An underactuated unmanned ship course tracking control system based on extreme learning

Abstract

The application discloses an underactuated unmanned ship route tracking control system based on extreme learning, which comprises an establishing module I, an establishing module II, an establishing module III, an identifying module and a control module. Based on the identified unmodeled dynamics, parameter disturbance, external environment disturbance and the rest dynamic unknown items, and the longitudinal sight line guidance law, a robust adaptive route tracking control method based on extreme learning is adopted, the output weight based on the single hidden layer feedforward network SLFN approximation and the corresponding estimated error adaptive rate are designed to approximate the unknown items and reduce the approximation error, the identification precision is improved, the longitudinal controller and the bow controller are designed to compensate for the unmodeled dynamics, parameter disturbance, external environment disturbance and the rest dynamic unknown items, so that the unmanned ship is asymptotically stable at the dynamics level, the tracking control of the unmanned ship sailing along the expected path is realized, the tracking precision is improved, and the global asymptotic stability of the whole closed loop system is improved.

Description

Technical Field

[0001] The present invention belongs to the field of unmanned ship motion control and relates to an under-actuated unmanned ship route tracking control system based on extreme speed learning. Background Art

[0002] With the rapid development of marine resource development and advanced control technology, underactuated marine vehicles (UMV) have attracted widespread attention in both military and civilian fields. UMV is a typical underactuated system because it uses two independent control inputs to adjust the three-dimensional output. At present, the motion control of UMV mainly includes stabilization [1] , trajectory tracking [2] and route tracking [3,4] ,It is very important to follow the predefined route without time constraints.,Therefore, ,path tracking control plays a vital role when performing maritime missions in harsh ,environment and extreme maneuvers.

[0003] Path tracking control is mainly divided into two modules: guidance and control. Guidance usually refers to kinematic control, which generates guidance signals containing the desired heading angle or surge velocity by designing the guidance law. The control module is the dynamic control, which enables the UMV dynamics to strictly track the guidance signal by designing the controller input, ultimately achieving path tracking. In the field of ship motion control, line-of-sight (LOS) guidance is a key component of ship motion control. [5] The effectiveness of has been widely recognized in both theory and practice. [6] In 2003, the LOS guidance law was first applied to UMV path tracking, that is, the LOS projection algorithm was used to track the segmented route actually connected by waypoints. However, the above work ignored the influence of sideslip angle. Obviously, when facing large environmental disturbances such as wind, waves and ocean currents, the UMV path tracking accuracy will be seriously affected. Caharija et al. [7] Taking the sideslip angle as a slowly time-varying unknown term, the integral line-of-sight (ILOS) guidance was proposed to compensate for the sideslip angle. [8] An adaptive line-of-sight (ALOS) guidance method was proposed to solve the sideslip problem through adaptive compensation. Considering the ocean current, Moe et al. [9] proposed a LOS guidance law based on relative velocity. However, the above LOS-based guidance law has a common phenomenon in the entire route tracking process. At the same time, the surge speed is defined as a user-defined parameter. In this case, the UMV is actually controlled only by the steering torque of the rudder, which not only reduces the overall maneuverability but also increases the control burden of the rudder.

[0004] The control module aims to make the UMV track the guidance signal as accurately as possible. Common control methods include backstepping control

[10] , sliding mode control [11,12] and feedback linearization

[13] , etc. However, in practical applications, the UMV is inevitably affected by complex hydrodynamic forces, unmodeled dynamics, uncertainties and environmental disturbances, which undoubtedly makes model-based techniques infeasible to some extent. In this regard, Rout et al.

[14] proposed a partially known dynamics adaptive neural network control law with state constraints, which can quickly and accurately identify complex unknown quantities. Wang et al.

[15] designed an auxiliary observation dynamic to accurately identify the above nonlinearities using a fuzzy logic observer. It is worth noting that these fixed-structure approximators require prior system knowledge of the UMV to predefine a large number of hidden nodes in the high-dimensional input space, resulting in the curse of dimensionality problem. Unlike deterministic approximators, Huang et al. [16,17] proposed an extreme learning machine (ELM) based on a single-hidden layer feedforward network (SLFN), in which the hidden layer nodes can be randomly generated, and the output weights are determined only by the Moore-Penrose pseudo-inverse method, so that extremely fast regression and classification can be achieved. In the control field, the target observation or function is usually not available, so an adaptive control scheme based on ELM is necessary. For this purpose, Wang et al. [18,19] proposed an extreme learning control (ELC) scheme using SLFN, which achieved high accuracy in trajectory tracking and error approximation of fully driven unmanned ships. However, compared with the tracking control method of fully driven unmanned ships, the complex unknown quantities of underactuated unmanned ships are difficult to be fully handled due to the underactuation characteristics in the sway dynamics.

[0005] The prior art has the following problems:

[0006] (1) The traditional guidance law generally has a singularity phenomenon when tracking the navigation path, and the longitudinal velocity is a user-defined parameter, which results in the actual underactuated unmanned ship being controlled only by the steering torque of the rudder, not only reducing the overall maneuverability, but also increasing the maneuvering burden of the rudder.

[0007] (2) In practical applications, underactuated unmanned ships are inevitably subject to complex hydrodynamics, unmodeled dynamics, parameter uncertainty, and environmental interference. Traditional model-based technologies find it difficult to handle these complex unknowns. Although intelligent approximation algorithms such as artificial neural networks can identify the above unknowns, these fixed-structure approximators require prior system knowledge on the underactuated unmanned ship to predefine a large number of hidden nodes in the high-dimensional input space, which leads to the "dimensionality explosion" problem.

[0008] (3) When identifying complex unknowns online, the single-channel learning mechanism will always have a certain approximation residual. If this residual is ignored, the path tracking accuracy of the under-actuated unmanned ship will be reduced. Summary of the Invention

[0009] In order to solve the above problems, the technical solution adopted by the present invention is: an underactuated unmanned ship route tracking control system based on rapid learning, comprising:

[0010] Establishing Module I: used to establish the kinematic equations of the underactuated unmanned vessel;

[0011] Establishing Module II: used to establish the path tracking error dynamic equation based on the kinematic equation of the underactuated unmanned vessel;

[0012] Establishing Module III: This is used to establish a surge line-of-sight guidance law that can make the unmanned vessel asymptotically stable at the kinematic level, so that when the vessel is navigating along the desired path, the error between the unmanned vessel and the desired path gradually decreases;

[0013] Identification module: used to identify the unmodeled dynamics, parameter disturbances, external environmental interference, and other dynamic lumped unknowns during the navigation process of the unmanned ship using an extremely fast learning online identification method;

[0014] Control module: It is used to adopt a robust adaptive path tracking control method based on extreme learning based on the identified unmodeled dynamics, parameter disturbances, external environmental interference and other dynamic lumped unknowns, as well as the longitudinal and longitudinal line of sight guidance law. It designs the output weights based on the single hidden layer feedforward network SLFN approximation and the corresponding estimation error adaptive rate to approximate the lumped unknowns and reduce the approximation error, thereby improving the identification accuracy. It also designs the longitudinal controller and the heading controller to compensate for the unmodeled dynamics, parameter disturbances, external environmental interference and other dynamic lumped unknowns, so that the unmanned ship is asymptotically stable at the dynamic level and realizes the tracking control of the unmanned ship according to the desired path.

[0015] Furthermore, the dynamic equation of the underactuated unmanned vessel is expressed as follows:

[0016]

[0017] lu ,l v ,l r It includes not only unmodeled dynamics, parameter disturbances, and external environmental disturbances, but also the lumped unknowns of other dynamics, which will be observed later to achieve model-free control of the UMV dynamics. (u, v, r) are the surge velocity, sway velocity, and bow angular velocity of the UMV, and τ u is the surge control force, τ r is the steering torque; m 11 、m 33 is the ship mass inertia coefficient, are the first-order derivatives of u, v, and r respectively.

[0018] Furthermore, the expression of the path tracking error dynamic equation is as follows:

[0019]

[0020] Where: θ is the route update parameter, φ p is the tangent angle of the route reference point relative to the geodetic coordinate system, u is the longitudinal speed, ψ is the heading angle, β is the sideslip angle, and u t is the moving speed of the reference point on the route.

[0021] Furthermore, the expression of the turbulent line of sight guidance law is as follows:

[0022]

[0023] Among them, φ p is the tangent angle at the reference point on the reference route, Δ>0 is the foresight distance, and the expected sideslip angle β d With the longitudinal speed u d is defined as:

[0024]

[0025] Among them, k1>0, and u d The minimum value is set to:

[0026] u d min=k1Δ (15)

[0027] Furthermore, the process of using the rapid learning online identification method to identify the unmodeled dynamics, parameter disturbances, external environmental interference, and other dynamic lumped unknowns during the navigation process of the unmanned ship is as follows:

[0028] A single hidden layer feedforward network SLFN with N hidden nodes is used to online identify the following lumped unknown term l(x):

[0029] l(x)=WT h(x; C; Φ) (20)

[0030] Where W=[w1,...,w n ]∈R N×n ,w i =[w i 1 ,...,w i N ] T is the output weight, h=[h1,...,h N ] T ∈R N is a function with parameters C=[c1,...,c N ] T ∈R m×N and Φ=[φ1,...,φ N ] T ∈R N The normalized output of the activation function, N is the number of hidden layer nodes;

[0031] Assume that there is an optimal SLFN, where N hidden nodes are randomly generated and the parameter C∈R m×N and Φ∈R N , use the minimum function approximation error to identify the nonlinear function l(x):

[0032]

[0033] Among them, ε * (x) = [ε * 1,...,ε * n ] T is the vector of minimum function approximation error MFAE and satisfies Optimal output weight W * It is derived from the following formula.

[0034]

[0035] Furthermore, the expressions of the output weights based on SLFN approximation and the corresponding estimation error adaptation rate are as follows:

[0036]

[0037] Among them, k w ,k ε >0, set Ω 1 w ,Ω 2 w ,Ω 1 ε ,Ω 2ε The definition is as follows:

[0038]

[0039] Among them, M 1 w ,M 2 w ,M 1 ε ,M 2 ε is the corresponding upper bound, is the estimator of the SLFN output weight, is the estimator of the approximate residual, u e is the surge velocity error, s is the first-order linear sliding surface, h=[h1,...,h N ] T ∈R N is a function with parameters C=[c1,...,c N ] T ∈R m×N and Φ=[φ1,...,φ N ] T ∈R N The normalized output of the activation function, x is a vector containing the longitudinal, transverse and angular velocities of the heading, k w ,k ε is a coefficient greater than 0.

[0040] Furthermore: the longitudinal controller τ u The design is as follows:

[0041]

[0042] Among them, k u >0,u e =uu d Longitudinal velocity tracking error, is the estimated value of l1:

[0043]

[0044] Furthermore: the heading controller design process is as follows:

[0045] Introduce the following first-order linear sliding surface s:

[0046] s=k ψ ψ e +r e (42)

[0047] Among them, k ψ >0,ψ e =ψ-ψd ,

[0048] The heading controller is designed as follows:

[0049]

[0050] Among them, k s >0, is the estimated value of l2 in (3):

[0051]

[0052] The present invention provides an underactuated unmanned vessel route tracking control system based on rapid learning, which has the following advantages:

[0053] (1) The longitudinal swell line-of-sight guidance law is adopted to guide the longitudinal swell speed and heading angle simultaneously, thus avoiding the singularity problem in the guidance process, reducing the operating burden of the rudder, and improving the overall maneuverability of the under-actuated unmanned ship.

[0054] (2) The unknown dynamics including system uncertainty and external interference are encapsulated into a lumped unknown term, and the single hidden layer feedforward network of the extreme learning machine is used to randomly generate hidden layer nodes to identify the unknown term online, avoiding reliance on system prior knowledge and the "dimensionality explosion" problem.

[0055] (3) By designing an adaptive compensator for the approximation residual, i.e., formulas (26) and (28), the output weights and approximation residuals of the single hidden layer feedforward network are updated online simultaneously, forming a dual-channel learning mechanism. This not only enhances the approximation capability but also improves the tracking accuracy, which contributes to the global asymptotic stability of the entire closed-loop system. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] 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 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 labor.

[0057] Figure 1 This is a schematic diagram of the UMV route tracking;

[0058] Figure 2 It is UMV’s EL-RAPFC solution;

[0059] Figure 3 It is the SLFN structure diagram;

[0060] Figure 4 is the route tracking performance,

[0061] Figure 5 is the along-track and cross-track error, where (a) the along-track error, (b) the cross-track error,

[0062] Figure 6 is the EL-PAPFC surge and heading angle tracking, where (a) the surge tracking, (b) the heading angle tracking,

[0063] Figure 7 is the RAPFC surge and heading angle tracking, where (a) the surge tracking, (b) the heading angle tracking,

[0064] Figure 8 is the surge and heading angle tracking error, where (a) the surge tracking error, (b) the heading angle tracking error,

[0065] Figure 9 is the unknown dynamics l and its approximation where (a) the surge unknown dynamics and its estimate, (b) the heading unknown dynamics and its estimate,

[0066] Figure 10 is the estimate error, where (a) the surge estimate error, (b) the heading estimate error,

[0067] Figure 11 is the longitudinal and heading control input to the UMV, where (a) the surge control force, (b) the steering torque. DETAILED DESCRIPTION

[0068] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict, and the present application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0069] To make the objectives, 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 in combination with the drawings of the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, but not all the embodiments. The description of the at least one exemplary embodiment is actually only illustrative, but not as any limitation on the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the protection scope of the present application.

[0070] An underactuated unmanned ship course tracking control system based on extreme learning, comprising:

[0071] A building module I is configured to build a kinematic equation of the underactuated unmanned ship.

[0072] Establishing Module II: used to establish the path tracking error dynamic equation based on the kinematic equation of the underactuated unmanned vessel;

[0073] Establishing Module III: This is used to establish a surge line-of-sight guidance law that can make the unmanned vessel asymptotically stable at the kinematic level, so that when the vessel is navigating along the desired path, the error between the unmanned vessel and the desired path gradually decreases;

[0074] Identification module: used to identify the unmodeled dynamics, parameter disturbances, external environmental interference, and other dynamic lumped unknowns during the navigation process of the unmanned ship using an extremely fast learning online identification method;

[0075] Control module: It is used to adopt a robust adaptive path tracking control method based on extreme learning based on the identified unmodeled dynamics, parameter disturbances, external environmental interference and other dynamic lumped unknowns, as well as the longitudinal and longitudinal line of sight guidance law. It designs the output weights based on the single hidden layer feedforward network SLFN approximation and the corresponding estimation error adaptive rate to approximate the lumped unknowns and reduce the approximation error, thereby improving the identification accuracy. It also designs the longitudinal controller and the heading controller to compensate for the unmodeled dynamics, parameter disturbances, external environmental interference and other dynamic lumped unknowns, so that the unmanned ship is asymptotically stable at the dynamic level and realizes the tracking control of the unmanned ship according to the desired path.

[0076] Figure 1 This is a schematic diagram of the UMV route tracking;

[0077] Figure 2 It is UMV’s EL-RAPFC solution;

[0078] The process of expressing the kinematic equation of the underactuated unmanned vessel is as follows:

[0079] The kinematic model of the underactuated unmanned marine vehicle (UMV) is shown below:

[0080]

[0081] Where (x, y, ψ) is the position and heading angle of the UMV in the Earth coordinate system, (u, v, r) is the surge velocity, sway velocity, and pitch angular velocity of the UMV, and UMV guidance mainly refers to kinematic control.

[0082] Due to the influence of internal unmodeled dynamics, parameter perturbations, and external interference, the dynamics of the UMV can be expressed as follows:

[0083]

[0084] Among them, m ii(i=1,2,3) and d ii (i=1,2,3) represents the ship's mass inertia coefficient and the hydrodynamic damping coefficients of surge, sway and bow. The system control input is the surge control force τ u and steering torque τ r ,(τ δu ,τ δv ,τ δr ) is a complex unknown quantity that includes unmodeled dynamics, uncertainties, and external disturbances. The dynamic equation (2) can be further designed as:

[0085]

[0086] l u ,l v ,l r It includes not only unmodeled dynamics, parameter perturbations, and external environmental disturbances, but also the lumped unknowns of other dynamics, which will be observed later to achieve model-free control at the UMV dynamics level. are the first-order derivatives of u, v, and r respectively.

[0087]

[0088] l u ,l v ,l r It is composed of the UMV internal dynamics, parameter uncertainty and external disturbances. Due to the simultaneous existence of internal differentials and external disturbances, the above-mentioned lumped unknown parameters cannot be accurately approximated by nonlinear mapping.

[0089] Control objective: Design controller τ u and τ r , so that the UMV position (x, y) can track the parameterized route (x p (θ),y p (θ)).

[0090] Further: The reference route is determined by a parameter θ that does not depend on time. The reference route is based on the current point (x p (θ),y p (θ)) constructs a tangential reference coordinate system, and the rotation angle relative to the geodetic coordinate system is φ p :

[0091] φ p =arctan(x′ p (θ),y′ p (θ)) (5)

[0092] in:

[0093]

[0094] Derivative along formula (1):

[0095]

[0096] Among them, u t is the moving speed of the reference point on the route:

[0097]

[0098] Define the sideslip angle β as:

[0099]

[0100] The expression of the path tracking error dynamic equation is as follows:

[0101]

[0102] Where: θ is the route update parameter, φ p is the tangent angle of the route reference point relative to the geodetic coordinate system, u is the longitudinal speed, ψ is the heading angle, β is the sideslip angle, and u t is the moving speed of the reference point on the route.

[0103] Furthermore, the expression of the turbulence line-of-sight guidance law is as follows:

[0104]

[0105] Among them, φ p is the tangent angle at the reference point on the reference route, Δ>0 is the foresight distance, and the expected sideslip angle β d With the longitudinal speed u d is defined as:

[0106]

[0107] Where, k1>0, and in this application u d The minimum value is set to:

[0108] u d min=k1Δ (15)

[0109] Designed surge speed u d It is helpful to stabilize the route tracking error. e When it converges to 0, the reference velocity approaches a designed constant k1Δ.

[0110] The expected moving speed of the route is:

[0111] u t =u dcos(ψ d -φ p )+k2x e -u d tanβ d sin(ψ d -φ p ) (16)

[0112] Among them, k2>0.

[0113] Theorem 1: Under the guidance laws (12), (14) and (16), the tracking error x e and vertical tracking error y e It can converge to 0 globally asymptotically.

[0114] Proof: Design the following Lyapunov function:

[0115]

[0116] Derivative (17) and error dynamics (11) yield:

[0117]

[0118] Substituting guidance laws (12), (14) and (16) into (18), we obtain:

[0119]

[0120] Among them, k = min(k1, k2), Theorem 1 proves that the longitudinal oscillation line-of-sight guidance law proposed in this application can make the UMV asymptotically stable at the kinematic level.

[0121] Furthermore, the process of using the rapid learning online identification method to identify the unmodeled dynamics, parameter disturbances, external environmental interference, and other dynamic lumped unknowns during the navigation process of the unmanned ship is as follows:

[0122] The nonlinear term in Equation (3) is actually unknown. A single hidden layer feedforward network SLFN with N hidden nodes is used to online identify the following lumped unknown term l(x): Figure 3 It is the SLFN structure diagram;

[0123] l(x)=W T h(x; C; Φ) (20)

[0124] Where W=[w1,...,w n ]∈R N×n ,w i =[w i 1 ,...,w iN ] T is the output weight, h=[h1,...,h N ] T ∈R N is a function with parameters C=[c1,...,c N ] T ∈R m×N and Φ=[φ1,...,φ N ] T ∈R N The normalized output of the activation function, N is the number of hidden layer nodes;

[0125] Assume that there is an optimal SLFN, which exists in theory. The current SLFN is obtained by the adaptive update law (25) and (27), which is infinitely close to the theoretical optimal SLFN, where N hidden nodes are randomly generated and the parameter C∈R m×N and Φ∈R N , use the minimum function approximation error to identify the nonlinear function l(x):

[0126] l(x)=l * (x)+ε *

[0127] =W *T h(x;C;Φ)+ε * (twenty one)

[0128] Among them, ε * (x) = [ε * 1,...,ε * n ] T is the vector of the Minimal Functional Approximation Error (MFAE) and satisfies Optimal output weight W * It is derived from the following formula.

[0129]

[0130] In this part, combining SLFN approximation and adaptive residual estimation, an Extreme Learning-Based Robust Adaptive Path Following Control (EL-RAPFC) method is proposed.

[0131] The design process of the output weights and the corresponding estimation error adaptation rate based on SLFN approximation is as follows:

[0132] Since the optimal weight W* is not available, we rewrite the optimal SLFN in (21) as follows:

[0133]

[0134] in, It's W * The estimated value of is the output weight error, and ε is the actual approximation residual:

[0135]

[0136] In order to enable the controller to adapt to the unknown dynamics l(u,v,r), the following output weights based on SLFN approximation and the corresponding estimation error adaptation rate are designed:

[0137]

[0138] Among them, k w ,k ε >0, set Ω 1 w ,Ω 2 w ,Ω 1 ε ,Ω 2 ε The definition is as follows:

[0139]

[0140] Among them, M 1 w ,M 2 w ,M 1 ε ,M 2 ε is the corresponding upper bound, is the estimator of the SLFN output weight, is the estimator of the approximate residual, u e is the surge velocity error, s is the first-order linear sliding surface, h=[h1,...,h N ] T ∈R N is a function with parameters C=[c1,...,c N ] T ∈R m×N and Φ=[φ1,...,φ N ] T ∈R N is the normalized output of the activation function, and x is a vector containing the longitudinal, transverse and heading angular velocities.

[0141] The actual approximation residual ε consists of two parts, namely MFAEε * and Both are unknown quantities. The former (i.e. ε * ) corresponds to a reconstruction error that cannot be further minimized, which is caused by the estimation error of the output weights and the random hidden nodes. To improve the estimation accuracy, this application will also perform adaptive estimation of MFAE.

[0142] Furthermore, the longitudinal controller design process is as follows:

[0143] Longitudinal controller τ u The design is as follows:

[0144]

[0145] Among them, k u >0,u e =uu d Longitudinal velocity tracking error, is the estimated value of l1 in (3):

[0146]

[0147] Theorem 2: Using the robust longitudinal control law of Equation (33), combined with the output weights of Equations (25) and (26) and the corresponding estimation error adaptation rate, the longitudinal swell guidance speed u in Equation (14) can be calculated as d Perform global asymptotic tracking.

[0148] Proof: Design the following Lyapunov function:

[0149]

[0150] in, is the estimated vector of output weight errors.

[0151] Taking its derivative and following the dynamics (3) we can get:

[0152]

[0153] Considering the adaptation rate in (25) and (26), there are four cases:

[0154] like

[0155]

[0156] like

[0157]

[0158] If

[0159]

[0160] If

[0161]

[0162] Combining (37)-(40) and (36), we have

[0163]

[0164] This shows that u e , are bounded. By further derivation and using Barbalat's lemma, we can obtain that u e is globally asymptotically stable.

[0165] After the above derivation, Theorem 2 is proved.

[0166] Further, the heading controller is designed as follows:

[0167] To facilitate the controller design, we introduce the following first-order linear sliding surface s:

[0168] s = k ψ ψ e +r e (42)

[0169] where k ψ > 0, ψ e = ψ - ψ d ,

[0170] The heading controller is designed as follows:

[0171]

[0172] where k s > 0, is the estimation of l2 in (3):

[0173]

[0174] Theorem 3: Using the robust heading control law (43), combined with the output weight and the corresponding estimation error adaptive rate of (27), (28), the surge guidance velocity ψ d in (12) can be globally asymptotically tracked.

[0175] Proof: We design the following Lyapunov function:

[0176]

[0177] Combine (42), take the derivative of (45), and substitute (43).

[0178]

[0179] Combining the update rates in (27) and (28), there are also four cases. The calculation process is similar to (37)-(40), and we can get:

[0180]

[0181] Therefore, s, are all bounded. By further derivation and using Barbalats' lemma, we can get that the sliding surface s is globally asymptotically convergent to 0. s =0, we have:

[0182]

[0183] Design the following Lyapunov function:

[0184]

[0185] Derivative of it:

[0186]

[0187] This shows that ψ e is globally asymptotically stable, and Theorem 3 is proved.

[0188] Combining Theorems 1, 2, and 3, we can make the path tracking error (x e ,y e ) converges asymptotically to zero, and both the surge and heading guidance signals can be tracked accurately.

[0189] A path tracking control method for an underactuated unmanned vessel based on extreme rapid learning comprises the following steps:

[0190] S1: Establish the kinematic equations of the underactuated unmanned vessel;

[0191] S2: Based on the kinematic equation of the underactuated unmanned vessel, the path tracking error dynamic equation is established;

[0192] S3: Establishing a surging sight-line guidance law that can make the unmanned vessel asymptotically stable at the kinematic level, so that when the vessel navigates along the desired path, the error between the unmanned vessel and the desired path gradually decreases;

[0193] S4: Use the rapid learning online identification method to identify the unmodeled dynamics, parameter disturbances, external environmental interference and other dynamic lumped unknowns during the navigation process of the unmanned ship;

[0194] S5: Based on the identified unmodeled dynamics, parameter disturbances, external environmental interference, and other dynamic lumped unknowns, as well as the longitudinal and longitudinal line-of-sight guidance law, a robust adaptive path tracking control method based on extreme learning is adopted. The output weights and corresponding estimation error adaptive rate based on the single-hidden layer feedforward network SLFN (SLFN) approximation are designed to approximate the lumped unknowns and reduce the approximation error, thereby improving the identification accuracy. The longitudinal controller and the bow controller are designed to compensate for the unmodeled dynamics, parameter disturbances, external environmental interference, and other dynamic lumped unknowns, so that the unmanned ship is asymptotically stable at the dynamic level, and the tracking control of the unmanned ship to navigate along the desired path is realized.

[0195] The steps S1 / S2 / S3 are executed in sequence, and S5 is executed after S3 and S4 are executed;

[0196] A readable storage medium stores a program module, wherein the program module is executed in a processor to implement any one of the methods described above.

[0197] In order to verify the effectiveness and superiority of the method proposed in this invention, this application conducted a simulation study and comprehensive comparison on Cybership I, which is a UMV with a length of 1.19m and a mass of 17.6kg. The main parameters are as follows: 11 =19kg,m 22 =35.2kg, m 33 =4.2kg. For simulation setup, assume that the internal unknown parameter is d 11 =4kg / s,d 22 =1kg / s,d 33 =10kg / s. The external disturbance is:

[0198]

[0199] The initial state of the system is set to: [x(0), y(0), ψ(0)] T =[10,0,0] T ,[u(0),v(0),r(0)] T =[0,0,0] T ,The parameterized route is defined as follows:

[0200]

[0201] in, The desired moving speed u of the route t is given by the guidance law (16).

[0202] The guidance signal design based on EL-RAPFC is as follows:

[0203]

[0204] Other user-defined parameters of the EL-RAPFC scheme are as follows: Δ=2, k1=1.5, k2=2, k u =2,k ψ =2,k s =2,k w =8,k ε =10.

[0205] The actual route and the reference route are as follows Figure 4 As shown in Figure 3, the proposed EL-RAPFC scheme can achieve significant performance and stronger anti-interference ability compared with the RAPFC scheme without extreme learning approximation.

[0206] Figure 5 are the longitudinal and vertical errors, where (a) is the longitudinal error and (b) is the vertical error.

[0207] from Figure 5 It can be observed that the path tracking error of the EL-RAPFC scheme can converge smoothly to zero, while the longitudinal and vertical errors of the RAPFC scheme cannot converge to zero in the case of complex unknowns.

[0208] Figure 6 is the EL-PAPFC surge velocity and heading angle tracking, where (a) surge velocity tracking, (b) heading angle tracking,

[0209] Figure 7 is the RAPFC surge velocity and heading angle tracking, where (a) surge velocity tracking, (b) heading angular velocity tracking,

[0210] Figure 8 is the tracking error of the surge velocity and heading angle, where (a) is the surge velocity tracking error, (b) is the heading angle tracking error,

[0211] Figure 6 、 Figure 7 and Figure 8 The EL-RAPFC scheme demonstrates superior tracking performance for guidance signals when faced with complex unknowns. The actual signal can accurately track the guidance signal. In contrast, when there are multiple unknowns, the RAPFC scheme cannot achieve accurate tracking.

[0212] Figure 9 is the unknown dynamic l and its approximation where (a) surge unknown dynamics and estimation, (b) heading unknown dynamics and estimation,

[0213] Figure 10 is the estimation error, where (a) surge estimation error, (b) heading estimation error,

[0214] The dual-channel learning mechanism consisting of SLFN online approximation and adaptive residual compensation significantly improves the control performance of the EL-RAPFC scheme, as shown in Figure 9 and Figure 10 .

[0215] Figure 11 is the surge and heading control input of the UMV, where (a) surge control force, (b) steering torque. The above results show that the proposed EL-RAPFC scheme is very effective.

[0216] 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 it; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand: 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.

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Claims

1. A route tracking control system for an underactuated unmanned vessel based on extremely rapid learning, characterized by: include: Establishing Module I: used to establish the kinematic equations of the underactuated unmanned vessel; Establishing Module II: used to establish the path tracking error dynamic equation based on the kinematic equation of the underactuated unmanned vessel; Establishing Module III: This is used to establish a surge line-of-sight guidance law that can make the unmanned vessel asymptotically stable at the kinematic level, so that when the vessel is navigating along the desired path, the error between the unmanned vessel and the desired path gradually decreases; Identification module: used to identify the unmodeled dynamics, parameter disturbances, external environmental interference, and other dynamic lumped unknowns during the navigation process of the unmanned ship using an extremely fast learning online identification method; Control module: Based on the identified unmodeled dynamics, parameter disturbances, external environmental disturbances, and other dynamic lumped unknowns, as well as the longitudinal and longitudinal line-of-sight guidance law, a robust adaptive path tracking control method based on extreme learning is adopted. The output weights and corresponding estimation error adaptive rate based on the single hidden layer feedforward network (SLFN) approximation are designed to approximate the lumped unknowns and reduce the approximation error, thereby improving the identification accuracy. A longitudinal controller and a heading controller are designed to compensate for the unmodeled dynamics, parameter disturbances, external environmental disturbances, and other dynamic lumped unknowns, so that the unmanned vessel is asymptotically stable at the dynamic level and achieves tracking control of the unmanned vessel along the desired path. The process of using the rapid learning online identification method to identify the unmodeled dynamics, parameter disturbances, external environmental interference, and other dynamic lumped unknowns during the navigation process of the unmanned ship is as follows: Using a N The single hidden layer feedforward network SLFN with hidden nodes is used to online identify the following lumped unknown items : (20) in, , is the output weight, With parameters and The normalized output of the activation function, N is the number of hidden layer nodes; Assume that there exists an optimal SLFN, where N Hidden nodes are randomly generated, parameters and , using the minimum function approximation error to identify nonlinear functions : (21) in, is the vector of minimum function approximation error MFAE and satisfies , optimal output weight It is derived from the following formula: (22) The expressions of the output weights based on SLFN approximation and the corresponding estimation error adaptation rate are as follows: (25) (26) (27) (28) in, , gather The definition is as follows: (29) (30) (31) (32) in, is the corresponding upper bound, 、 is the estimator of the SLFN output weight, 、 is an estimator of the approximate residual, is the surge velocity error, is a first-order linear sliding surface, With parameters and The normalized output of the activation function, is a vector that includes surge, sway, and heading angular velocity; The longitudinal controller The design is as follows: (33) in, , Longitudinal velocity tracking error, is the ship's mass inertia coefficient; for Estimated value of: (34) The heading controller design process is as follows: Introduce the following first-order linear sliding surface s: (42) in, , , is the heading angle, ; r is the yaw angular velocity; The heading controller is designed as follows: (43) in: is the ship's mass inertia coefficient; in, , for Estimated value of (44) 。 2. The underactuated unmanned vessel route tracking control system based on extremely rapid learning according to claim 1, characterized in that: The expression of the dynamic equation of the underactuated unmanned vessel is as follows: (3) It includes not only unmodeled dynamics, parameter disturbances, and external environmental disturbances, but also the lumped unknowns of other dynamics, which will be observed later to achieve model-free control of the UMV dynamics. are the surge speed, sway speed and yaw angular velocity of the UMV, For vertical and horizontal control, is the steering torque; 、 is the ship mass inertia coefficient, , , are the first-order derivatives of u, v, and r respectively.

3. The underactuated unmanned vessel path tracking control system based on extremely rapid learning according to claim 1, characterized in that: The expression of the path tracking error dynamic equation is as follows: (11) in: is the tangent angle of the route reference point relative to the geodetic coordinate system, is the sideslip angle, is the moving speed of the reference point on the route, is the vertical speed, is the heading angle.

4. The underactuated unmanned vessel path tracking control system based on extremely rapid learning according to claim 3, characterized in that: The expression of the turbulent line of sight guidance law is as follows: (12) in, is the tangent angle of the route reference point relative to the geodetic coordinate system, is the forward sight distance, is the vertical error, and the desired sideslip angle and longitudinal velocity is defined as: (13) in: is the sway velocity; (14) in, , and The minimum value is set to: (15)。

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