[0122] Where: φ q and χ q Indicates the scheduled time control signal; φ z ,χ z Indicates the distance to the predetermined time signal; φ θ ,χ θ Indicates the angle predetermined time signal;

[0123] S3: obtaining a virtual controller of the jet arm submarine cable laying robot according to a predetermined time controller, and defining a longitudinal velocity error and an angular velocity error according to the virtual controller;

[0124] And the virtual controller includes a longitudinal velocity virtual controller and an angular velocity virtual controller;

[0125] The specific steps include:

[0126] S31: Based on the anti-ocean current motion model of the jet-arm submarine cable-laying robot, a virtual controller of the jet-arm submarine cable-laying robot is constructed according to the logarithmic obstacle function and the predetermined time controller;

[0127] And the virtual controller includes a longitudinal velocity virtual controller and an angular velocity virtual controller;

[0128] The expression of the longitudinal velocity virtual controller is:

[0129]

[0130] The expression of the angular velocity virtual controller is:

[0131]

[0132] Where: and Represents a virtual control signal; Represents x d ,y d The first derivative of

[0133] S32: Perform first-order low-pass filtering on the virtual controller to obtain the first-order filter output error; and define the longitudinal velocity error and angular velocity error of the jet arm submarine cable laying robot based on the first-order filter output error, and its expression is:

[0134]

[0135] s v =v-α fv

[0136] s ω =ω-α fω

[0137] Where: s fv With s fω Represents the output error of the first-order filter; α fv With α fω represents the filtered signal; and Indicates a virtual control signal; s v ,s ω represent the longitudinal velocity error and angular velocity error respectively;

[0138] And the expression for first-order low-pass filtering of the virtual controller is:

[0139]

[0140] Where: α cv ,α cωdenote the input of the first order low pass filter in the longitudinal velocity direction and the angular velocity direction, respectively; a fω (0) denotes the initial value of a cω (0) denotes the initial value of a cv (0) denotes the initial value of a cω (0) denotes the initial value of a cv (0) denotes the initial value of a cω (0) denotes the initial value of a denotes the first derivative of a fv (0) denotes the first derivative of a denotes the first derivative of a fω (0) denotes the first derivative of a fv (0) denotes the first derivative of a fω (0) denotes the first derivative of a

[0141]

[0142] In the formula, Δ and Δ denote continuous functions with the independent variable being Δ v and Δ ω , respectively; and denote normal numbers;

[0143] The embodiment also includes a known transformation for performing a simulation experiment, as shown below:

[0144] According to the derivative formula of the anti-current motion model, the derivative of the position error and the heading tracking error is

[0145]

[0146] Based on the derivative formula and the predetermined time controller, the following can be obtained

[0147]

[0148] S4: Constructing a parameter adaptive law according to the longitudinal velocity error and the angular velocity error;

[0149] The parameter adaptive law includes a longitudinal velocity adaptive law and an angular velocity adaptive law;

[0150] Specifically, the following steps are included:

[0151] Based on the fuzzy logic system, the uncertain term λ in the anti-current motion model is approximated, and λ = -Av + BF, λ = [λ v λ ω ] T , wherein λ v denotes an unknown function term about the longitudinal velocity; λ ω denotes an unknown function term about the angular velocity;

[0152] The expression of the unknown function term in the anti-ocean current motion model approximated by the fuzzy logic system is:

[0153]

[0154] Where: W v * represents the adaptive parameter W v The optimal parameter vector of ω * represents the adaptive parameter W ω The optimal parameter vector of ; Indicates is a continuous function of a variable; Indicates is a continuous function of a variable; and represents the variables related to the longitudinal velocity v and angular velocity ω; ε v With ε ω Represents the approximation error and satisfies and and represents a positive constant; and Represent the basis functions of the fuzzy logic system;

[0155] S42: constructing a parameter adaptive law based on the longitudinal velocity error and the angular velocity error in combination with step S41; the parameter adaptive law includes a longitudinal velocity adaptive law and an angular velocity adaptive law;

[0156] The expression of the longitudinal velocity adaptation law is:

[0157]

[0158] The expression of the angular velocity adaptive law is:

[0159]

[0160] Where: represents the parameter adaptive law and i=v,ω;δ v ,δ ω represents the design parameters and δ v >0,δ ω >0;Γ v ,Γ ω represents the designed control gain matrix; W v * estimated value of; W ω * estimated value of;

[0161] S5: Constructing a disturbance observer based on the virtual controller and the parameter adaptive law to obtain an actual controller for the ocean current resistant trajectory tracking of the jet arm seabed cable laying robot;

[0162] Specifically comprising the following steps:

[0163] S51: Constructing a disturbance observer based on the virtual controller and the parameter adaptive law;

[0164] The expression of the disturbance observer is

[0165]

[0166] In the formula, ξ v and ξ ω represent the observed state; r v and r ω respectively represent unknown disturbances in the longitudinal velocity direction and the angular velocity direction; and respectively represent the estimated values of the unknown disturbances r v and r ω ; k rv and k rω represent positive design constants; and represent the first derivatives of ξ v and ξ ω ; T represents transposition;

[0167] S52: Constructing an actual controller for the ocean current resistant trajectory tracking of the jet arm seabed cable laying robot based on the disturbance observer, and the expression is

[0168]

[0169] In the formula, τ v , τ ω represent the actual control signals for the ocean current resistant trajectory tracking; k v , k ω represent design parameters.

[0170] To sum up, the beneficial effects of the embodiment are:

[0171] First, in the existing seabed cable laying robot research method, the modeling of the seabed cable laying robot is not perfect, and the embodiment completes the modeling in combination with the characteristics of the seabed cable laying robot and the characteristics of the tracked mobile robot. The accurate modeling of kinematics and dynamics makes it easier to achieve trajectory tracking control of the seabed cable laying robot.

[0172] Second, in this embodiment, the influence of interference factors such as seabed currents on the submarine cable-laying robot is taken into consideration, and a disturbance observer is designed, which improves the practical application value of the submarine cable-laying robot. Therefore, it is more universal and convincing than previous research.

[0173] Third, while most control algorithms for submarine cable-laying robots can achieve the desired control objectives, they cannot guarantee completion within a pre-set timeframe. Therefore, this embodiment employs the time-predetermined theory to ensure that the submarine cable-laying robot's trajectory tracking achieves the desired control effect within a pre-set timeframe.

[0174] At the same time, based on the same invention essence, the present invention also provides an anti-ocean current trajectory tracking control system for a jet arm submarine cable laying robot, such as Figure 7 As shown, it includes a model creation module, a virtual controller module, an adaptive law module, a disturbance observer module and a predetermined time module;

[0175] The predetermined time module is used to obtain a position error and a heading tracking error according to a given reference trajectory based on an anti-ocean current motion model, and to construct a predetermined time controller based on the position error and the heading tracking error;

[0176] The virtual controller module is used to obtain a virtual controller of the jet arm submarine cable laying robot according to a predetermined time controller based on an anti-ocean current motion model;

[0177] And the virtual controller includes a longitudinal velocity virtual controller and an angular velocity virtual controller;

[0178] And define the longitudinal velocity error and angular velocity error according to the virtual controller;

[0179] The adaptive law module is used to construct a parameter adaptive law based on the anti-ocean current motion model according to the longitudinal velocity error and the angular velocity error;

[0180] The parameter adaptive law includes a longitudinal velocity adaptive law and an angular velocity adaptive law;

[0181] The disturbance observer module is used to construct a disturbance observer according to a virtual controller and a parameter adaptive law, and to construct an actual controller for anti-ocean current trajectory tracking of a jet arm submarine cable-laying robot based on the disturbance observer.

[0182] In a specific embodiment, the connection relationship between the modules is as follows: the output end of the model creation module is connected to the input ends of the predetermined time module, the virtual controller module and the adaptive law module respectively;

[0183] The output end of the predetermined time module is connected to the input end of the virtual controller module;

[0184] The output ends of the virtual controller module are connected with the input ends of the adaptive law module and the disturbance observer module respectively.

[0185] The output end of the adaptive law module is connected with the input end of the disturbance observer module, and the output end of the disturbance observer module is connected with the control input end of the jet arm seabed cable laying robot.

[0186] The model creating module is used for constructing the anti-ocean current motion model of the jet arm seabed cable laying robot.

[0187] In the trajectory tracking control of the seabed cable laying robot, the given reference trajectory, reference distance, reference relative azimuth angle signal and position vector η information of the seabed cable laying robot are input into the predetermined time module, the predetermined time module analyzes and calculates the input information to obtain predetermined time parameter φ q and χ q (q=z, θ), which are input into the virtual controller module, meanwhile, the velocity vector υ information of the seabed cable laying robot is input into the virtual controller module, the virtual controller module analyzes and calculates the input information to obtain the virtual control signal of the virtual controller and The virtual controller module inputs the obtained virtual control signal and into the disturbance observer module and the adaptive module respectively. Meanwhile, the velocity vector υ information of the seabed cable laying robot is input into the adaptive law module, the adaptive law module analyzes and calculates the input information to obtain adaptive parameter which is input into the disturbance observer module, the disturbance observer module analyzes and calculates the input signal from the outside to obtain actual control signal τ v and τ ω , finally, the disturbance observer module inputs the actual control signal into the seabed cable laying robot. The design goal of the embodiment is that the trajectory tracking control system of the seabed cable laying robot can effectively overcome the ocean current disturbance after introducing the disturbance observer and the predetermined time control method, and can further realize the collision avoidance and connectivity maintenance of the seabed cable laying robot in combination with the specified performance theory.

[0188] The simulation results of the embodiment are shown in Figures 2 to 6 . Figure 2 is the two-dimensional plane trajectory tracking curve diagram of the seabed cable laying robot according to the actual task requirement, through the diagram, it can be seen that the seabed cable laying robot is constrained in the specified area; Figure 3 is the relative distance error curve diagram between the seabed cable laying robot and the following trajectory, through the analysis diagram, it can be known that the relative distance error can converge to the vicinity of zero within the predetermined time. Figure 4is a relative angle error curve between the undersea cable laying robot and the following trajectory, and the analysis graph shows that the relative angle error can converge to the vicinity of zero within a predetermined time; Figures 5 to 6 respectively represent the longitudinal input signal τ v and the rotational direction input signal τ ω of the undersea cable laying robot, and the graphs show that the introduced disturbance observer can overcome the disturbance influence to limit the control input within a specified range; the simulation result graphs and the obtained table show that the designed undersea cable laying robot trajectory tracking controller can eliminate the disturbance influence of the ocean current and achieve the stability requirement within a predetermined time, and finally achieve the expected undersea cable laying robot trajectory tracking task requirement.

[0189] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for tracking and controlling the trajectory of a jet-arm submarine cable-laying robot against ocean currents, characterized in that: The specific steps include: S1: Constructing an anti-ocean current motion model for the jet-arm submarine cable-laying robot; S2: Based on the anti-ocean current motion model, the position error and heading tracking error are obtained according to the given reference trajectory, and a scheduled time controller is constructed based on the position error and heading tracking error; The specific steps include: S21: Based on the anti-ocean current motion model, according to the given reference trajectory Get the position error, where ; And the position error is ， Where: Indicates the position horizontal coordinate error; Indicates the horizontal coordinate of the expected position; Indicates the position ordinate error; Indicates the desired position ordinate; Indicates position error; The horizontal and vertical coordinates representing the two-dimensional coordinate position of the submarine cable laying robot; And obtain the heading tracking error based on the position error, its expression is: Where: Indicates the horizontal coordinate error of the position and position ordinate error the associated ideal heading angle; and ; represents the inverse tangent function; represents the deflection angle; S22: Construct error constraints based on position error and heading tracking error, and its expression is: Where: and represents the boundary function to be set, and ; S23: Construct a scheduled time performance function based on the error constraint condition, and design the boundary function as follows: Where: represents the scheduled time performance function; Indicates convergence accuracy; represents the order of the system; , , Indicates the design parameters required according to actual needs, and , , ; S24: Construct a logarithmic barrier function based on the designed boundary function, and its expression is: Where: represents an intermediate variable and ; represents an intermediate variable and ; represents the natural logarithm function; and represents the barrier function with respect to the position error; represents the obstacle function with respect to the heading tracking error; S25: Derivative the logarithmic barrier function to obtain the scheduled time controller, which is expressed as ， Where: and Indicates a predetermined time control signal; Indicates the distance to the predetermined time signal; Indicates the angle predetermined time signal; S3: Obtaining a virtual controller of the jet arm submarine cable laying robot according to a predetermined time controller; And the virtual controller includes a longitudinal velocity virtual controller and an angular velocity virtual controller; And define the longitudinal velocity error and angular velocity error according to the virtual controller; S4: Construct parameter adaptive law based on longitudinal velocity error and angular velocity error; The parameter adaptive law includes a longitudinal velocity adaptive law and an angular velocity adaptive law; S5: Construct a disturbance observer based on a virtual controller and parameter adaptation law to obtain a practical controller for the current-resistant trajectory tracking of the jet-arm submarine cable-laying robot; The specific steps include: S51: Constructing a disturbance observer based on a virtual controller and parameter adaptation law; The expression of the disturbance observer is: Where: and Indicates the observation state; and Represent the unknown disturbances in the longitudinal velocity direction and angular velocity direction respectively; and Respectively represent unknown interference and estimated value of; and represents a positive design constant; and express and The first derivative of represents transpose; Indicates the actual control signal for anti-ocean current trajectory tracking; represents the parameter adaptation law and ; Represents adaptive parameters The optimal parameter vector of ; Represents adaptive parameters The optimal parameter vector of ; express estimated value of; express estimated value of; and Represents the output error of the first-order filter; and represents the filtered signal; represent the longitudinal velocity error and angular velocity error respectively; express The filter time constant; express The filter time constant; , Respectively represent the input of the first-order low-pass filter in the longitudinal velocity direction and the angular velocity direction; and Represent the basis functions of the fuzzy logic system; and Indicates the longitudinal velocity and angular velocity variables; S52: Based on the disturbance observer, a practical controller for tracking the trajectory of the jet-arm submarine cable-laying robot against ocean currents is constructed. Its expression is: Where: Indicates the actual control signal for anti-ocean current trajectory tracking; Represents design parameters.

2. The anti-ocean current trajectory tracking control method of a jet arm submarine cable laying robot according to claim 1 is characterized in that: The anti-ocean current motion model of the jet arm submarine cable laying robot constructed in S1 is: , , , Where: represents the position-deflection angle vector of the jet arm submarine cable laying robot; The horizontal and vertical coordinates representing the two-dimensional coordinate position of the submarine cable laying robot; represents the deflection angle; represents the velocity vector in the coordinate system of the jet arm submarine cable laying robot; represents the longitudinal velocity; represents angular velocity; ,and and Represent the actual control signals of the jet arm submarine cable laying robot in the longitudinal and rotational directions respectively; ,and , and They represent the resistance on the left and right tracks of the jet-arm submarine cable-laying robot respectively; represents the suspension rope force acting on the robot; Indicates the angle between the robot's suspension rope and the direction of movement; It represents the component of the reaction force of the nozzle on the robot in the direction of robot movement; Indicates the angle between the nozzle and the spray arm; Indicates the angle between the spray arm and the direction of movement; Indicates drag resistance; ,and Indicates the distance from the track center to the robot's geometric center; represents the steering resistance torque; ,and and Indicates the disturbance of the submarine current, and satisfies , ; and Respectively and The upper bound of , , , represents the parameter matrix; , They represent the total mass and the moment of inertia of the submarine cable-laying robot underwater respectively; Indicates the positive friction coefficient between the left track and the soil; Indicates the positive friction coefficient between the right track and the soil; and Respectively represent the left and right tracks; represents the track moment of inertia; represents the traction coefficient; represents the rotation radius of the track drive wheel, and Represents the uncertainty in the anti-ocean current motion model.

3. The anti-ocean current trajectory tracking control method of a jet arm submarine cable laying robot according to claim 2 is characterized in that: The S3 specifically includes the following steps: S31: Based on the anti-ocean current motion model of the jet-arm submarine cable-laying robot, a virtual controller of the jet-arm submarine cable-laying robot is constructed according to the logarithmic obstacle function and the predetermined time controller; And the virtual controller includes a longitudinal velocity virtual controller and an angular velocity virtual controller; The expression of the longitudinal velocity virtual controller is: The expression of the angular velocity virtual controller is: Where: and Represents a virtual control signal; express The first derivative of S32: Performing first-order low-pass filtering on the virtual controller to obtain a first-order filter output error; The longitudinal velocity error and angular velocity error of the jet arm submarine cable laying robot are defined according to the output error of the first-order filter, and their expressions are: Where: and Represents the output error of the first-order filter; and represents the filtered signal; and Represents a virtual control signal; represent the longitudinal velocity error and angular velocity error respectively; And the expression for first-order low-pass filtering of the virtual controller is: ， ； ， ， Where: , Respectively represent the input of the first-order low-pass filter in the longitudinal velocity direction and the angular velocity direction; express , The initial value of express The filter time constant; express The filter time constant; express The first derivative of express The first derivative of .

4. The anti-ocean current trajectory tracking control method of a jet arm submarine cable laying robot according to claim 3 is characterized in that: The S4 specifically includes the following steps: S41: Approximating the uncertainty in ocean current motion models based on fuzzy logic systems and , ,in represents the unknown function term related to the longitudinal velocity; Represents the unknown function term about angular velocity; The expression of the unknown function term in the anti-ocean current motion model approximated by the fuzzy logic system is: ， Where: Represents adaptive parameters The optimal parameter vector of ; Represents adaptive parameters The optimal parameter vector of ; Indicates is a continuous function of a variable; Indicates is a continuous function of a variable; and Indicates the longitudinal velocity and angular velocity variables; and Represents the approximation error and satisfies and , and represents a positive constant; and Represent the basis functions of the fuzzy logic system; S42: constructing a parameter adaptive law based on the longitudinal velocity error and the angular velocity error in combination with step S41; The parameter adaptive law includes a longitudinal velocity adaptive law and an angular velocity adaptive law; The expression of the longitudinal velocity adaptation law is: The expression of the angular velocity adaptive law is: Where: represents the parameter adaptation law and ; , represents the design parameters and , ; , represents the designed control gain matrix; express estimated value of; express estimated value.

5. A system based on the anti-ocean current trajectory tracking control method of the jet arm submarine cable laying robot according to claim 1, characterized in that: It includes a model creation module, a virtual controller module, an adaptive law module, a disturbance observer module and a predetermined time module; The model creation module is used to construct an anti-ocean current motion model of the jet arm submarine cable laying robot; The predetermined time module is used to obtain a position error and a heading tracking error according to a given reference trajectory based on an anti-ocean current motion model, and to construct a predetermined time controller based on the position error and the heading tracking error; The virtual controller module is used to obtain a virtual controller of the jet arm submarine cable laying robot according to a predetermined time controller based on an anti-ocean current motion model; And the virtual controller includes a longitudinal velocity virtual controller and an angular velocity virtual controller; And define the longitudinal velocity error and angular velocity error according to the virtual controller; The adaptive law module is used to construct a parameter adaptive law based on the anti-ocean current motion model according to the longitudinal velocity error and the angular velocity error; The parameter adaptive law includes a longitudinal velocity adaptive law and an angular velocity adaptive law; The disturbance observer module is used to construct a disturbance observer according to a virtual controller and a parameter adaptive law, and to construct an actual controller for anti-ocean current trajectory tracking of a jet arm submarine cable-laying robot based on the disturbance observer.

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