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In order to understand the appropriate field of view (FOV) size of celestial automatic navigation systems for surface ships, we investigate the variations of measurement accuracy of star position and probability of successful star identification with respect to FOV, focusing on the decreasing number of observable star magnitudes and the presence of physically covered stars in marine environments. The results revealed that, although a larger FOV reduces the measurement accuracy of star positions, it increases the number of observable objects and thus improves the probability of star identification using subgraph isomorphism-based methods. It was also found that, although at least four objects need to be observed for accurate identification, four objects may not be sufficient for wider FOVs. On the other hand, from the point of view of celestial navigation systems, a decrease in the measurement accuracy leads to a decrease in positioning accuracy. Therefore, it was found that maximizing the FOV is required for celestial automatic navigation systems as long as the desired positioning accuracy can be ensured. Furthermore, it was found that algorithms incorporating more than four observed celestial objects are required to achieve highly accurate star identification over a wider FOV., Comment: 15 pages, 10 figures

Leveraging empirical data is crucial in the development of accurate and reliable virtual models for the advancement of autonomous ship technologies and the optimization of port operations. This study presents an in-depth analysis of ship berthing and unberthing maneuvering characteristics by utilizing a comprehensive dataset encompassing the operation of a full-scale ship in diverse infrastructural and environmental conditions. Various statistical techniques and time-series analysis were employed to process and interpret the operational data. A systematic analysis was conducted on key performance variables, including approach speed, drift angles, turning motions, distance from obstacles, and actuator utilization. The results demonstrate significant discrepancies between the empirical data and the established maneuvering characteristics. These findings have the potential to significantly enhance the accuracy and reliability of conventional maneuvering models, such as the Mathematical Modeling Group (MMG) model, and improve the conditions used in captive model tests for the identification of maneuvering model parameters. Furthermore, these findings could inform the development of more robust autonomous berthing and unberthing algorithms and digital twins.

There is a growing demand for simulators for the research and development of maritime autonomous surface ships (MASS) and the approval of autonomous navigation algorithms. Simulators are used for purposes such as evaluation and training and are taken on various configurations accordingly. The ship maneuvering mathematical model used in such a simulator is an important element that characterizes the simulator. In this paper, we discuss the dynamic model of the hull and its position in the simulator that will be required for MASSs in the future. It also discusses guidelines for selecting an appropriate model, which has not been discussed extensively in previous studies. Finally, we discuss the functional requirements that simulators should have., Comment: 21 pages, 3 figures, Submitted to Journal of Marine Science and Technology

Research on vessel automation and autonomy is currently being conducted by various countries and institutions. Safe and accurate ship control algorithms are crucial to realize automated operation. Actuator drive constraints of a target ship may jeopardize the stability of the control law and require complex theory. In this study, we include a penalty term to the control law gain optimization stage of dynamic positioning systems to account for the amounts by which the actuator input value and its rate of change exceed the constraint. The parameters for generating a suitable reference path for the control law are identified simultaneously with the control gains. The simulation results show that the proposed method can realize control parameters and a reference design with excellent tracking performance while determining the cost of the controller design by considering the effects of both the actuators and rate saturation., Comment: 9 pages, 5 figures, preprint submitted to the Journal of Marine Science and Technology

Parametric rolling is a parametric excitation phenomenon caused by GM variation in waves. There are a lot of studies of the estimation the conditions, the occurrence, and the amplitude of parametric rolling. On the other hand, there are relatively few cases in which theoretical methods for estimating parametric roll amplitudes in irregular waves have been validated in tank tests. The primary objective of this study is to validate theoretical estimation methods for the parametric roll amplitude in irregular waves and improve their accuracy. First, the probability density functions (PDF) of the parametric roll amplitude obtained from the model ship motion experiment in irregular waves are compared with that obtained from theoretical estimation methods. Second, the method to improve the accuracy of estimation of the roll restoring variation in irregular waves is suggested. Third, the method to estimate the distribution of the maximum amplitude of parametric rolling in irregular waves. As a result, the PDFs of the roll amplitude obtained from the experiments differ from the results of theoretical estimation. After that, by correcting GM variation, the results of theoretical estimation are closer to the experimental results. Moreover, by the theoretical estimation method using the moment equation, the qualitative estimation for the PDF of the maximum roll amplitude is succeeded., Comment: 12 pages, 23 figures, This paper is under review now by JMST(Journal of Marine Science and Technology)

Autonomous ships are essentially designed and equipped to perceive their internal and external environment and subsequently perform appropriate actions depending on the predetermined objective(s) without human intervention. Consequently, trajectory planning algorithms for autonomous berthing must consider factors such as system dynamics, ship actuators, environmental disturbances, and the safety of the ship, other ships, and port structures, among others. In this study, basing the ship dynamics on the low-speed MMG model, trajectory planning for an autonomous ship is modeled as an optimal control problem (OCP) that is transcribed into a nonlinear programming problem (NLP) using the direct multiple shooting technique. To enhance berthing safety, besides considering wind disturbances, speed control, actuators' limitations, and collision avoidance features are incorporated as constraints in the NLP, which is then solved using the Sequential Quadratic Programming (SQP) algorithm in MATLAB. Finally, the performance of the proposed planner is evaluated through (i) comparison with solutions obtained using CMA-ES for two different model ships, (ii) trajectory planning for different harbor entry and berth approach scenarios, and (iii) feasibility study using stochastically generated initial conditions and positions within the port boundaries. Simulation results indicate enhanced berthing safety as well as practical and computational feasibility making the planner suitable for real-time applications.

The broaching that follows the surf-riding is a dangerous phenomenon that can lead to the capsizing of a vessel due to its violent yaw motion. Most of the previous studies on surf-riding phenomena in irregular waves have been conducted by replacing irregular waves with regular waves. In contrast, this study provides suggestions on how to directly calculate nonlinear surge motion in irregular seas. In this study, the statistical aspects of the surf-riding phenomenon are first presented. Then, under several approximations, we show how to calculate the probability density function theoretically. Although the results obtained are based on strong approximations, it is found that the nonlinear surge oscillations in irregular following seas can be explained from a qualitative point of view.

In this paper, a fine-tuning method of the parameters in the MMG model for the real-scale ship is proposed. In the proposed method, all of the arbitrarily indicated target parameters of the MMG model are tuned simultaneously in the framework of SI using time series data of real-sale ship maneuvering motion data to steadily improve the accuracy of the MMG model. Parameter tuning is formulated as a minimization problem of the deviation of the maneuvering motion simulated with given parameters and the real-scale ship trials, and the global solution is explored using CMA-ES. By constraining the exploration ranges to the neighborhood of the previously determined parameter values, the proposed method limits the output in a realistic range. The proposed method is applied to the tuning of 12 parameters for a container ship with five different widths of the exploration range. The results show that, in all cases, the accuracy of the maneuvering simulation is improved by applying the tuned parameters to the MMG model, and the validity of the proposed parameter fine-tuning method is confirmed., Comment: 13 pages, 11 figures, a preprint submitted to Ocean Engineering

In high-speed maritime operations, the broaching phenomenon can pose a significant risk when navigating in following/quartering seas. The occurrence of this phenomenon can result in a violent yaw motion, regardless of the steering effort, which, in turn, cause the resulting centrifugal force to capsize a vessel. A necessary condition for the occurrence of broaching is the surf-riding phenomenon. Therefore, the International Maritime Organization (IMO) has set up criteria to include theoretical formulas for estimating the occurrence of surf-riding phenomena. The theoretical equation used in the IMO's second-generation intact stability criteria (SGISC) to estimate the surf-riding threshold is based on Melnikov's method. This paper presents nonlinear equations describing the forward and backward motions of a ship. However, such equations cannot be directly solved; therefore, we proposed the use of and explain various approximate solution methods, including Meknikov's method. Subsequently, the relationship between the theoretical prediction method of the surf-riding threshold rooted in Melnikov's method and the IMO's SGISC is determined.

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 Technology

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 Technology

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 figures

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.

Among ship maneuvers, berthing/unberthing maneuvers are one of the most challenging and stressful phases for captains. Concerning burden reduction on ship operators and preventing accidents, several researches have been conducted on trajectory planning to automate berthing/unberthing. However, few studies have aimed at assisting captains in berthing/unberthing. The trajectory to be presented to the captain should be a maneuver that reproduces human captain's control characteristics. The previously proposed methods cannot explicitly reflect the motion and navigation, which human captains pay particular attention to reduce the mental burden in the trajectory planning. Herein, mild constraints to the trajectory planning method are introduced. The constraints impose certain states (position, bow heading angle, ship speed, and yaw angular velocity), to be taken approximately at any given time. The introduction of this new constraint allows imposing careful trajectory planning (e.g., in-situ turns at zero speed or a pause for safety before going astern), as if performed by a human during berthing/unberthing. The algorithm proposed herein was used to optimize the berthing/unberthing trajectories for a large car ferry. The results show that this method can generate the quantitatively equivalent trajectory recorded in the actual berthing/unberthing maneuver performed by a human captain., Comment: 16 pages, 12 figures, an accepted manuscript of a published paper on Ocean Engineering

A simulation environment of harbor maneuvers is critical for developing automatic berthing. Dynamic models are widely used to estimate harbor maneuvers. However, human decision-making and data analysis are necessary to derive, select, and identify the model because each actuator configuration needs an inherent mathematical expression. We proposed a new dynamic model for arbitrary configurations to overcome that issue. The new model is a hybrid model that combines the simplicity of the derivation of the Taylor expansion and the high degree of freedom of the MMG low-speed maneuvering model. We also developed a method to select mathematical expressions for the proposed model using system identification. Because the proposed model can easily derive mathematical expressions, we can generate multiple models simultaneously and choose the best one. This method can reduce the workload of model identification and selection. Furthermore, the proposed method will enable the automatic generation of dynamic models because it can reduce human decision-making and data analysis for the model generation due to its less dependency on the knowledge of ship hydrodynamics and captive model test. The proposed method was validated with free-running model tests and showed equivalent or better estimation performance than the conventional model generation method., Comment: 30 pages, 11 figures, a preprint under review

A VecTwin rudder system comprises twin fishtail rudders with reaction fins to increase its performance. With a constant propeller revolution number, the vessel can execute special low-speed maneuvers like hover, crabbing, reverse, and rotation. Such low-speed maneuvers are termed dynamic positioning (DP), and a DP vessel should be fully/overly actuated with several thrusters. This article introduces a novel and experimental VecTwin positioning system (VTPS) without making the ship fully/overly actuated. Unlike the usual dynamic positioning system (DPS), the VTPS is developed for low-speed operations in a calm harbor area. It is designed upon an assumption that the forces due to the interaction between the rudders, the propeller, and the hull are linear with the rudder angles within a range around the hover rudder angle. The linear relationship is obtained through linear regression of the results from several CFD simulations. The VTPS implements a PID controller that regulates the actuator forces to achieve the given low-speed positioning objective. It was tested in combined automatic docking and position-keeping experiments where disturbances from the environment exist. It shows promising potential for a practical application but with further improvements.

Automation of berthing maneuvers in shipping is a pressing issue as the berthing maneuver is one of the most stressful tasks seafarers undertake. Berthing control problems are often tackled via tracking a predefined trajectory or path. Maintaining a tracking error of zero under an uncertain environment is impossible; the tracking controller is nonetheless required to bring vessels close to desired berths. The tracking controller must prioritize the avoidance of tracking errors that may cause collisions with obstacles. This paper proposes a training method based on reinforcement learning for a trajectory tracking controller that reduces the probability of collisions with static obstacles. Via numerical simulations, we show that the proposed method reduces the probability of collisions during berthing maneuvers. Furthermore, this paper shows the tracking performance in a model experiment., Comment: 14 pages, 15 figures, Submitted to Journal of Marine Science and Technology

Container ships encounter large roll angles and high acceleration, and container loss remains a problem. This study proposes a method for calculating the probability density function~(PDF) of roll angular and cargo lateral accelerations. First, the moment values of these accelerations are derived using the linearity of expectation and the validity of this method is examined. Second, the PDF shapes of these accelerations are proposed and their coefficients are determined using the obtained moment values. Our proposed method can be used to derive the PDFs of roll angular and cargo lateral accelerations., Comment: 9 pages, 8 figures, preprint

In the usual framework of control, a reference trajectory is needed as the set point for a feedback controller. This reference trajectory can be generated by solving a trajectory optimization problem. This problem is a continuous optimal control problem (OCP) that is transcribed into a finite-dimensional nonlinear optimization problem (NLP) and solved by SQP. For an underactuated conventional vessel, the mathematical model can be very intricate, hence the NLP itself. This causes significant computational time. This article demonstrates that the balance between the feasibility of the reference trajectory and the computational time can be achieved for an underactuated vessel in a disturbed and restricted environment. This is done by: (1) using an almost-globally optimal offline solution as a warm start in a semionline trajectory optimization to speed up the calculation, (2) including the prediction of wind dynamics, and (3) representing the ship as a rigid body and using a predefined boundary to generate the necessary spatial constraints via a point-in-polygon method that ensure a collision-free trajectory in a nonconvex region. Incorporation of these three things maintains a safe and dynamically feasible trajectory where the warm start gives a considerable computational speedup and better results than that without a warm start.

Parametric rolling is one of the dangerous dynamic phenomena. In order to discuss the safety of a vessel when a dangerous phenomenon occurs, it is important to estimate the probability of certain dynamical behavior of the ship with respect to a certain threshold level. In this paper, the moment values are obtained by solving the moment equations. Since the stochastic differential equation(SDE) is needed to obtain the moment equations, the Autoregressive Moving Average(ARMA) filter is used. The effective wave is modeled by using the 6th-order ARMA filter. In addition, the parametric excitation process is modeled by using a non-memory transformation obtained from the relationship between GM and wave elevation. The resulting system of equations is represented by the 8th-order It\^o stochastic differential equation, which consists of a second-order SDE for the ship motion and a 6th-order SDE for the effective wave. This system has nonlinear components. Therefore, the cumulant neglect closure method is used as higher-order moments need to be truncated. Furthermore, the probability density function of roll angle is determined by using moment values obtained from the SDE and the moment equation. Here, two types of the probability density function are suggested and have a good agreement., Comment: preprint, 13 pages, 14 figures. accepted (Journal of Marine Science and Technology)

Accurate maneuvering estimation is essential to establish autonomous berthing control. The system-based mathematical model is widely used to estimate the ship's maneuver. Commonly, the system parameters of the mathematical model are obtained by the captive model test (CMT), which is time-consuming to construct an accurate model suitable for complex berthing maneuvers. System identification (SI) is an alternative to constructing the mathematical model. However, SI on the mathematical model of ship's maneuver has been only conducted on much simpler maneuver: turning and zig-zag. Therefore, this study investigates the SI on a mathematical model capable of berthing maneuver. The main contributions of this study are as follows: (i) construct the system-based mathematical model on berthing by optimizing system parameters with a reduced amount of model tests than the CMT-based scheme; (ii) Find the favorable choice of objective function and type of training data for optimization. Global optimization scheme CMA-ES explored the system parameters of the MMG model from the free-running model's trajectories. The berthing simulation with the parameters obtained by the proposed method showed better agreement with the free-running model test than parameters obtained by the CMT. Furthermore, the proposed method required fewer data amounts than a CMT-based scheme., Comment: 16 pages, 8 figures, preprint

Several studies on ship maneuvering models have been conducted using captive model tests or computational fluid dynamics (CFD) and physical models, such as the maneuvering modeling group (MMG) model. A new system identification method for generating a low-speed maneuvering model using recurrent neural networks (RNNs) and free running model tests is proposed in this study. We especially focus on a low-speed maneuver such as the final phase in berthing to achieve automatic berthing control. Accurate dynamic modeling with minimum modeling error is highly desired to establish a model-based control system. We propose a new loss function that reduces the effect of the noise included in the training data. Besides, we revealed the following facts - an RNN that ignores the memory before a certain time improved the prediction accuracy compared with the "standard" RNN, and the random maneuver test was effective in obtaining an accurate berthing maneuver model. In addition, several low-speed free running model tests were performed for the scale model of the M.V. Esso Osaka. As a result, this paper showed that the proposed method using a neural network model could accurately represent low-speed maneuvering motions., Comment: 13 pages, 7 figures, submitted to Journal of Marine Science and Technology for peer-review

To realize autonomous shipping, autonomous berthing and unberthing are some of the technical challenges. In the past, numerous research have been done on the optimization of trajectory planning of berthing problems. However, these studies assumed only a simple berth and did not consider obstacles. Optimization of trajectory planning on berthing and unberthing in actual ports must consider the spatial constraints and maintain sufficient distance to obstacles. The main contributions of this study are as follows: (i) a collision avoidance algorithm based on the ship domain which has variable size by the ship speed is proposed, to include the spatial constraints to optimization; (ii) the effect of wind disturbance is taken into account to the trajectory planning to make a feasible trajectory based on the capacity limit of actuators; (iii) showing that the optimization method for berthing is also eligible for the unberthing, which has been almost neglected; (iv) waypoints are included to the optimization process, to make optimization easier on practical applications. The authors tested the proposed method on two existing ports. The proposed method performed well on both the berthing and the unberthing problem and optimized the control input and the trajectory while avoiding collision with the complex obstacles., Comment: 19 pages, 17 figures, Published on Ocean Engineering

We propose an approach to saddle point optimization relying only on oracles that solve minimization problems approximately. We analyze its convergence property on a strongly convex--concave problem and show its linear convergence toward the global min--max saddle point. Based on the convergence analysis, we develop a heuristic approach to adapt the learning rate. An implementation of the developed approach using the (1+1)-CMA-ES as the minimization oracle, namely Adversarial-CMA-ES, is shown to outperform several existing approaches on test problems. Numerical evaluation confirms the tightness of the theoretical convergence rate bound as well as the efficiency of the learning rate adaptation mechanism. As an example of real-world problems, the suggested optimization method is applied to automatic berthing control problems under model uncertainties, showing its usefulness in obtaining solutions robust to uncertainty., Comment: Accepted for ACM TELO