Maneuvering Model Research Articles

Development of a mathematical model for harbor maneuvers to realize modeling automation

A simulation environment of harbor maneuvers is critical for developing automatic berthing. Mathematical models are widely used to estimate harbor maneuvers. However, user’s analysis and decision are necessary to derive, select, and identify the model because each actuator configuration needs an inherent mathematical expression. We proposed a new mathematical 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 expressions 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 mathematical models because it can reduce user’s 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.

Manoeuvring in shallow and confined water with model predictive track controllers

Abstract Autonomous and computer-assisted navigation, for example through portable pilot units and data-driven decision supportive systems, is in full development. Remote-controlled vessels (manned but without a captain steering continuously on board) are used in Belgium (by Seafar in inland shipping) but also in other countries. A model predictive controller has been used to investigate environmental and operational parameters for the passage of the river Seine in Paris by different ship types. These fast-time simulations have been compared with simulations in real time executed by skippers on a ship manoeuvring simulator or measured real life tracks. A good predictability of the real situation requires accurate manoeuvring models. But what if this accuracy cannot be guaranteed? An illustration is made by comparing the tracks if, in the prescience prediction phase for the controller, wind or bank effects are neglected or doubled. The development of model predictive deep reinforcement learning control algorithms for navigation will be one of the challenges of the Data-driven Smart Shipping project that started May 2024.

Identification modeling of ship manoeuvring motion based on ISSA-SVR

This paper introduces the sparrow search algorithm–support vector regression (SSA-SVR) for the first time to improve the precision of mathematical modelling for ship motion through parameter identification. To address the nonsmoothness in ship motion, this study proposes a multistrategy enhanced modelling method named the improved SSA-SVR (ISSA-SVR) for predicting ship motion. Using the KRISO container ship (KCS) test data, this study establishes first-order linear response, second-order nonlinear response, and manoeuvring model group mathematical models through ISSA-SVR identification. The generalisability of the models derived from support vector regression, backpropagation neural networks, particle swarm optimisation-SVR, SSA-SVR, and ISSA-SVR is validated using distinct data from different samples. The results show that the algorithmic model proposed herein excels in prediction compared with other algorithms, thus highlighting its superior generalisation. Furthermore, the proposed method offers solutions with increased accuracy and improved stability for modelling ship motion.

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

A 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\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ anh$$\\end{document}) function and auxiliary variables are introduced to deal with the input constraints. Furthermore, using the feature of the derivative of tanh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ anh$$\\end{document} 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.

Evaluation of hydrodynamic coefficients and sensitivity analysis of a work-class remotely operated vehicle using planar motion mechanism tests

This paper presents a comprehensive analysis of the hydrodynamic forces and moments relating to the drag on an open-frame work-class remotely operated vehicle (ROV) AUTO-1000. We describe the results of planar motion mechanism experiments conducted with the aim of modeling and simplifying the mathematical maneuverability model for such an ROV. The scale of the model is 1:4. Various experiments are performed in a nonlinear wave channel. The flow speeds in the static drag tests range from ±0.2–±0.5 m/s and the angle in the drift tests is less than 10°. The motion frequencies of the dynamic tests range from 0.25 to 3.14 rad/s. The amplitude of the translation motions is 0.03 m and the largest angular amplitude in the rolling tests is 5°. The viscous and inertial hydrodynamic coefficients are estimated. Normalized sensitivity coefficients are used to investigate the sensitivity of both the viscous and inertial hydrodynamic coefficients considering the multi-degree-of-freedom motion and velocity effect. The drag, drift, and stationary random motions are used to examine the sensitivity. A comparison of the motion simulation results given by simplified and complete models shows that a threshold normalized sensitivity coefficient value of 0.01 is suitable for filtering the ROV coefficients.

Real-time simulation of ship overtake maneuvering at different water depths with a ship motion controller

This study aimed to predict ship trajectories in deep and shallow waters in real-time by properly accounting for the effects of hydrodynamic interactions on ship maneuvering. Ship maneuverability and motion control were investigated under hydrodynamic interactions arising from the effects of water depth, ship speed, and lateral distance between interacting ships on parallel courses. The Maneuvering Modeling Group (MMG) model was used, and the hydrodynamic interaction effect was estimated using an efficient three-dimensional potential-flow code that can run in real time. The influence of water depth on ship maneuverability was analyzed. The ship velocity response to the hydrodynamic interactions and maneuvering motion was simulated during the overtaking process of two ships at a range of water depths, lateral distances, and speeds. The findings suggest that, in shallow waters, changing the heading of the ship becomes more difficult, and the course deviation associated with the overtaking maneuver of two ships also increases. A conventional proportional-integral-derivative (PID) controller was employed for course-keeping. When the ratio of the water depth to ship draft was less than 2.0, the PID controller continued to perform effectively for the overtaking ship. For the overtaken ship, the effectiveness of the controller was diminished owing to the relatively low rudder effect at slow speeds.

Intelligent sequential multi-impulse collision avoidance method for non-cooperative spacecraft based on an improved search tree algorithm

The problem of collision avoidance for non-cooperative targets has received significant attention from researchers in recent years. Non-cooperative targets exhibit uncertain states and unpredictable behaviors, making collision avoidance significantly more challenging than that for space debris. Much existing research focuses on the continuous thrust model, whereas the impulsive maneuver model is more appropriate for long-duration and long-distance avoidance missions. Additionally, it is important to minimize the impact on the original mission while avoiding non-cooperative targets. On the other hand, the existing avoidance algorithms are computationally complex and time-consuming especially with the limited computing capability of the on-board computer, posing challenges for practical engineering applications. To conquer these difficulties, this paper makes the following key contributions: (A) a turn-based (sequential decision-making) limited-area impulsive collision avoidance model considering the time delay of precision orbit determination is established for the first time; (B) a novel Selection Probability Learning Adaptive Search-depth Search Tree (SPL-ASST) algorithm is proposed for non-cooperative target avoidance, which improves the decision-making efficiency by introducing an adaptive-search-depth mechanism and a neural network into the traditional Monte Carlo Tree Search (MCTS). Numerical simulations confirm the effectiveness and efficiency of the proposed method.

Four-quadrant propeller hydrodynamic performance mapping for improving ship motion predictions

On the path toward fully autonomous sea vessels, forecasting a ship’s exact velocity and position during its route plays a crucial role in dynamic positioning, target tracking, and autopilot operations of the unmanned body navigating toward predetermined locations. This paper addresses the prediction of the operational performance of a free-running submarine advancing in a straight route (in surge motion). Along with the forward advancing vessel (straight-ahead motion) the study covers all possible scenarios of ship’s surge, including crash-ahead, crash-back, and astern motions. Conventional maneuvering models cannot handle motions other than forward advancement due to the absence of propeller data in all four quadrants of hydrodynamic performance map. This study proposes an approach for predicting submarine performance in all these surge conditions by utilizing four-quadrant propeller performance and resistance test data. We developed an in-house code, SMot4QP, to simulate ship speed and position in the time domain. We obtained satisfying results for the straight-ahead and crash-ahead motions, while the crash-back and astern maneuvers require further refinement due to propeller wake interaction with the hull. The proposed method is capable of predicting the motions of all types of vessels using the ship’s resistance and four-quadrant propeller test results. Thus, SMot4QP offers a fast and robust alternative to computationally expensive free-running self-propulsion simulations for operational performance prediction in broader naval applications.

Control method for the ship track and speed in curved channels

Due to natural and external influences in curved channels, ships frequently require adjustments in course and speed, posing challenges for existing control methods. Particularly lacking are speed control methods suitable for curved channel navigation. This study initially developed a three-degree-of-freedom MMG model incorporating external interference. It introduced an OP-PID heading controller merging optimal control strategies with traditional PID, adaptable to both external conditions and ship speed, validated through heading control simulations. The study analysed the ship's speed change process, deriving a mathematical expression for advance distance, and proposed a dichotomy-based speed control method to determine speed change points, addressing differential equations with unknown integrands. To mitigate uncertainty errors like parameter inaccuracies in ship maneuvering models and dynamic environmental disturbances, the study proposed a comprehensive control approach. This approach integrates model predictive control, feedback compensation, segment identification, and an enhanced line-of-sight (LOS) guidance method alongside the OP-PID course controller and dichotomy-based speed control. Simulation experiments in the Dongboliao Channel compared the proposed and existing methods. Results demonstrate the proposed method's capability to handle frequent course and speed adjustments effectively, even under model errors and external interference, showcasing superior track deviation and course control accuracy over existing methods.

Imitation learning for aerobatic maneuvering in fixed-wing aircraft

This study focuses on the task of developing automated models for complex aerobatic aircraft maneuvers. The approach employed here utilizes Behavioral Cloning, a technique in which human pilots supply a series of sample maneuvers. These maneuvers serve as training data for a Machine Learning algorithm, enabling the system to generate control models for each maneuver. The optimal instances for each maneuver were chosen based on a set of objective evaluation criteria. By utilizing these selected sets of examples, resilient models were developed, capable of reproducing the maneuvers performed by the human pilots who supplied the examples. In certain instances, these models even exhibited superior performance compared to the pilots themselves, a phenomenon referred to as the “clean-up effect”. We also explore the application of transfer learning to adapt the developed controllers to various airplane models, revealing compelling evidence that transfer learning is effective for refining them for targeted aircraft. A comprehensive set of intricate maneuvers was executed through a meta-controller capable of orchestrating the fundamental maneuvers acquired through imitation. This undertaking yielded promising outcomes, demonstrating the proficiency of several Machine Learning models in successfully executing highly intricate aircraft maneuvers. This paper is an extended version of the previously ICCS 2023 published conference paper [1] .

A temporal prediction model for ship maneuvering motion based on multi-head attention mechanism

In real-world maritime conditions, accurately predicting ship maneuvering motion over ultrashort periods can enhance the development of more precise vessel control algorithms. This study proposes a prediction model for ship maneuvering that utilizes a multi-head attention mechanism. To form a basis for this data-driven approach, we gathered training data from turning and zigzag tests of a ship conducted in natural sea environments. The model's predictive capability is assessed by comparing two strategies over a fixed 30-time-step forecast horizon: iterative multi-step forecasting (IMS) and direct multi-step forecasting (DMS). Notably, the model employs distinct attention layers to examine the temporal relationships among various motion variables across the three degrees of freedom in the output. Moreover, it uses separate attention layers to explore the distinct time response traits of the input motion states and control signals. The results demonstrate that different motion state variables display unique temporal correlations under different signal sequences, and the proposed network architecture effectively captures these temporal response traits.

Towards autonomous inland shipping: a manoeuvring model in confined waterways

ABSTRACT Autonomous inland water vessels are essential for promoting intelligent and sustainable waterborne transport. An accurate ship manoeuvring model ensures reliable control strategies and enhances navigation safety. Although ship manoeuvrability models have existed for decades, few studies address shallow and restricted waters. This study introduces a manoeuvring model for inland water vessels, accounting for confinement effects on ship motion. The Manoeuvring Modelling Group (MMG) model in open water serves as the baseline, incorporating empirical methods for shallow water and bank effects. This approach aims to provide a fast and accurate prediction of vessel motion response. The model was validated with free-running experimental data of a pusher-barge model from turning tests at three water depths. Additional case studies highlight shallow water impact compared to infinite water performance under bank effects. Finally, course-keeping case studies are presented, integrating a Proportional-Derivative controller with combined river current and bank-induced forces..

Numerical simulation study on ship manoeuvrability in mountainous rivers: Comprehensively considering effects of nonuniform flow, shallow water, narrow banks, winds and waves

Ships navigating inland waterways, especially mountainous waterways, may encounter complex navigation environments. Under these circumstances, the force of the ship is extremely complex, the attitude of the ship may be unstable, and the control performance may decrease, possibly resulting in marine accidents. In this study, a modular-type manoeuvring model (MMG) is used to develop a ship manoeuvring model that comprehensively considers multiple factors. Based on this model, numerical simulations are conducted on the ship Seiun Maru, and Esso Osaka; the simulation results are found to be in good agreement with the results of real ship motions. Then, numerical simulations are conducted on the navigation of a 500-ton ship in a typical mountainous waterway, the Suoluo Rapids in the Lancang River, and the impact of the complex environment in this area on the safety of ship navigation is explored. The results reveal that ignoring the influence of environmental factors may put ships in dangerous situations when navigating mountain waterways. In addition, the model can effectively simulate the manoeuvring motion of a ship in a typical mountain waterway, and the calculation cost is negligible. This study provides valuable suggestions for long-distance ship manoeuvring in complex inland river environments.

Integrating Computational Fluid Dynamics for Maneuverability Prediction in Dual Full Rotary Propulsion Ships: A 4-DOF Mathematical Model Approach

To predict the maneuverability of a dual full rotary propulsion ship quickly and accurately, the integrated computational fluid dynamics (CFD) and mathematical model approach is performed to simulate the ship turning and zigzag tests, which are then compared and validated against a full-scale trial carried out under actual sea conditions. Initially, the RANS equations are solved, employing the Volume of Fluid (VOF) method to capture the free water surface, while a numerical simulation of the captive model test is conducted using the rigid body motion module. Secondly, hydrodynamic derivatives for the MMG model are obtained from the CFD simulations and empirical formula. Lastly, a four-degree-of-freedom mathematical model group (MMG) maneuvering model is proposed for the dual full rotary propulsion ship, incorporating full-scale simulations of turning and zigzag tests followed by a full-scale trial for comparative validation. The results indicate that the proposed method has a high accuracy in predicting the maneuverability of dual full-rotary propulsion ships, with an average error of less than 10% from the full-scale trial data (and within 5% for the tactical diameters in particular) in spite of the influence of environmental factors such as wind and waves. It provides experience in predicting the maneuverability of a full-scale ship during the ship design stage.

Prediction of horizontal and vertical turning maneuvers of a generic submarine model by closed-form solutions and CFD

Turning maneuvering performance of a generic submarine in both the horizontal and vertical planes is investigated using closed-form (analytical) solutions and the Computational Fluid Dynamics (CFD) method. The aim is to provide a simple yet improvable method throughout the design phase of an underwater vehicle. Both the turning circle maneuver in the horizontal plane and the rising maneuver in the vertical plane are performed. Vehicle trajectories are obtained using closed-form solutions and a linearized maneuvering model with a limited set of hydrodynamic coefficients computed from the CFD model. The derivation of the closed-form solution is based on the basic mechanical principles of steady circular motion, while the hydrodynamic coefficients are determined via steady CFD simulations using a single grid topology. The steady turning diameter serves as the figure of merit in a turning circle maneuver. For the rising maneuver, trajectories predicted by both methods are directly compared. The methods are found to be in good agreement for both maneuvers. Maneuvering predictions made with the linear coefficient set are also open to development. As the design of the submarine evolve, nonlinear and coupled effects can be included in the mathematical model by incorporating related hydrodynamic coefficients to obtain more accurate results.

Defense penetration strategy for unmanned surface vehicle based on modified soft actor–critic

This paper investigates the defense penetration problem for unmanned surface vehicle (USV) with limited detection range under unknown defenders. A novel end-to-end defense penetration strategy is proposed for the USV based on modified soft actor–critic (MSAC). Specifically, the state–action space of the attacker is designed by combining the maneuvering model of USV and detection information. To guide the USV to reach the target area under the interception of defenders, the penetration reward is constructed. Then, the long short-term memory network (LSTM) is applied in the actor–critic network design. A dynamic training mechanism is proposed by combining curriculum learning and multi-memory pools, which aims to improve the success rate of defense penetration. Finally, simulation results validate the effectiveness and superiority of the proposed defense penetration method for the USV suffering from unknown defenders. The higher success rate can be guaranteed by using MSAC compared to the previous methods.

Online prediction of ship maneuvering motions based on adaptive weighted ensemble learning under dynamic changes

Dynamic changes in ship maneuverability challenge the accuracy and effectiveness of ship maneuvering models. This paper proposes an online prediction method based on the adaptive weighted ensemble learning framework, which can adaptively update the model according to changes in maneuverability, especially for reoccurring changes. The method contains two main mechanisms: the change monitoring mechanism and the adaptive weighting mechanism. The former identifies the change in ship dynamics and decides when to incorporate a new base model; the latter adjusts the weights of the base models to align with current scenarios, thus ensuring the predictive accuracy. To assess the method’s effectiveness under varying ship dynamics, the online prediction of ship maneuvering motions under speed-induced dynamic changes is investigated. Compared with the offline model, the result demonstrates the superiority of the adaptive weighted ensemble model. The proposed method can consistently provide accurate predictions in the scenarios with reoccurring changes, and can also enhance the model capability by adjusting weights to cope with some unencountered changes.

Fast-running CFD calculations of the ONR Tumblehome performing maneuvers in calm water and in waves using a Gaussian process regression propeller and rudder model

The accurate and efficient prediction of vessel maneuvering characteristics in calm water and in waves using numerical methods is challenging. The objective of this work is to demonstrate the use of a Gaussian Process Regression based data-driven propeller and rudder model for vessel maneuvering in both calm water and in waves. The data-driven propeller and rudder model is trained with CFD simulations of the discretized propeller and rudder operating in the behind condition at different forward speeds, drift angles, and rudder angles. The data-driven propeller and rudder model enables the accurate calculation of maneuvering performance with low computational expense. This work describes the process for training and implementing the data-driven propeller and rudder model in a CFD package. The calm water zigzag and turning circle maneuvering characteristics for the ONR Tumblehome are evaluated and are compared to archival experiments. Furthermore, the maneuvering characteristics are evaluated in regular waves with several different wave conditions. In addition to demonstrating the accurate and efficient calculation of maneuvering performance, this work provides a multi-fidelity database of propeller and rudder forces at different forward speeds and drift angles, which can be used to train future data-driven propeller and rudder models.

UAV Swarm Centroid Tracking for Edge Computing Applications Using GRU-Assisted Multi-Model Filtering

When an unmanned aerial vehicles (UAV) swarm is used for edge computing, and high-speed data transmission is required, accurate tracking of the UAV swarm’s centroid is of great significance for the acquisition and synchronization of signal demodulation. Accurate centroid tracking can also be applied to accurate communication beamforming and angle tracking, bringing about a reception gain. Group target tracking (GTT) offers a suitable framework for tracking the centroids of UAV swarms. GTT typically involves accurate modeling of target maneuvering behavior and effective state filtering. However, conventional coordinate-uncoupled maneuver models and multi-model filtering methods encounter difficulties in accurately tracking highly maneuverable UAVs. To address this, an innovative approach known as 3DCDM-based GRU-MM is introduced for tracking the maneuvering centroid of a UAV swarm. This method employs a multi-model filtering technique assisted by a gated recurrent unit (GRU) network based on a suitable 3D coordinate-coupled dynamic model. The proposed dynamic model represents the centroid’s tangential load, normal load, and roll angle as random processes, from which a nine-dimensional unscented Kalman filter is derived. A GRU is utilized to update the model weights of the multi-model filtering. Additionally, a smoothing-differencing module is presented to extract the maneuvering features from position observations affected by measurement noise. The resulting GRU-MM method achieved a classification accuracy of 99.73%, surpassing that of the traditional IMM algorithm based on the same model. Furthermore, our proposed 3DCDM-based GRU-MM method outperformed the Singer-KF and 3DCDM-based IMM-EKF in terms of the RMSE for position estimation, which provides a basis for further edge computing.

Left-Turn Lane Capacity Estimation based on the Vehicle Yielding Maneuver Model to Pedestrians at Signalized Intersections

Crossing pedestrians may significantly affect the capacity of the left-turn (LT) lane at signalized intersections while sharing the same signal phase in the left-hand traffic system, the quantitative estimation method is still not intensively discussed when considering the vehicle yielding maneuver. Despite the Road Traffic Act in Japan mandating vehicles to yield to pedestrians, instances of vehicles crossing in front of pedestrians are frequent. This study aims to refine the evaluation of LT lane capacity by introducing a novel vehicle yielding maneuver model, considering factors such as pedestrian numbers, crosswalk length, and signal timing. The model, developed using data from various Japanese crosswalks, is subjected to Monte Carlo simulation for validation. Comparative analysis with existing methods in Japanese and U.S. manuals, along with observed data, highlights the effectiveness of our model. This innovative approach has the potential to mitigate vehicle–pedestrian conflicts and reduce air pollution. By incorporating techniques such as signal optimization and two-stage crossing, our model contributes to sustainability while maintaining efficient traffic flow.