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

A ship steering control 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 ($\tanh$) function and auxiliary variables are introduced to deal with the input constraints. Furthermore, using the feature of the derivative of $\tanh$ function, auxiliary systems are successfully derived in the strict-feedback form. The backstepping method is utilized to construct the feedback control law for the resulting cascade system. The proposed steering control is verified in numerical experiments, and the result shows that the tracking of the target heading angle is successful using the proposed control law.Comment: 12 pages, 6 figures, a preprint submitted to the Journal of Marine Science and Technolog

Melnikov Integral Formula for Beam Sea Roll Motion Utilizing a Non-Hamiltonian Exact Heteroclinic Orbit (Part II)

In the research filed of nonlinear dynamical system theory it is well known that a homoclinic/heteroclinic point leads to unpredictable motions, such as chaos. Melnikov’s method enables us to judge whether the system has a homoclinic/heteroclinic orbit. Therefore, in order to assess a vessels safety against capsizing, Melnikov’s method has been applied for the investigations of chaos that appears in beam sea rolling. This is because chaos is closely related to capsizing incidents. In a previous paper 1), the formula to predict the capsizing boundary by applying Melnikov’s method to analytically obtain the non-Hamiltonian heteroclinic orbit, was proposed. However, in that paper, limited numerical investigation had been carried out. Therefore further comparative research between the analytical and numerical results is conducted, with the result being that the formula is validated

Melnikov integral formula for beam sea roll motion utilizing a non-Hamiltonian exact heteroclinic orbit

Chaos appearing in a ship roll equation in beam seas, known as the escape equation, has been intensively investigated so far because it is closely related to capsizing accident. In particular, many applications of Melnikov integral formula have been reported in the existing literature. However, in all the analytical works concerning with the escape equation, Melnikov integral is formulated utilizing a separatrix for Hamiltonian part or a numerically obtained heteroclinic orbit for non-Hamiltonian part, of the original escape equation. To overcome such limitations, this paper attempts to utilise an analytical expression of the non-Hamiltonian part. As a result, an analytical procedure making use of a heteroclinic orbit of non-Hamiltonian part within the framework of Melnikov integral formula is provided

Analytical methods to predict the surf-riding threshold and the wave-blocking threshold

For the safe design and operation of high-speed craft it is important to predict their behaviour in waves. There still exists a concern, however, in the framework of the International Maritime Organization (IMO) with regards to the stability criteria. In particular, for high-speed craft, the higher limit of operational speed resulting in wave blocking as well as the lower limit known as the surf-riding threshold are important features. Therefore, by applying the polynomial approximation to wave induced surge force including the nonlinear surge equation, an analytical formula in order to predict the wave blocking and surf-riding thresholds is proposed. Comparative results of the surf-riding threshold and wave blocking threshold utilizing the proposed formula and the numerical bifurcation analysis indicate fairly good agreement. In addition, previously proposed analytical formulae are inclusively examined. It is concluded that the analytical formulae based on a continuous piecewise linear approximation and Melnikov’s method agrees well with the wave blocking threshold and the surf-riding threshold obtained by the numerical bifurcation analysis and the free-running model experiment. As a result, it is considered that these two calculation methods could be recommended for the early design stage tool for avoiding broaching and bow-diving

Data Augmentation Methods of Parameter Identification of a Dynamic Model for Harbor Maneuvers

A dynamic model for an automatic berthing and unberthing controller has to estimate harbor maneuvers, which include berthing, unberthing, approach maneuvers to berths, and entering and leaving the port. When the dynamic model is estimated by the system identification, a large number of tests or trials are required to measure the various motions of harbor maneuvers. However, the amount of data that can be obtained is limited due to the high costs and time-consuming nature of full-scale ship trials. In this paper, we improve the generalization performance of the dynamic model for the automatic berthing and unberthing controller by introducing data augmentation. This study used slicing and jittering as data augmentation methods and confirmed their effectiveness by numerical experiments using the free-running model tests. The dynamic model is represented by a neural network-based model in numerical experiments. Results of numerical experiments demonstrated that slicing and jittering are effective data augmentation methods but could not improve generalization performance for extrapolation states of the original dataset.Comment: 12 pages, 11 figures, Submitted to Journal of Marine Science and Technolog

Comparison of stochastic stability boundaries for parametrically forced systems with application to ship rolling motion

Numerous accidents caused by parametric rolling have been reported on container ships and pure car carriers (PCCs). A number of theoretical studies have been performed to estimate the occurrence condition of parametric rolling in both regular and irregular seas. Some studies in random wave conditions have been the approximate extension of the occurrence conditions for regular waves (e.g. Maki et al). Furthermore, several researches have been based on the stochastic process in ocean engineering (Roberts and Dostal). This study tackled the parametric rolling in irregular seas from the stability of the system's origin. It provided a novel theoretical explanation of the instability mechanism for two cases: white noise parametric excitation and colored noise parametric excitation. The authors then confirmed the usefulness of the previously provided formulae by Roberts and Dostal through numerical examples.Comment: 10 pages, 4 figure

Analytical methods to predict the surf-riding threshold and the wave-blocking threshold

For the safe design and operation of high-speed craft it is important to predict their behaviour in waves. There still exists a concern, however, in the framework of the International Maritime Organization (IMO) with regards to the stability criteria. In particular, for high-speed craft, the higher limit of operational speed resulting in wave blocking as well as the lower limit known as the surf-riding threshold are important features. Therefore, by applying the polynomial approximation to wave induced surge force including the nonlinear surge equation, an analytical formula in order to predict the wave blocking and surf-riding thresholds is proposed. Comparative results of the surf-riding threshold and wave blocking threshold utilizing the proposed formula and the numerical bifurcation analysis indicate fairly good agreement. In addition, previously proposed analytical formulae are inclusively examined. It is concluded that the analytical formulae based on a continuous piecewise linear approximation and Melnikov’s method agrees well with the wave blocking threshold and the surf-riding threshold obtained by the numerical bifurcation analysis and the free-running model experiment. As a result, it is considered that these two calculation methods could be recommended for the early design stage tool for avoiding broaching and bow-diving

A study on the implementation of nonlinear Kalman filter applying MMG model

Many technologies need to be established to realize autonomous ships. In particular, accurate state estimation in real time is one of the most important technologies. In the ship and ocean engineering fields, there have been many studies on state estimation using nonlinear Kalman filters. Several methods have been proposed for nonlinear Kalman filters. However, there is insufficient verification on the selection of which filter should be applied among them. Therefore, this study aims to validate the filter selection to provide a guideline for filter selection. The effects of modeling error, observation noise, and type of maneuvers on the estimation accuracy of the unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF) used in this study were investigated. In addition, it was verified whether filtering could be performed in real time. The results show that modeling error significantly impacts the estimation accuracy of the UKF and EnKF. However, the observation noise and types of maneuvers did not have an impact like the modeling error. Thus, we obtained the guideline that UKF and EnKF should be used differently depending on the required computation time. We also obtained that keeping the modeling error sufficiently small is essential to improving the estimation accuracy.The version of record of this article, first published in Journal of Marine Science and Technology (Japan), is available online at Publisher’s website: https://doi.org/10.1007/s00773-023-00953-

Nonlinear dynamics of ship capsizing at sea

Capsizing is one of the worst scenarios in oceangoing vessels. It could lead to a high number of fatalities. A considerable number of studies have been conducted until the 1980s, and one of the discoveries is the weather criterion established by the International Maritime Organization (IMO). In the past, one of the biggest difficulties in revealing the behavior of ship-roll motion was the nonlinearity of the governing equation. On the other hand, after the mid-1980s, the complexity of the capsizing problem was uncovered with the aid of computers. In this study, we present the theoretical backgrounds of the capsizing problem from the viewpoint of nonlinear dynamics. Then, we discuss the theoretical conditions and mechanisms of the bifurcations of periodic solutions and numerical attempts for the bifurcations and capsizing

Covariance Matrix Adaptation Evolutionary Strategy with Worst-Case Ranking Approximation for Min--Max Optimization and its Application to Berthing Control Tasks

In this study, we consider a continuous min--max optimization problem $\min_{x \in \mathbb{X} \max_{y \in \mathbb{Y}}}f(x,y)$ whose objective function is a black-box. We propose a novel approach to minimize the worst-case objective function $F(x) = \max_{y} f(x,y)$ directly using a covariance matrix adaptation evolution strategy (CMA-ES) in which the rankings of solution candidates are approximated by our proposed worst-case ranking approximation (WRA) mechanism. We develop two variants of WRA combined with CMA-ES and approximate gradient ascent as numerical solvers for the inner maximization problem. Numerical experiments show that our proposed approach outperforms several existing approaches when the objective function is a smooth strongly convex--concave function and the interaction between $x$ and $y$ is strong. We investigate the advantages of the proposed approach for problems where the objective function is not limited to smooth strongly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty.ngly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty