Nonlinear Manoeuvring Model Research Articles

Nonlinear steering control law under input magnitude and rate constraints with exponential convergence

AbstractA ship steering control law is designed for a nonlinear maneuvering model whose rudder manipulation is constrained in both magnitude and rate. In our method, the tracking problem of the target heading angle with input constraints is converted into the tracking problem for a strict-feedback system without any input constraints. To derive this system, hyperbolic tangent ($$\tanh$$ tanh ) function and auxiliary variables are introduced to deal with the input constraints. Furthermore, using the feature of the derivative of $$\tanh$$ tanh function, auxiliary systems are successfully derived in the strict-feedback form. The backstepping method is utilized to construct the control input for the resulting cascade system. The proposed steering control law is verified in numerical experiments, and the result shows that the tracking of the target heading angle is successful using the proposed control law.

Effect of Sampling Rate in Sea Trial Tests on the Estimation of Hydrodynamic Parameters for a Nonlinear Ship Manoeuvring Model

This paper explores the impact of sampling rates during sea trials on the estimation of hydrodynamic parameters in a nonlinear manoeuvring model. Sea trials were carried out using an offshore patrol vessel and test data were collected. A nonlinear manoeuvring model is introduced to characterise the ship’s manoeuvring motion, and the truncated least squares support vector machine is employed to estimate nondimensional hydrodynamic coefficients and their corresponding uncertainties using the 25°–25° zigzag test. To assess the influence of the sampling rates, the training set is resampled offline with 14 sampling rates, ranging from 0.2 Hz to 5 Hz, encompassing a rate 10 times the highest frequency component of the signal of interest. The results show that the higher sampling rate can significantly diminish the parameter uncertainty. To obtain a robust estimation of linear and nonlinear hydrodynamic coefficients, the sampling rate should be higher than 10 times the highest frequency component of the signal of interest, and 3–5 Hz is recommended for the case in this paper. The validation is also carried out, which indicates that the proposed truncated least square support vector machine can provide a robust parameter estimation.

Indirect inference approach for parameter estimation of non linear manoeuvring models of a ROV based on model basin trials

ABSTRACT In this work, indirect inference (II) techniques are applied to estimate the parameters of a non-linear manoeuvring model of a remotely operated vehicle (ROV). In the application of this method, a set of auxiliary statistics is established in the optimisation process in order to improve the efficiency of the estimated parameters. For the parameter estimation, data from different tests are available, which were carried out with a ROV in the facilities of the Centro de Experiencias Hidrodinámicas del Pardo INTA/CEHIPAR, Madrid. The model obtained is validated by means of graphical and statistical methods with the acquired data and the statistical properties of the estimated parameters are evaluated by means of a Monte Carlo study.

Data-Driven Parameter Estimation of Nonlinear Ship Manoeuvring Model in Shallow Water Using Truncated Least Squares Support Vector Machines

A data-driven method, the truncated LS-SVM, is proposed for estimating the nondimensional hydrodynamic coefficients of a nonlinear manoeuvring model. Experimental data collected in a shallow water towing tank are utilized in this study. To assess the accuracy and robustness of the truncated LS-SVM method, different test data sizes are selected as the training set. The identified nondimensional hydrodynamic coefficients are presented, as well as the corresponding parameter uncertainty and confidence intervals. The validation is carried out using the reference data, and statistical measures, such as the correlation coefficient, centred RMS difference, and standard deviation are employed to quantify the similarity. The results demonstrate that the truncated LS-SVM method effectively models the hydrodynamic force prediction problems with a large training set, reducing parameter uncertainty and yielding more convincing results.

Robust Parameter Estimation of an Empirical Manoeuvring Model Using Free-Running Model Tests

The work presents the identification and validation of the hydrodynamic coefficients for the surge, sway, and yaw motion. This is performed in two ways: using simulated data and free-running test data. The identification and validation with the simulation data are carried out using a 25° turning test and a 20°−20° zigzag manoeuvring test. For the free-running test data, two zigzag manoeuvres are used: 30°−30° zigzag for identification and 20°−20° zigzag for validation. A nonlinear manoeuvring model is proposed based on the standard Euler equations, and the hydrodynamic coefficients are computed using empirical equations. To obtain robust results, the truncated singular value decomposition is employed to diminish the multicollinearity and the parameter uncertainties due to noise. The validation is carried out by comparing the result of the measured values with the predictions obtained using the manoeuvring models. Finally, a sensitivity analysis for the simulation data is performed to understand the influence of the parameters in the manoeuvres.

Iterative Self-Tuning Minimum Variance Control of a Nonlinear Autonomous Underwater Vehicle Maneuvering Model

This paper addresses the problem of control design for a nonlinear maneuvering model of an autonomous underwater vehicle. The control algorithm is based on an iteration technique that approximates the original nonlinear model by a sequence of linear time-varying equations equivalent to the original nonlinear problem and a self-tuning control method so that the controller is designed at each time point on the interval for trajectory tracking and heading angle control. This work makes use of self-tuning minimum variance principles. The benefit of this approach is that the nonlinearities and couplings of the system are preserved, unlike in the cases of control design based on linearized systems, reducing in this manner the uncertainty in the model and increasing the robustness of the controller. The simulations here presented use a torpedo-shaped underwater vehicle model and show the good performance of the controller and accurate tracking for certain maneuvering cases.

Parameter computation for a Lagrangian mechanical system model of a submerged vessel moving near a free surface

This paper describes the computation of parameters for a Lagrangian mechanical system model of a submerged vessel moving near an otherwise calm free surface using a medium-fidelity potential flow code. The software uses the boundary element method to solve for the flow potential on the body and the free surface. The model, a system of integro-differential equations involving functions of the velocity potential, is the “maneuvering” component of a Lagrangian nonlinear maneuvering and seakeeping model that was introduced in earlier work. Here, this nonlinear maneuvering model is reformulated and the potential flow software is modified to support parameter computations. Parameters are computed for a prolate spheroid moving parallel to a calm free surface at a constant forward speed. This motion induces a steady flow with respect to the body, which results in a steady surge force, heave force and pitch moment. These longitudinal forces and moment are computed using the reformulated Lagrangian nonlinear maneuvering model and the results are compared with basic panel code solutions for various depths and Froude numbers and for various computational parameter values.

Comparing generic and vectorial nonlinear manoeuvring models and parameter estimation using optimal truncated least square support vector machine

An optimal truncated least square support vector machine (LS-SVM) is proposed for the parameter estimation of nonlinear manoeuvring models based on captive manoeuvring tests. Two classical nonlinear manoeuvring models, generic and vectorial models, are briefly introduced, and the prime system of SNAME is chosen as the normalization forms for the hydrodynamic coefficients. The optimal truncated LS-SVM is introduced. It is a robust method for parameter estimation by neglecting the small singular values, which contribute negligibly to the solutions and increase the parameter uncertainty. The parameter with a large uncertainty is sensitive to the noise in the data and have a poor generalization performance. The classical LS-SVM and optimal truncated LS-SVM are used to estimate the parameters, and the effectiveness of optimal truncated LS-SVM is validated. The parameter uncertainty for both nonlinear manoeuvring models is discussed. The generalization performance of the obtained numerical models is further tested against the validation set, which is completely left untouched in the training. The R2 goodness-of-fit criterion is used to demonstrate the accuracy of the obtained models.

Truncated least square support vector machine for parameter estimation of a nonlinear manoeuvring model based on PMM tests

A new version of least square support vector machine (LS-SVM), the truncated LS-SVM, is proposed to estimate the nondimensionalized hydrodynamic coefficients. Truncated LS-SVM is shown to be an efficient and robust method that avoids the costly matrix inversion operation in classical LS-SVM using the singular values decomposition. Meanwhile, the smaller singular values are neglected considering their negligible contribution to the solutions. In order to get a robust parameter estimation, the model simplification of the nonlinear manoeuvring model is carried out using a leave-one-out method, considering the trade-off between the parameter uncertainty and accuracy of the numerical model. The simplified manoeuvring model and the values of nondimensionalized hydrodynamic coefficients are presented. The coefficients are estimated using Planar motion mechanism (PMM) tests, which were carried out in a towing tank. The validation process is carried to validate the generalization performance of the obtained numerical model using the PMM test data.

Use of AIS data for guidance and control of path-following autonomous vessels

This paper carries out research on the prototype of an autonomous vessel that is normally used for passenger transportation. A path generation system is proposed using a dynamic time warping algorithm based on Automatic Identification System history data. In order to ensure strong stability properties, a nonlinear controller with globally exponentially stability is introduced for the heading controller. The least square support vector machine is employed to estimate the parameters of the control model based on full-scale manoeuvring tests. The identified results are validated with analytical values. The kinematics and control object of path-following are presented, and a time-varying vector field guidance law is proposed for the path-following control of autonomous vessels. The guidance and control subsystems are interconnected and form a cascade structure. The stability of the coupled guidance and control system is carried out using the cascaded system theory. The proof ensures that the equilibrium point of the cascaded system is uniformly semiglobally exponentially stable. Path following scenario was considered in the presence of currents based on a nonlinear manoeuvring model. Simulation studies were used to verify the theoretical results.

Manoeuvring modelling of a containership in shallow water based on optimal truncated nonlinear kernel-based least square support vector machine and quantum-inspired evolutionary algorithm

Nonlinear implicit models are proposed for manoeuvring simulation of a container model in shallow water. A series of Planar Motion Mechanism tests of the DTC ship model carried out in a towing tank with shallow water is used for training the nonlinear implicit manoeuvring model. A novel method, nonlinear kernel-based Least Square Support Vector Machine (LS-SVM), is proposed to approximate the nonlinear manoeuvring model. It is a robust method for regression modelling with a low computational cost by reducing the dimensionality of the kernel matrix. The radial basis function kernel is employed in the SVMs to guarantee the performance of the approximation. The quantum-inspired evolutionary algorithm (QEA) is used to search the optimal value of the predefined parameters of the nonlinear kernel-based LS-SVM. The optimal truncated LS-SVM is used to train the nonlinear regression models for ship manoeuvring, and the generalization performance of the obtained nonlinear manoeuvring models is further tested against the validation set. The R2 goodness-of-fit criterion is used to demonstrate the accuracy of the obtained models.

Hydrodynamic coefficient estimation for ship manoeuvring in shallow water using an optimal truncated LS-SVM

An optimal truncated least square support vector machine (LS-SVM) is proposed for the parameter estimation of a nonlinear manoeuvring model in shallow water. A nonlinear manoeuvring model in shallow water is briefly introduced and the hydrodynamic coefficients are normalized. A series of Planar Motion Mechanism tests of the DTC ship model carried out in a towing tank with shallow water are used in the study for the estimation of the parameters of the manoeuvring model. The contribution of this paper is to propose the use of the optimal truncated LS-SVM, which is a robust method for parameter estimation that diminishes the uncertainty successfully and has a low computational cost by reducing the dimensionality of the kernel matrix. The classical least square method is also employed to estimate the parameters, and the results are compared with the optimal truncated LS-SVM. The parameter uncertainty is discussed, and the performance of the obtained nonlinear manoeuvring models is tested against a validation set that was left completely untouched during the training. The R2 goodness-of-fit criterion is used to demonstrate the accuracy of the obtained models.

Uncertainty analysis of the hydrodynamic coefficients estimation of a nonlinear manoeuvring model based on planar motion mechanism tests

Uncertainty analysis of the identified hydrodynamic coefficients of a nonlinear manoeuvring model is presented in this paper. The classical parameter estimation method, Least Square, is briefly introduced, and the uncertainty of the hydrodynamic coefficients due to the noise in the measured data is analysed using singular value decomposition. Then, two methods, truncated singular values decomposition and Tikhonov regularization, are introduced to diminish the uncertainty. A nonlinear manoeuvring mathematical model of a marine surface ship is derived using Lagrange's method. The dimensionless hydrodynamic coefficients are obtained using the Least Squares method, truncated singular values decomposition and Tikhonov regularization with Planar Motion Mechanism test data. The validation process is carried out to test the performance and accuracy of the resulting nonlinear manoeuvring models. The result shows that identification of the uncertain parameters using the truncated singular values decomposition and Tikhonov regularization resulted in good estimating the parameters and significantly diminish the uncertainty.

Simulation of the overtaking maneuver between two ships using the non-linear maneuvering model

The overtaking maneuver of two Esso Bernicia 1.9×105 DWT tankers was investigated using the system-based maneuvering method. The Brix model was incorporated to account for the overtaking interactions. Forces/moment acting on the ship hulls and maneuvering motions were analyzed for both ships during the overtaking. The influences of the speed ratio and the passing distance were specially studied. Two fitting formulas for the minimum distance during the overtaking were finally established as functions of the two factors respectively. They can be used to predict the minimum distance during an overtaking maneuver under similar conditions to avoid marine accidents.

Improving parameter estimation efficiency of a non linear manoeuvring model of an underwater vehicle based on model basin data

In this work, a methodology is proposed for the improvement of the parameter estimation efficiency of a non-linear manoeuvring model of a torpedo shaped unmanned underwater vehicle. For this purpose, data from different tests, were carried out with the aforementioned vehicle at the facilities of the CEHIPAR (Canal de Experiencias Hidrodinámicas de El Pardo), Madrid. In the proposed methodology, the following aspects are taken into account in order to improve the parameter estimation efficiency: selection of the sampling period, smoothing of the data acquired in the tests, considering a compromise between bias and variance of the smoothing filter to be applied, analysis of the classical linear regression model proposed in each trial from the statistical point of view for the estimation of the parameters. Improvements in efficiency are verified by graphical and statistical methods.

Path Following of Marine Surface Vessels Using Bow and Aft Rudders in Wave Fields

This paper investigates the feasibility of using both bow and aft rudders to achieve better maneuverability and path following performance of marine surface vessels in waves. A nonlinear maneuvering model for the S175 containership is first introduced to facilitate the evaluation of path following performance. The original aft rudder is then replaced by the new bow-aft rudder combination. Open-loop simulation result shows that the new design can make the ship more maneuverable with a smaller total rudder area. For the path following controller design, the model predictive control (MPC) approach is adopted to enforce the rudder actuation constraints. In order to achieve offset-free path following in waves, a modified MPC scheme is proposed where a linear quadratic regulator (LQR) is used to first stabilize the system so that the offset-free MPC scheme can be further applied. Simulations confirm the validity of the hybrid scheme and the path following performance using both bow and aft rudders appears to be better.

Two-step identification of non-linear manoeuvring models of marine vessels

This paper presents the identification of non-linear ship manoeuvring models. It is a gray box approach in which some of the parameters of the models are known, and where a novel identification scheme for non-linear manoeuvring models based on two steps is proposed. In the first step, the structure of the model is selected using the stepwise method, and the parameters which present greater uncertainty are estimated. In the second step, a refinement of the estimates in the first step is carried out using a non-linear prediction error method with the unscented Kalman filter. As an application example, we consider a modern high-speed trimaran ferry using a full-scale trial and simulated data sets.

Fuzzy autopilot for ship maneuvering

A fuzzy autopilot algorithm for maneuvering of surface ships is proposed and its performance studied. A mathematical model for nonlinear maneuvering of cargo ships has been used in conjunction with the proposed fuzzy autopilot. The autopilot works with two error measures that are inputs, error in heading angle and the offset error from the desired path, and has the command rudder angle as the output. Input variable fuzzification, fuzzy associative memory rules and output set defuzzification schemes using Mamdani minimum inference method are described. The proposed control scheme has been verified for a variety of straight line and curved trajectories using a nonlinear maneuvering model of Mariner class vessel.

System identification for nonlinear maneuvering of large tankers using artificial neural network

This paper deals with the application of nonparametric system identification to a nonlinear maneuvering model for large tankers using artificial neural network method. The three coupled maneuvering equations in this model for large tankers contain linear and nonlinear terms and instead of attempting to determine the parameters (i.e. hydrodynamic derivatives) associated with nonlinear terms, all nonlinear terms are clubbed together to form one unknown time function per equation which are sought to be represented by the neural network coefficients. The time series used in training the network are obtained from simulated data of zigzag maneuvers and the proposed method has been applied to these data. The neural network scheme adopted in this work has one middle or hidden layer of neurons and it employs the Levenberg–Marquardt algorithm. Using the best choices for the number of hidden layer neurons, length of training data, convergence tolerance etc., the performance of the proposed neural network model has been investigated and conclusions drawn.

Autopilot and track-keeping algorithms for high-speed craft

A track autopilot predictor (TAP) system for high-speed craft with waterjet propulsion systems has been developed and installed on-board four catamarans. The TAP system includes automatic control modes for steady-state course-keeping, turning and track-keeping. A special harbour mode and a hydrodynamic predictor based on a non-linear manoeuvring model of the ship are also included. The paper describes the design of the control algorithms used in the autopilot and track-keeping systems. The design is based on a combination of velocity scheduling, pole placement and a feed-forward model for turning. The performance of the algorithms is illustrated in full-scale experiments.