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Navigation Vector based Ship Manoeuvring Prediction
Abstract
A novel mathematical framework for predicting ship maneuvers within a short time interval is presented in this study. The first part of this study consists of estimating the required vessel states and parameters by considering a kinematic vessel maneuvering model. That is supported by an extended Kalman filter (EKF), where vessel position, heading, yaw rate and acceleration measurements are used. Then, the estimated vessel states and parameters are used to derive the respective navigation vectors that consist the pivot point information. The second part of this study consists of predicting the future vessel position and orientation (i.e. heading) within a short time interval by a vector product based algorithm, where the respective navigation vectors are used. The main advantage in this method is that the proposed framework can accommodate external environmental conditions in ship navigation and that feature improves the predictability of vessel maneuvers. Finally, the proposed mathematical framework is simulated and successful computational results in predicting ship maneuvers are presented in this study. Therefore, that can be implemented in modern integrated bridge systems to improve the navigation safety in maritime transportation.
... The induced external forces and moments caused by irregular waves or wind can also bring additional complexity in nonlinear ship maneuvering behaviors (Janssen et al., 2017). The second issue lies in the implementation of simplistic mathematical models, which are mainly employed in ship behavior prediction (Perera, 2017). These models are assumed to operate under constant state and parameter conditions; therefore, their performance may be degraded when exposed to varying environmental conditions. ...
... It should also be noted that ships, particularly those with large tonnage, exhibit specific maneuvering behaviors (Molland, 2008). Ocean-going vessels are prone to drift due to underactuated conditions, which can result in potential near-miss or collision situations during navigation (Perera, 2017). Accurate estimation of ships' states, especially in the sway direction in order to find the ship's pivot point, is necessary (Seo, 2016). ...
... Consequently, the established state-space models and algorithms must be capable of providing precise estimates under such circumstance. Estimated states in sway direction with a longer convergence period (Perera, 2017), or a large delay and bias (Wang et al., 2022b), need to be avoided. ...
Advanced ship predictors can generally be considered as a vital part of the decision-making process of autonomous ships in the future, where the information on vessel maneuvering behavior can be used as the source of information to estimate current vessel motions and predict future behavior precisely. Hence, the navigation safety of autonomous vessels can be improved. In this paper, vessel maneuvering behavior consists of continuous-time system states of two kinematic motion models—Curvilinear Motion Model (CMM) and Constant Turn Rate & Acceleration (CTRA) Model. The two state estimation algorithms—the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) are implemented on these two models with certain modifications so that they can be compatible with discrete-time measurements. Four scenarios obtained by a combination of models and estimation algorithms are implemented on simulated ship maneuvering data of a bridge simulator and verified via the proposed estimation algorithm stability and consistency test. The simulation results show that the EKF tends to be unstable with the CMM. The estimates of other three scenarios can be considered as having higher stability and consistency, unless sudden actions or vessel heading variations have occurred. The CTRA is also proven to be more robust compared to the the CMM. As a result, a suitable combination of mathematical models and estimation filters can be considered to support advanced ship predictors in the future.
... It is worth mentioning that their results are based on ground vehicle testings that only the velocity in the surge direction is considered. Similar to the CMM model proposed in [11], a novel method that contains surge and sway velocities of a vessel as parts of the ship maneuvering model is introduced in [14] and this model is also studied in [15]. Combined with the concept of a pivot point [16], this novel model could also be used to predict most of the related vessel states with higher accuracy during a short period. ...
... Combined with the concept of a pivot point [16], this novel model could also be used to predict most of the related vessel states with higher accuracy during a short period. However, the simulation results in [14,15] show that the estimation efficiency and accuracy of surge and sway velocities cannot compare with other vessel states. ...
... Both models are established under a fixed right-hand coordinate system-the North-East-Down system so that the measurements of heading are consistent with common measurement systems. The CMM is derived from the kinematic equations in [11] and inherits the features where and are assigned as state variables [14]. This model is fairly general in that it can reduce to special cases such as a constant velocity model, constant acceleration model, and constant turning model [12]. ...
Autonomous shipping with adequate decision support systems is widely considered as a high-potential development direction in the maritime industry in the upcoming years. Prediction technologies are one of the key components in these decision support systems and they usually require a large number of data sets to estimate vessel states. Certain vessel motion models are generally implemented with the above-mentioned prediction technologies to improve the accuracy and robustness of the estimated states. In contrast to wider research studies of different motion models for the applications of ground vehicles, the studies of appropriate motion models for maritime transport applications are still insufficient. Therefore, it is necessary to develop reliable motion models for vessels, and that can improve the decision supporting capabilities in future vessels, especially in autonomous shipping.
In this paper, two kinematic motion models which can be used to estimate various vessel maneuvering states are examined and compared. In the current stage, the proposed models are used to investigate ship maneuvers produced by a ship bridge simulator. Two nonlinear filter algorithms combined with Monte Carlo-based simulation tests are applied to estimate the respective vessel states. In the conclusion, a comprehensive comparison of the estimation algorithms is presented with the estimated vessel states. Hence, this study provides robust and convenient estimation algorithms that can support autonomous shipping navigation in the future.
... More advanced techniques, e.g. [9,10], where extended Kalman filters were utilized, can aid in predicting more complex ship behavior. However, such techniques will not be useful for prediction horizons greater than a few minutes. ...
... The final layer will have an output dimension corresponding to the number of classes, i.e. clusters, discovered by the clustering module. A softmax layer then computes the final output by scaling the output between 0 and 1 according to (10). ...
... The network can in this manner learn what to look at in order to most effectively conduct a prediction. The outputs are then run through a softmax layer as in (10). This generates an attention distribution, , over the encoder hidden states, where each attention value can be viewed as a weight for the corresponding encoder hidden state. ...
This study presents a deep learning framework to support regional ship behavior prediction using historical AIS data. The framework is meant to aid in proactive collision avoidance, in order to enhance the safety of maritime transportation systems. In this study, it is suggested to decompose the historical ship behavior in a given geographical region into clusters. Each cluster will contain trajectories with similar behavior characteristics. For each unique cluster, the method generates a local model
to describe the local behavior in the cluster. In this manner, higher fidelity predictions can be facilitated compared to training a model on all available historical behavior. The study suggests to cluster historical trajectories using a variational recurrent autoencoder and the Hierarchical Density-Based Spatial Clustering of Applications with Noise algorithm. The past behavior of a selected vessel is then classified to the most likely clusters of behavior based on the softmax distribution. Each local model consists of a sequence-to-sequence model with attention. When utilizing the deep learning framework, a user inputs the past trajectory of a selected vessel, and the framework outputs the most likely future trajectories. The model was evaluated using a geographical region as a test case, with successful results.
... The vessel state and parameter estimation can take priority over the future trajectory prediction since the latter requires the estimation results. Nowadays, linear predictions of vessel future trajectories based on the current speed and course values are popular in ship navigation (Perera, 2017). Such linear predictions have limitations to support SA, while making decisions in complex ship encounter situations. ...
... It is well-known that vessels with large drafts have relatively slow responses, where such models are the most suitable approach. Such slow reactions can occur even, when the surrounding environment changes quickly (Perera, 2017). Therefore, kinematic models can be well suited to predict vessel motions during a short time range. ...
... A possible reason for this situation can relate to the system model uncertainties or the high dimensionality of systems (Snyder et al., 2008). The simulation results by the EKF algorithm using this same model shows that convergence rates of ( ) and ( ) are relatively slow compared with other's (Perera, 2017), therefore a more detail analysis for the estimation of these two states is necessary. ...
The vessel state and parameter estimation is essential to ship
maneuvering and collision avoidance. This study presents an application of a particle filter algorithm to estimate vessel states and parameters. Particularly, to capture the impact of the vessel underactuated property and complex environmental-induced disturbances, the estimation process contains a kinematic curvilinear motion model that describes vessel motions. The estimated result can help ship navigators or onboard computers to well comprehend present vessel maneuvering conditions. Besides, it can also serve as a necessary data source for future trajectory predictions for ocean-going vessels. Therefore, it can be integrated into situation awareness type applications in vessels that can improve the navigation safety for both manned and autonomous vessels.
... Predicting ship behaviour [10], accurately ahead of time in a close ship encounter situation, can support the decision maker, i.e. human or system, to take appropriate collision avoidance actions, and can also be a solution to ship under-actuation behaviour. Therefore, unexpected ship motions due to vessel under-actuation can be observed as the collision risk and adequate actions by both humans and systems can be taken to prevent possible collision and near-miss situations. ...
... heading) within a shorter time period. This approach has been investigated in [10], where its capabilities are presented in a simulated environment. This consists of a simplified mathematical framework that is presented in Figure 4. ...
... It has been shown that the current vessel position and orientation (i.e. heading), measured by on-board sensor measurements with an appropriate mathematical algorithm, can be used to estimate the future vessel position and orientation [10]. The algorithm is briefly discussed in this section and consists of two sections. ...
Autonomous ship navigation in a mixed environment, where remote-controlled, autonomous and manned vessels are interacting, is considered. These vessels can have various encounter situations, therefore adequate knowledge on such situations should be acquired to take appropriate navigation actions. That has often been categorized as situations awareness in a mixed environment, where appropriate tools and techniques to improve the knowledge on ship encounter situations should be developed. Hence, possible ship collision and near-miss situations can be avoided by both humans as well as systems. The collision risk assessment has an important role in ship situations and that can eventually be used towards the respective collision avoidance actions. Ship collision avoidance actions are regulated by the International Regulations for Preventing Collisions at Sea 1972 (COLREGs) in open sea areas and additional local navigation rules and regulations can also enforce especially in confined waters and maritime traffic lanes in these vessels. It is expected that the COLREGs and other navigation rules and regulations will be interpreted by both humans as well as systems in future vessels and those interpretations will be executed in to collision avoidance actions. Therefore, adequate understanding on situation awareness should be achieved to overcome possible regulatory failure due to human and system decisions, i.e. avoid possible collision or near-miss situations in a mixed environment. This study focuses on identifying such challenges in future ship encounters with possible solutions to improve situation awareness in a mixed environment.
... With the aid of these technologies and equipment, improving perception and understanding of nearby situations becomes achievable, particularly in scenarios with limited visibility. However, it is crucial to note that many of these systems still rely on simplistic linear mathematical models for ship trajectory prediction (Perera, 2017). Linear predictions may pose a risk of significant errors, particularly by overlooking potential collision points in close encounter situations. ...
... Particularly, the models can be combined with some practical tips in ship maneuvering so that the prediction can become more accurate and actionable. The implementation of a ship's pivot point is a good practice to support the local scale trajectory prediction (Perera, 2017). Another method involves employing different neural networks. ...
The marine navigation environment can become further complex when ships with different autonomy levels are introduced. To ensure navigation safety in such mixed environment, advanced ship predictors type technologies are essential in aiding ship navigators to attain the highest levels of situation awareness (SA). Consequently, precise ship trajectory prediction, specifically within a short prediction horizon, should be included in such predictors as an indispensable component. This study introduces two methods for ship trajectory prediction on a local scale: the kinematic-based method and the Gate Recurrent Unit (GRU)-Pivot Point (PP)-based method. The first method utilizes kinematic motion models to predict a ship trajectory. In the second method, the GRU is trained to generate the predictions of related ship navigation states. The ship’s PP is then extracted from these predicted states, subsequently providing a predicted ship trajectory. Both methods are validated using simulated maneuvering exercises to assess their effectiveness, with a prediction horizon of 90 seconds. The results show that the kinematic-based method excels in the predictions during ship’s stable stages, i.e., steady-state conditions. Meanwhile, the GRU-PP-based method exhibits robust performances in cases when new rudder orders are executed, i.e., transient conditions. It is considered that these applications can provide significant benefits in maritime SA in present and future ship navigation.
... However, AI DSS for navigators onboard are still in a relatively early development phase compared to e.g., the automotive sector (Munim et al., 2020). For developers, a major challenge is that a ship's trajectory is much more difficult to model in a predictive algorithm than a car, as it is influenced by environmental conditions, complex hydrodynamic effects or other ships (Perera, 2017). Further, traffic regulation is less bounded at sea than on land, and includes concepts like "good seamanship" that are difficult to codify in algorithms (Azimi et al., 2020). ...
... Further, traffic regulation is less bounded at sea than on land, and includes concepts like "good seamanship" that are difficult to codify in algorithms (Azimi et al., 2020). Finally, many AI applications are developed and tested mainly in ship simulators due to cost reasons, making it more difficult to account for real-world issues like erroneous onboard sensors (Perera, 2017). Considering the environmental context and the sociotechnical onboard system, the maritime domain presents an interesting study context to investigate potential tensions between contextual complexity and the pursuit to develop high-accuracy AI DSS outside of conventional organizational confines. ...
... Sutulo S (2002) [2] studied ship maneuvering simulations, focusing on two essential methods: dynamic and kinematic prediction models, emphasizing improved kinematic prediction techniques. Rigatos (2013) [3] explored dynamic ship positioning using sensor fusion techniques based on Kalman and Particle Filtering algorithms, while Perera (2017) [4] used an extended Kalman filter and vector-based algorithms for short-term ship maneuver prediction. Fossen (2018) [5] introduced an exogenous Kalman filtering (XKF)-based ship motion prediction method, leveraging real-time Automatic Identification System (AIS) data for visualization and motion prediction. ...
... Sutulo S (2002) [2] studied ship maneuvering simulations, focusing on two essential methods: dynamic and kinematic prediction models, emphasizing improved kinematic prediction techniques. Rigatos (2013) [3] explored dynamic ship positioning using sensor fusion techniques based on Kalman and Particle Filtering algorithms, while Perera (2017) [4] used an extended Kalman filter and vector-based algorithms for short-term ship maneuver prediction. Fossen (2018) [5] introduced an exogenous Kalman filtering (XKF)-based ship motion prediction method, leveraging real-time Automatic Identification System (AIS) data for visualization and motion prediction. ...
The stability of navigation in waves is crucial for ships, and the effect of the waves on navigation stability is complicated. Hence, the LSTM neural network technique is applied to predict the course changing of a ship in different wave conditions, where K-means clustering analysis is used for the category of the ship’s navigation data to improve the quality of the database. In this paper, the effect of the initial database obtained by the K-means clustering analysis on prediction accuracy is studied first. Then, different input features are used to establish the database to train the neural network, and the influence of the database by different input features on the accuracy of the navigation prediction is discussed and analyzed. Finally, multi-task learning is used to make the neural network better predict the navigation in various wave conditions. Using the improved neural network model, the course of an autopilot ship in waves is predicted, and the results show that the current database and the neural network model are accurate enough for the course prediction of the autopilot ship in waves.
... The AIS-based vessel trajectory can be regarded as an ordered series of timestamped points. Many classical approaches, including Kalman filter [44] and its variants [45], [46], were employed to perform time-series (i.e., trajectory) prediction. The extended Kalman filter (EKF), which formulated vessel position, velocity and acceleration, was proposed to predict vessel trajectories under noisy conditions [45]. ...
... The extended Kalman filter (EKF), which formulated vessel position, velocity and acceleration, was proposed to predict vessel trajectories under noisy conditions [45]. To further improve the prediction reliability, the EKF and vector product-based algorithm were combined to estimate the vessel sailing direction and future position [46]. ...
The maritime Internet of Things (IoT) has recently emerged as a revolutionary communication paradigm where a large number of moving vessels are closely interconnected in intelligent maritime networks. However, the tremendous growth of vessel trajectories, collected from the combined satellite-terrestrial AIS (automatic identification system) base stations, could lead to unsatisfactory maritime safety and efficacy. To promote smart traffic services in maritime IoT, it is necessary to accurately and robustly predict the spatiotemporal vessel trajectories. It is beneficial for collision avoidance, maritime surveillance, and abnormal behavior detection, etc. Motivated by the strong learning capacity of deep neural networks, this work proposes an AIS data-driven trajectory prediction framework, whose main component is a long short term memory (LSTM) network. In particular, the vessel traffic conflict situation modeling, generated using the dynamic AIS data and social force concept, is embedded into the LSTM network to guarantee high-accuracy vessel trajectory prediction. In addition, a mixed loss function is reconstructed to make our prediction results more reliable and robust in different navigation environments. Several quantitative and qualitative experiments have been implemented on realistic AIS-based vessel trajectories. Our results have demonstrated that the proposed method could achieve satisfactory prediction performance in terms of accuracy and robustness.
... Ship motion prediction models range from completely transparent kinetic models Triantafyllou et al. (1983), through kinematic models Perera (2017) to regression models Brandsaeter and Vanem (2018) and black-box Machine Learning (ML) models Yin et al. (2017). Each domain has their own strengths and weaknesses. ...
... Kinematic models disregard the forces induced by a ship moving on the surface of the ocean and apply only the relation between acceleration/velocity and heading to get positions. A complete method of estimation and prediction of vessel trajectories is presented in Perera (2017). An extended Kalman filter was used to estimate the states of a kinematic ship maneuvering model. ...
... Predicting ship behavior as in Perera (2017) can provide decision support to navigators to make appropriate collision avoidance maneuvers. Advanced techniques, e.g. ...
... In this approach, a local and global scale ship predictor were suggested. At a local scale, techniques such as those outlined in Perera (2017) can be utilized to aid in short term trajectory predictions in order to aid in effective collision avoidance maneuvers once a collision is deemed imminent. On the global scale however, long term trajectory predictions, on the scale of 5-30 min, are conducted. ...
Advances in artificial intelligence are driving the development of intelligent transportation systems, with the purpose of enhancing the safety and efficiency of such systems. One of the most important aspects of maritime safety is effective collision avoidance. In this study, a novel dual linear autoencoder approach is suggested to predict the future trajectory of a selected vessel. Such predictions can serve as a decision support tool to evaluate the future risk of ship collisions. Inspired by generative models, the method suggests to predict the future trajectory of a vessel based on historical AIS data.
Using unsupervised learning to facilitate trajectory clustering and classification, the method utilizes a cluster of historical AIS trajectories to predict the trajectory of a selected vessel. Similar methods predict future states iteratively, where states are dependent upon the prior predictions. The method in this study, however, suggests predicting an entire trajectory, where all states are predicted jointly. Further, the method estimates a latent distribution of the possible future trajectories of the selected vessel. By sampling from this distribution, multiple trajectories predicted. Finally, the uncertainties of predicted vessel positions in relation to the estimated trajectories are also quantified in this study.
... Thirdly, a large number of sensors are required to estimate system states and parameters. Even though these challenges can partially be addressed by estimating a subset of health parameters (i.e. a reduced order mathematical model) [22] and incorporating sensor noise into estimation algorithms [23,24] with additional disturbance attention methods [25], the complexities (i.e. nonlinearities) in GPA and PSC approaches can still degrade the HMAs of gas turbine engines. ...
... Similarly, the lower and upper confidence bounds for λ can be calculated by (16) and the outcome can be written as: One should note that the 81% conservative simultaneous confidence bounds for λ and β are presented in (24) and (25) with α = .1 and γ = .1. These model parameters are used to derive the following figures. ...
System reliability of offshore power plants with several gas turbine engines is analyzed in this study to understand the failure intensity of a selected gas turbine engines under varying maintenance activities. A set of event data of a selected gas turbine engine is considered to identify system failure intensity levels, where unknown maintenance actions were implemented (i.e. various repairs disturb the failure rate). A non-homogeneous Poisson process (NHPP) is used to model the age dependent failure intensity of the same gas turbine engine and the maximum likelihood estimation (MLE) approach for calculating the respective model parameters is proposed. Several failure intensity rates (i.e. varying failure trends) in these models (i.e. during the system age of the gas turbine engine) are observed. Furthermore, these varying failure trend models are evaluated with actual failure events of the same gas turbine engine by considering two goodness-of-fit tests: Cramer-von Mises and Chi-square tests. Finally, system reliability of this gas turbine engine under failure transition, failure intensity, mission reliability and mean time between failures (MTBF) is also discussed in this study.
... Several 26 similar methods for collision candidate identification have been proposed in succession, see (Ylitalo,27 2010). These methods won popularity in detecting collision candidate and estimating the number of 28 them in ports and waterways, e.g. ( interval for determination, the results of these methods are sensitive to the parameter settings and could 48 contain duplicate detection of the same process. 49 The safe boundary is a kind of threshold which considers spatial proximity as criteria of collision 50 candidate. ...
... instances in time could possibly be overlooked or, vice versa, hence the reliability concerning model 47 settings is also influenced. 48 To improve related study, in this paper, the perspective from which to determine collision 49 candidates is changed. Ship encountering is a process in which ships approach each other and finally 50 depart from each other. ...
Maritime accidents have been imposing various risks to individuals and societies in terms of human and property loss, and environmental consequences. For probabilistic risk analysis and management, collision candidate detection is the first step. Therefore, it is of great importance to further improve methods to detect possible collision scenarios. This paper proposes a Time Discrete Non-linear Velocity Obstacle (TD-NLVO) method for collision candidate detection, which is based on the Non-linear Velocity Obstacle algorithm and tested on historical AIS data (Automatic Identification System). Collision candidates are detected based on the perspective which considers a ship encounter as a process, rather than analysing traffic data at certain time slices. Case studies on single encounters of ship traffic in waterways environments are conducted and presented in this paper. The results indicate that the TD-NLVO method can effectively detect collision candidates which satisfy pre-set criteria. A comparison between seven other popular AIS data-based collision candidate methods is performed, and the results indicate that the proposed method outperforms the other methods regarding its robustness towards the choice of parameter settings.
... Early research emphasized using statistical models that considered external environmental factors and hydrodynamic parameters (Yoshimura, 1986;Khan et al., 2005). The Kalman filter, known for being a recursive, linear, and minimum variance filter, has found extensive application in dynamic ship positioning and short-term maneuver predictions (Rigatos, 2013;Perera, 2017). However, predicting motion using the ship's motion state equation and physical models is significantly affected by external environmental hydrodynamic parameters and computational fluid dynamics, making it less effective for short-term predictions. ...
Irregular waves exhibit complex and erratic behavior, posing significant challenges for accurate short-term ship motion forecasting. Reliable ship navigation depends on precise motion predictions, necessitating effective feature extraction from wave data to enhance predictive models. This study proposes a hybrid model integrating a wavelet principal component analysis (WPCA) for dimensionality reduction with an optimized double circulation-long short-term memory (DC-LSTM) network. The WPCA method retains key variance components, reducing redundant data while preserving critical wave characteristics. The DC-LSTM model is optimized using both internal and external circulation mechanisms to enhance learning efficiency and stability. Numerical simulation data are used to train and validate the model. Compared with conventional LSTM and PCA-LSTM models, the proposed WPCA-DC-LSTM model improves R² by 14% and reduces RMSE by 12% in validation datasets. The model demonstrates robust generalization, effectively capturing nonlinear and high-dimensional wave features. The results indicate that the hybrid model effectively mitigates the influence of redundant data, reduces prediction randomness, and improves stability in handling wave-induced ship movements. The study highlights the broad applicability of the WPCA-DC-LSTM model for complex maritime data analysis and ship motion forecasting.
... Although there are numerous works dealing with ship maneuvering, the authors focus rather on developing models and methods capable of reproducing and predicting a ship trajectory (Perera, 2017;Stec, 2015;Xing-Kaeding et al., 2006), while the systematic studies on the impact of operational and environmental conditions, including the aforementioned problem of short-term variations of irregular waves, on ship trajectories patterns are lacking. ...
In times of progressive automation of the marine industry, accurate modeling of ship maneuvers is of utmost importance to all parties involved in maritime transportation. Despite the existence of modern collision- avoidance algorithms using 6DOF motion models to predict ship trajectories in waves, the impact of stochas- tic realization of irregular waves is usually neglected and remains under-investigated. Therefore, herein, this phenomenon and its impact were investigated in the case study of the passenger ship’s turning. To this end, statistical and spatiotemporal distributions of ship positions and corresponding trajectory parameters were analyzed. This was made using massive 6DOF simulation data with particular attention to the observed extremes. Additionally, the minimum number of wave realizations has been determined using different methods in various simulation scenarios and afterward compared concerning parameters’ impact and existing dependencies. The results indicate that for simulated scenarios, the required number of wave realizations should be at least 20, but in rough seas should be greater than 30. These values satisfy an acceptable and operationally reasonable error limit reaching 15% of the ship’s length overall. The obtained results may be of interest to autonomous ship developers, scholars, and marine industry representatives working on intelligent collision-avoidance solutions and ship maneuvering models.
... The curvilinear motion model (CMM) and the constant turn rate and acceleration model (CTRA) represent two kinematic motion models which can encompass diverse motions exhibited by ships. As a result, these models are widely employed in numerous research studies to provide essential ship navigation states (Perera, 2017;Wang et al., 2023). Nevertheless, it is important to recognize that these kinematic motion models operate under the assumption of constant accelerations and turn rates. ...
With the progress of innovative technologies, ships in the future with
different autonomy levels are anticipated to enter the realm of maritime
transportation. As a result, the scenarios of multi-ship encounters at sea
can become more complex and the risk of potential collisions can be
difficult to elevate. To support navigation safety and guarantee the
required situation awareness level, it is therefore essential to acquire ship
navigation states with a greater degree of precision. The Kalman Filter
(KF)-based techniques are one of the popular approaches for deriving the
ship navigation state by merging the prior estimates from physics-based
models with measurements from onboard sensors. However, many KF based
estimates are calculated by assuming constant system and
measurement uncertainties during the iterative process. In this study, an
adaptive tuning mechanism in the KF-based techniques is utilized to
estimate ship navigation states. This approach enables the estimation
processes to skillfully reduce both system and measurement noise
estimations. Consequently, it results in the generation of smoother and
more responsive estimates of the respective vessel states, particularly
when confronted with variations in rudder orders or encountering
abnormal measured positions.
... Although there are numerous works dealing with ship maneuvering, the authors focus rather on developing models and methods capable of reproducing and predicting a ship trajectory (Perera, 2017;Stec, 2015;Xing-Kaeding et al., 2006), while the systematic studies on the impact of operational and environmental conditions, including the aforementioned problem of short-term variations of irregular waves, on ship trajectories patterns are lacking. ...
... However, in some situations, these vessels can result in close encounter situations, where more advanced localized predictors to evaluate the respective close ship encounter situations should be considered. Therefore, the respective ship collision risk on a more localized scale should be considered in such situations (Perera, 2017). Appropriate techniques to facilitate a localized collision risk methodology in shipping by considering complex vessel encountering situations are the main scope of this study. ...
There are various advanced algorithms developed to search for optimal solutions, i.e. optimal navigation trajectories, have been utilized for collision avoidance among ocean-going vessels by the research community. It is noted that such optimization solutions may not be a mandatory requirement in realistic ship encounter situations, due to the main reason that a slight change of course or speed conditions can completely eliminate possible close encounter situations among vessels. Furthermore, ocean-going vessels may not have the capabilities to satisfy all necessary conditions of such optimal navigation trajectories due to complex environmental conditions and ship under-actuation situations. Even though ship collision avoidance can be considered a simpler problem, the complexity comes from the collision risk estimation process. Therefore, this study further discusses the respective methodology that can be utilized towards detecting possible complex close ship encounter situations and their associated risk that may result in collision situations as the main contribution. Such a methodology based on ship relative motions in estimating the relative navigation trajectories among vessels should be adopted to facilitate the future of the shipping industry, especially under autonomous navigation.
... Researchers proposed a large variety of models for future ship position prediction. For example, the extended Kalman filter was used to estimate ship motion states and predict the trajectory of a vessel by means of a kinematic model [Perera et al., 2012;Sutulo et al., 2002;Perera, 2017]. Li et al. leveraged the Support Vector Machine to predict the heave motion under the impact of waves [Li et al., 2016]. ...
Model uncertainty is pervasive and inherent in the engineering field. It could bring potential risks in real applications, especially for ship behaviour prediction under environmental disturbances. The evaluation and quantification of model uncertainty are of importance for accurate ship motion prediction. This study applies model uncertainty analysis and sensitivity analysis methods to evaluate the ship motion model's level of uncertainty against environmental disturbances and ship manoeuvres. Firstly, three models are created based on the a dynamical model (Mariner) in Marine Systems Simulator. After that, models are tested on various predefined scenarios. The similarity of predicted tra-jectories and the reference is evaluated by Euclidean distance and used to quantify the uncertainty of models. Next, statistical analysis is used to analyze the uncertainty of models. Sensitivity analysis (SA) method called 'PAWN' and 'UnivariateSpline' interpolation technology are combined to identify which factors contribute the most to model's performance. The results suggest that the uncertainty caused by external factors varies from different models under different manoeuvres. SA can tell us which factors (wind angle, wind velocity, and surge speed) have a large influence to the model uncertainty given a ship maneuver. Such analyses, on the one hand, contribute operators to choosing the optimum model according to the current conditions for better ship motion prediction. On the other hand, they can pick up the most important factors for fast uncertainty modelling.
... These data sets can be used to estimate vessel states online, and the accuracy of estimated states needs to be guaranteed since poor quality of estimated states can cause the wrong prediction of vessel behaviors and finally lead to collisions or near-miss situations. Maneuvering behavior of vessels can be described by kinematic motion models in several studies (Li and Jilkov, 2003;Perera, 2017;Wang et al., 2022), and navigation states of vessels can be estimated by Kalman filter-based (KF) techniques with relatively high accuracy. However, as an implicit assumption that measured positions used in most kinematic motion models are actually the projected coordinates of the raw latitude/longitude data from GNSS systems, where the UTM coordinate system has generally been used. ...
Considering the distortion errors of projected coordinates and the switching property of vessel heading, coordinate conversion and switching correction methods are proposed to modify a kinematic motion model and the Unscented Kalman Filter (UKF). The coordinate conversion method utilizes the grid convergence from a Universal Transverse Mercator (UTM) projection to correct the vessel heading. The switching correction is embedded in the UKF
so that the innovations of vessel heading can be calculated correctly. The simulation results demonstrate that the proposed modifications in both model and algorithm can generate more
accurate estimated vessel states from two simulated maneuvers. Since a reliable estimation of vessel maneuvers is the prerequisite in many intelligent systems that support various decision making processes in maritime transportation, the proposed modifications can be therefore implemented into these systems to support navigation safety in high latitude areas.
... Shi (2009) [256] proposed a nonlinear model frame of a maneuvering ship based on an analysis of the hydrodynamics and preprocessed by a fixed interval KF smoothing algorithm. Perera (2010) [257], [258] presented a maneuvering ocean vessel model based on a curvilinear motion model, based on a linear position model for accurate trajectory estimation. Fossen [259] introduced a marine motion control unit that uses KF to reduce oscillatory wave-induced motion from velocity and position measurements and improve the heading angle. ...
The performance of inertial navigation systems is largely dependent on the stable flow of external measurements and information to guarantee continuous filter updates and bind the inertial solution drift. Platforms in different operational environments may be prevented at some point from receiving external measurements, thus exposing their navigation solution to drift. Over the years, a wide variety of works have been proposed to overcome this shortcoming, by exploiting knowledge of the system current conditions and turning it into an applicable source of information to update the navigation filter. This paper aims to provide an extensive survey of information aided navigation, broadly classified into direct, indirect, and model aiding. Each approach is described by the notable works that implemented its concept, use cases, relevant state updates, and their corresponding measurement models. By matching the appropriate constraint to a given scenario, one will be able to improve the navigation solution accuracy, compensate for the lost information, and uncover certain internal states, that would otherwise remain unobservable.
... Trajectory predictors are grouped into two categories; namely, white-box and black-box models. The most concise white-box model is the holonomic [20] and kinematic models [13]. They are widely used in collision avoidance algorithms because of their simple implementation, however, their prediction accuracy is much poorer than that of kinetic dynamic models due to their unrealistic assumptions. ...
A ship trajectory predictor plays a key role in the predictive decision making of intelligent marine transportation. For better prediction performance, the biggest technical challenge is how we incorporate prior knowledge, acquired during the design-stage experiments, into a data-driven predictor if the number of available real-world data is limited. This study proposes a new framework under co-simulation platform Vico for the development of a neural-network-based trajectory predictor with a pre-training phase. Vico enables a simplified vessel model to be constructed by merging a hull model, thruster models, and a controller using a co-simulation standard. Furthermore, it allows virtual scenarios, which describe what will happen during the simulation, to be generated in a flexible way. The fully-connected feedforward neural network is pre-trained with the generated virtual scenarios; then, its weights and biases are finetuned using a limited number of real-world datasets obtained from a target operation. In the case study, we aim to make a 30 s trajectory prediction of real-world zig-zag maneuvers of a 33.9m-length research vessel. Diverse virtual scenarios of zig-zag maneuvers are generated in Vico and used for the pre-training. The pre-trained neural network is further finetuned using a limited number of real-world data of zig-zag maneuvers. The present framework reduced the mean prediction error in the test dataset of the real-world zig-zag maneuvers by 60.8% compared to the neural network without the pre-training phase. This result indicates the validity of virtual scenario generation on the co-simulation platform for the purpose of the pre-training of trajectory predictors.KeywordsCo-simulationTrajectory predictionInformed machine learning
... It is applied to many collision avoidance algorithms [9]. Kinematic models are used in [10]. Aiming at better prediction accuracy, tremendous research effort has been dedicated to developing kinetic expressions of vessel dynamics that are referred to as dynamic models. ...
Onboard sensors contribute to data-driven understanding of complex and nonlinear ship dynamics in real time. By using sensors, precise ship trajectory prediction plays a key role in intelligent collision avoidance. A hybrid predictor makes prediction based on a mathematical model of which error is compensated by a black-box model. A Multiple-output Hybrid Predictor (MHP), which makes a long-horizon prediction at a time based on onboard sensor data, was developed in the previous study. However, it cannot handle a time series of future command assumption. This limitation hinders an MHP from being applied to the evaluation of future command assumption in the predictive decision making. A novel architecture of MHP presented in this study converts a long time series of future command assumption into a fixed-length model-based-predicted vessel state; then, it is included in inputs of a black-box error compensator. This idea is robust to multidimensionality of commands and long control horizon. Assuming a low-fidelity vessel model and a limited data are available, simulation experiments are conducted. The effect of environmental disturbances and maneuverings on the prediction performance is examined comprehensively for the first time. The present study successfully incorporates a long time series of future command assumption in an MHP. It reduces the mean error by 81.8% compared to a model-based predictor and by 45.6% compared to a data-driven predictor under Beaufort wind force scale 4 wave, wind, and ocean current. Present study expands the application of MHP to the predictive decision making of future autonomous ships.
... To aid in making these choices this paper proposes an onboard support tool, which will provide the vessel operator with predictions of the vessel position. These predictions originate from the hybrid predictor and span 30 seconds into the future [6], hereafter termed the prediction horizon. Key contributions of this paper includes the construction of a hybrid model for prediction of the future motion of a ship, and the use of data sampled onboard a coastal ship for training of the data-based model as well as verification of the prediction performance. ...
While automatic controllers are frequently used during transit operations and low-speed maneuvering of ships, ship operators typically perform docking maneuvers. This task is more or less challenging depending on factors such as local environment disturbances, number of nearby vessels, and the speed of the ship as it docks. This paper proposes a tool for onboard support that offers position predictions based on an integration of a supervised machine learning (ML) model of the ship into the ship dynamic model. The ML model is applied as a compensator of the unmodelled behaviour or inaccuracies from the dynamic model. The dynamic model increases the amount of predetermined knowledge about how the vessel is likely to move and thus reduces the black-box factor typically experienced in purely data-driven predictors. A prediction horizon of 30 seconds ahead of real time during docking operations is examined. History data from the 29-meter coastal displacement ship RV (Research Vessel) Gunnerus is applied to validate the approach. Results show that the inclusion of the data-based ML model significantly improves the prediction accuracy.
... 2. Compute the risk degree k ij using its fuzzy set f k ij ðÁÞ based on Table 2. 3. Compute the normalized weight w ji using equation (7). 4. Construct the fuzzy assessment matrix G using equation (15). 5. Compute the BPA m ji ðA k Þ using equation (17). 6. Construct the BPA matrix M using equation (18). ...
In order to reduce the influence of subjective factors on navigation risk assessment, we present a novel scheme based on the fuzzy Dempster–Shafer evidence theory in this article. At first, we deduce the fuzzy set after analyzing various indicators in actual vessel navigation as an example. What’s more, the current data can be adaptively transformed into quantitative information on the basis of two-order membership functions. Considering the inherent defects of standard Dempster–Shafer evidence framework, the assessment process is improved to combine the uncertain and conflicting evidences from available indicators to make reliable decision. Further, three propositions are derived to explain the proposed scheme step by step. Finally, the numerical study results indicate that the proposed scheme has satisfactory performance for vessel navigation risk assessment in the complex waters without any subjective factors.
Lubricating oil film within journal bearing is significantly affected by variations in journal shaft speed, especially sudden ones. Abrupt speed alterations may, in certain maneuverability and emergency situations, threaten the main journal bearing and can lead to the rapid deterioration and most possibly the complete failure of journal bearing and major pollution regarding the marine environment. Consequently, the study at hand introduces experimental test trials and the related outcomes regarding the two speed ranges of 50 and 200 rpm, which represent the worst conditions of ship maneuverability. They have comprised a non-stop rapid speed alteration from 50 rpm anticlockwise to 50 rpm clockwise. Additionally, they have been conducted under two modes of alteration, namely: Crash-stop at both an abrupt rapid as well as gradual speed alterations. The research scope has also been extended to trace the impacts of experimenting at a speed of 200 rpm on the lubricating oil film within journal bearing. Based on the conducted tests, the lubricating oil film within journal bearing was concluded to be severely affected under such extreme operating conditions. It is in those cases that lubricating oil film completely deteriorates and suffers the risk of wear, leading finally to the ultimate failure of journal bearing. Moreover, carrying out crash stop procedures at abrupt speed alterations at both 50 and 200 rpm has proven to be seriously detrimental to main bearing and thus to the lubricating oil film. It is in those serious operating conditions that the lubricating oil pressure extensively deteriorates and hence the hazardous contact is inevitable.
The performance of inertial navigation systems is largely dependent on the stable flow of external measurements and information to guarantee continuous filter updates and bind the inertial solution drift. Platforms in different operational environments may be prevented at some point from receiving external measurements, thus exposing their navigation solution to drift. Over the years, a wide variety of works have been proposed to overcome this shortcoming, by exploiting knowledge of the system current conditions and turning it into an applicable source of information to update the navigation filter. This paper aims to provide an extensive survey of information aided inertial navigation, broadly classified into direct, indirect, and model aiding. Each approach is described by the notable works that implemented its concept, use cases, relevant state updates, and their corresponding measurement models. By matching the appropriate constraint to a given scenario, one will be able to improve the navigation solution accuracy, compensate for the lost information, and uncover certain internal states, that would otherwise remain unobservable.
The Convention on the International Regulations for Preventing Collisions at Sea (COLREGs) comprises rules to prevent collisions at sea and is based on the qualitative rules and ordinary practice of seamen. However, because the criteria of the sailing rule interpretation are different, the problem of misunderstanding occurs owing to the difference in the interpretation between navigators and collision-avoidance algorithm designers. Therefore, this study aims to clarify the collision situations by understanding in the sailing rule interpretation of COLREGs. To identify the understanding of collision situations, we surveyed the navigators’ understanding of collision situations and reviewed the collision-avoidance algorithms used in recent studies. The survey results were analyzed based on head-on and crossing (HC) and crossing and overtaking (OC) situations. Results showed that navigators were unsure about whether the HC situation sailing rule should be applied to incoming vessels from the 008° and whether the overtaking or crossing situation should be applied to coming vessels at 160°. In OC situations, as the angle increased from 130°, it became difficult for navigators to interpret the navigation rules. A notable disparity emerged between the navigators’ understanding and the automated collision-avoidance algorithms. Moreover, it was confirmed that practical navigators exhibited divergent interpretations of these regulations. This study contributes to provide an understanding of COLREGs sailing rules based on the understanding of navigators and researchers.
Trajectory prediction is a critical technology for ensuring ship navigation safety, improving the efficiency of marine traffic control, and efficiently searching for maritime targets. This research proposes an Improved Social-STGCNN (IS-STGCNN) to increase the accuracy of ship trajectory prediction. This technique successfully combines the benefits of the spatio-temporal graph convolutional neural network (STGCNN) for extracting ship trajectory features and the benefits of the time-extrapolated convolutional neural network (TXP-CNN) for generating future ship trajectory using the obtained features. This method proposes a social-sampling strategy based on prior knowledge, i.e., the bumper model of ship safety assessment, to carry out negative sampling and enhances the effectiveness of the IS-STGCNN method in learning the concept of negative examples (such as collisions). The interaction force between ships is estimated in a novel way in the spatio-temporal graph convolutional neural network to improve high-precision feature extraction from ship trajectory. Model predictive control (MPC) is used to correct the output of trajectory prediction in order to fulfill kinematic constraints and assure prediction kinematic feasibility. The experiments are carried out using AIS data, and the findings reveal that IS-STGCNN outperforms the state-of-the-arts.
This volume constitutes revised selected papers from the four workshops collocated with the 19th International Conference on Software Engineering and Formal Methods, SEFM 2021, held virtually during December 6–10, 2021.
The 21 contributed papers presented in this volume were carefully reviewed and selected from a total of 29 submissions. The book also contains 3 invited talks.
SEFM 2021 presents the following four workshops:
CIFMA 2021 - 3rd International Workshop on Cognition: Interdisciplinary Foundations, Models and Applications;
CoSim-CPS 2021 - 5th Workshop on Formal Co-Simulation of Cyber-Physical Systems;
OpenCERT 2021 - 10th International Workshop on Open Community approaches to Education, Research and Technology;
ASYDE 2021 - 3rd International Workshop on Automated and verifiable Software sYstem Development.
Due to the Corona pandemic this event was held virtually.
The development of onboard sensors is bringing us to the next level of ship digitalization. Its ultimate goal is to ensure safe & efficient marine operation by ship intelligence. In particular, during a docking operation, situation awareness based on precise motion prediction is of great importance. Knowledge-based ship models, developed based on the understanding of ship dynamics and simplifications, have played an important role in ship intelligence. However, they do not fully handle highly nonlinear and complex ship dynamics in the docking operation beyond our explicit understanding. On the contrary, data-driven models deal with such non-linearity and complexity in a non-parametric manner, however, the maritime industry does not regard them as reliable and applicable models due to the lack of interpretability and the physics foundation. To alleviate this dilemma, this study proposes a physics-data co-operative ship dynamic model for the docking operation; a knowledge-based ship model serves as a physics foundation with supportive data-driven models compensating a single-step-ahead velocity prediction error made by a physics foundation model. Neural networks trained with onboard sensor data are employed in supportive data-driven models. In a case study, we conducted full-scale docking operations of a 28.9m-length research vessel Gunnerus. The results show that mean prediction error in a position at 30s future is reduced by 34.6% compared to that made solely by a physics foundation model. The present approach will be the first step in the development of high-fidelity and cost-efficient ship dynamic models, thus contributing to ship autonomy in the future.
Aim at the fore and aft asymmetry of unmanned surface vehicle (USV) and the loss of linear velocity, a static output feedback (SOF) H∞ control method is proposed by the sum of squares (SOS) based on two types of extended bounded real lemmas (EBRL) for heading regulation to guarantee the robustness and improve the rapidity. First, an asymmetric nonlinear heading error model with hydrodynamic parameters is established by the consideration of lack of linear velocity. Second, SOF controller with H∞ performance is presented for the asymmetric nonlinear USV model, and it's SOS conditions to solve controller parameters is deduced from EBRL by homogeneous Lyapunov function (HERBL) to maintain the system robustness. Further, the solution of SOF H∞ controller relies on the state feedback gain matrix, EBRL is deduced by quadratic Lyapunov function (QEBRL) to obtain the SOS conditions without the addition of an extended matrix to cut computing cost for the solution of the state feedback gain matrix. Finally, the heading control simulations for USV indicate that, QEBRL method takes less time for SOS conditions to solve the state feedback gain matrix, and SOF H∞ system of HERBL has a superior performance on the transient response and the robustness.
With the rapid developments of artificial intelligence (AI) and Internet of Things (IoT), a large number of autonomous and unmanned surface vessels will appear in the emerging marine transportation cyber-physical system (mTCPS). However, the tremendous growth of moving vessels could lead to unsatisfactory maritime safety and efficacy. To promote smart traffic services in IoT-enabled mTCPS, it is necessary to accurately and robustly predict the locations of moving vessels (i.e., vessel trajectories). The prediction results are beneficial for avoiding vessel collision, detecting abnormal behaviors, and improving maritime surveillance, etc. Motivated by the strong learning capacity of deep learning, this work proposes an intelligent data-driven vessel trajectory prediction framework based on the famous long short term memory (LSTM). To achieve accurate trajectory prediction, the vessel traffic conflict situation modeling, generated using the dynamic positioning data and social force concept, is embedded into the original LSTM network. Furthermore, a mixed loss function is reconstructed to make our trajectory prediction framework more reliable and robust under different experimental conditions. Both quantitative and qualitative experiments on realistic vessel trajectories have been implemented to demonstrate that our method could achieve superior trajectory prediction in terms of accuracy and robustness.
Th e article is devoted to the development of algorithms for predicting the trajectory of maneuvering objects based on nonparametric systems theory. The analysis of uncertainties affecting the modeling of the movement maneuvering water objects is presented. An overview of parametric, nonparametric and combined methods for predicting maneuvering water objects trajectory is given. The problem of high-precision autonomous control of the landing unmanned aerial vehicles on the landing vessel in the conditions of its irregular movement caused by meteorological conditions and active maneuvering is being solved. The method for predicting the trajectory of a vessel’s movement based on solving direct problems of dynamics using nonparametric systems theory is proposed. The advantages of the proposed method are that it’s not affected by model errors , due to the fact that it is based only on a retrospective analysis of several consecutive values of the spatial vessel coordinates. The proposed method differs from similar nonparametric methods in that it does not require statistical calculations, own training, or time-consuming tuning. The method does not imply the solution of identification model parameters, state and control actions problems and can be applied with any unknown linearizable input control actions, including when the model of the vessel’s motion dynamics is not identifiable. The results of numerical modeling for solution the problem of predicting the trajectory of an actively maneuvering small-sized landing vessel using a full nonlinear dynamic model with si x degrees of freedom are presented. The studies carried out confirm the efficiency, adequacy and very fast adjustment of the developed method under conditions of complete parametric and nonparametric uncertainty. The proposed method can be used to predict the trajectory of any vehicle under the condition of linearizability of its model and control signals over the observed time interval.
Ship trajectory from automatic identification system (AIS) provides crucial kinematic information for various maritime traffic participants (ship crew, maritime officials, shipping company, etc.), which greatly benefits the maritime traffic management in real-world. In that manner, ship trajectory smoothing and prediction attracts significant attentions in the maritime traffic community. To address the issue, an ensemble machine learning framework is proposed to remove outliers in the raw AIS data and predict ship trajectory variation tendency. Our method is verified on three typical ship trajectory segments, which is compared against other ship trajectory prediction models. The experimental results suggested that our proposed framework obtained higher prediction accuracy compared to the common trajectory prediction models in terms of typical error measurement indicators. The research findings can help maritime traffic participants obtain high-fidelity ship trajectory data, which supports making more reasonable traffic-controlling decisions.
Abstract We have explored tsunami current signals in maritime Automatic Identification System (AIS) data during the 2011 Tohoku, Japan, tsunami. The AIS data were investigated in detail taking into account ship motion and response to tsunami current. Ship velocity derived from AIS data was divided into two components in terms of the ship heading: heading-normal and heading-parallel directions. The heading-normal velocity showed good agreement with the simulated tsunami current, as mentioned in our former research. Here, we found the heading-normal velocity was contaminated by non-tsunami noises that were mostly related to the ship yaw motion around the pivot point. The noises due to the yaw motion were reasonably corrected in the heading-normal velocity. The corrected heading-normal velocity clearly showed better agreement with the simulated tsunami current. Although the heading-parallel velocity is basically the navigation speed, and is mostly controlled by ships’ captain, we could find the heading-parallel velocity was also drifted by tsunami currents. The corrected heading-normal velocity was still a ship response to the tsunami current. Based on an equation of a ship response to tsunami currents, we numerically estimated tsunami current from the corrected heading-normal velocity. We could find very slight improvements in estimating the tsunami currents, which indicated that this operation possibly worked as a secondary correction. Tsunami currents of tens of centimeters per second are expected to be suitably detected using AIS based on discussion on detection limit.
The aim of this research is to reduce Carbon Dioxide emission through enhanced propeller selection achieved by a more realistic identification of the true propeller operating point. By recognising that the ‘dead-ahead steady speed in flat calm water’ condition is not representative of the true operation of a ship in a seaway, a new paradigm is proposed. By taking into consideration the effects of wind and waves on the ship's true speed through the water and thus the probable load condition of the propeller, throughout the ship's mission, a probable propeller operating condition is identified. Propellers are then selected for both the original condition and the adapted condition, and their performance compared using time-domain mission simulations. The objective of the study is to demonstrate how the alternative propeller selection methodologies proposed, can on average provide greater overall efficiency.
Results from the case studies are encouraging, with a gain of 2.34% in open water propeller efficiency for a 3600 Twenty foot Equivalent Unit container ship, equating to a saving of 3.22% in Carbon Dioxide emissions.
A lot of simulation methods based on Maneuvering Modeling Group (MMG) model for ship maneuvering have been presented. Many simulation methods sometimes harm the adaptability of hydrodynamic force data for the maneuvering simulations since one method may be not applicable to other method in general. To avoid this, basic part of the method should be common. Under such a background, research committee on “standardization of mathematical model for ship maneuvering predictions” was organized by the Japan Society of Naval Architects and Ocean Engineers and proposed a prototype of maneuvering prediction method for ships, called “MMG standard method”. In this article, the MMG standard method is introduced. The MMG standard method is composed of 4 elements; maneuvering simulation model, procedure of the required captive model tests to capture the hydrodynamic force characteristics, analysis method for determining the hydrodynamic force coefficients for maneuvering simulations, and prediction method for maneuvering motions of a ship in fullscale. KVLCC2 tanker is selected as a sample ship and the captive mode test results are presented with a process of the data analysis. Using the hydrodynamic force coefficients presented, maneuvering simulations are carried out for KVLCC2 model and the fullscale ship for validation of the method. The present method can roughly capture the maneuvering motions and is useful for the maneuvering predictions in fullscale.
This paper presents a Recursive Neural Network (RNN) manoeuvring simulation model for surface ships. Inputs to the simulation are the orders of rudder angle and ship’s speed and also the recursive outputs velocities of sway and yaw. This model is used to test the capabilities of artificial neural networks in manoeuvring simulation of ships. Two manoeuvres are simulated: tactical circles and zigzags. The results between both simulations are compared in order to analyse the accuracy of the RNN. The simulations are performed for the Mariner hull. The data generated to train the network are obtained from a manoeuvrability model performing the simulation of different manoeuvring tests. The RNN proved to be a robust and accurate tool for manoeuvring simulation.
This paper focuses on a sliding mode controller for a partial feedback linearization applied unstable ship steering system. The ship steering system is analyzed in this study considering a nonlinear mathematical model that is derived by the second-order linear Nomoto model under unstable maneuverability conditions. The partial feedback linearization approach is proposed to simplify the nonlinear steering system, in which the rudder rate effects are removed. This separates the vessel steering system into two sectors of: linearized dynamics and internal dynamics. The sliding mode controller is applied to linearized dynamics. The stability of zero dynamics in internal dynamics is analyzed, as a part of the feedback linearization process. It is shown that the proposed sliding mode controller in vessel steering is robust against parameter and unstructured uncertainties, and bounded external disturbances. The robustness of the sliding mode controller is analyzed considering the Lyapunov stability theorem. Finally, the proposed controllers are simulated with respect to unstable steering conditions and successful computational results are also reported in this paper.
This study focuses on the formulation of collision detection facilities among vessels that can be integrated into an e-Navigation strategy in maritime transportation. The detection of potential collision situations by relative motions of vessels that consist of state and parameter uncertainties in vessel maneuvering is considered in this study. A two vessel collision situation is presented and an extended Kalman filter is used to estimate the relative bearing and relative course-speed vectors between vessels. The collision detection process consists of cross and dot products among vessel velocity, bearing and heading vectors. Finally, a collision/near-collision situation is simulated and successful results on the detection of a potential collision situation with respect to vessel maneuvering are illustrated in this study.
Complete nonlinear dynamic manoeuvering models of ships, with numerical values, are hard to find in the literature. This paper presents a modeling, identification, and control design where the objective is to manoeuver a ship along desired paths at different velocities. Material from a variety of references have been used to describe the ship model, its difficulties, limitations, and possible simplifications for the purpose of automatic control design. The numerical values of the parameters in the model is identified in towing tests and adaptive manoeuvering experiments for a small ship in a marine control laboratory.
We introduce a new method for synthesizing kinematic relationships for a general class of continuous backbone, or continuum , robots. The resulting kinematics enable real-time task and shape control by relating workspace (Cartesian) coordinates to actuator inputs, such as tendon lengths or pneumatic pressures, via robot shape coordinates. This novel approach, which carefully considers physical manipulator constraints, avoids artifacts of simplifying assumptions associated with previous approaches, such as the need to fit the resulting solutions to the physical robot. It is applicable to a wide class of existing continuum robots and models extension, as well as bending, of individual sections. In addition, this approach produces correct results for orientation, in contrast to some previously published approaches. Results of real-time implementations on two types of spatial multisection continuum manipulators are reported.
The glider coordinated control system (GCCS) uses a detailed glider model for prediction and a simple particle model for planning to steer a fleet of underwater gliders to a set of coordinated trajectories. The GCCS also serves as a simulation testbed for the design and evaluation of multivehicle control laws. In this brief, we describe the GCCS and present experimental results for a virtual deployment in Monterey Bay, CA and a real deployment in Buzzards Bay, MA.
This paper presents the experimental results of the tracking
control of a car-trailer system. The proposed scheme involves three
steps: 1) generate a path off-line using a path space iterative
algorithm; 2) linearize the kinematic model about a trajectory which is
constructed using the path; and 3) apply a time-varying linear quadratic
regulator to track the trajectory. Experiments presented include
parallel parking a car, docking a tractor-trailer vehicle, and parallel
parking a double tractor-trailer vehicle
The estimation of the heave, pitch, roll, sway, and yaw motions of a DD-963 destroyer is studied, using Kalman filtering
techniques, for application in VTOL aircraft landing.
The governing equations are obtained from hydrodynamic considerations in the form of Linear differential equations with frequency
dependent coefficients. In addition, nonminimum phase characteristics
are obtained due to the spatial integration of the water wave forces.
The resulting transfer matrix function is irrational and nonminimum phase. The conditions for a finite-dimensional approximation are considered and the impact of the various parameters is assessed.
A detailed numerical application for a DD-963 destroyer is presented and simulations of the estimations obtained from Kalman filters are discussed.
This paper provides mobility estimation and prediction for a variant of the GSM network that resembles an ad hoc wireless mobile network in which base stations and users are both mobile. We propose using a Robust Extended Kalman Filter (REKF) to derive an estimate of the mobile user's next mobile base station from the user's location, heading, and altitude, to improve connection reliability and bandwidth efficiency of the underlying system. Our analysis demonstrates that our algorithm can successfully track the mobile users with less system complexity, as it requires measurements from only one or two closest mobile base stations. Further, the technique is robust against system uncertainties caused by the inherent deterministic nature of the mobility model. Through simulation, we show the accuracy of our prediction algorithm and the simplicity of its implementation.
The size of ships has increased notably over recent decades. The size of harbours and ports has however not grown in proportion. As a result ship manoeuvring in harbours and ports has become more problematic, and more of an art than a science. The 'pivot point' concept can be useful in analysing slow ship manoeuvring and has therefore been widely adopted by practitioners and training institutions. As a result many practitioners now routinely plan confi ned manoeuvring using the 'pivot point' concept. Traditionally the 'pivot point' concept has been defi ned in a number of contradictory and inaccurate ways leading to confusion and mystifi cation. As a result many practitioners and trainers often rely on intuition to bridge the gap between reality and their fl awed understanding of theory. In this presentation the theoretical aspect of the pivot point is reviewed and correct defi nitions put forward and applied to basic and 'special' ship's manoeuvres.
Model-based predictive control approaches can be successfully applied to the trajectory tracking of wheeled mobile-robot applications if the process nonlinearity is considered, if real-time performance is achieved and if assumptions made in the control-law design are met when applied to a particular process. In this paper, continuous tracking-error model-based predictive control is presented. The controller's optimal actions are obtained from an explicit solution of the optimization criteria, which enables fast real-time applications. Due to its design in continuous time, its usage is not limited to the uniform sampling restrictions of a host computer, as is usually the case in discrete time design. Therefore, better performance is obtained in applications with non-uniform sampling, which is natural in many situations due to imperfect sensors, mismatched clocks, nondeterministic control delays or because of the unknown time of the pre-processing. The controller-design parameters are insensitive to the sampling time period, which contributes to simpler applications and greater robustness of the controller.
This paper focuses on an overview of weather routing and safe ship handling approaches in the future of shipping. Weather routing provides the recommendations on transportation routes prior to and during ship sailing under various navigation constraints under global weather forecasts. Safe ship handling provides the recommendations on vessel position, orientation and speed conditions that should execute at the previously recommended route (with safe navigation conditions) under local weather conditions. Both approaches that complement each other should be implemented simultaneously to achieve optimal and safe ship navigation conditions. That will facilitate towards future navigation tools in integrated bridge systems, where the respective environmental pollution due to the shipping industry should be minimized.
System identification of vessel steering associated with unstructured uncertainties is considered in this paper. The initial model of vessel steering is derived by a modified second-order Nomoto model (i.e., nonlinear vessel steering with stochastic state-parameter conditions). However, that model introduces various difficulties in system identification, due to the presence of a large number of states and parameters and system nonlinearities. Therefore, partial feedback linearization is proposed to simplify the proposed model, where the system-model unstructured uncertainties can also be separated. Furthermore, partial feedback linearization reduces the number of states and parameters and the system nonlinearities, given the resulting
reduced-order state model. Then, the system identification approach is carried out, for both models (i.e., full state model and reduced-order state model), resorting to an extended Kalman filter (EKF). As illustrated in the results, the reduced-order model was able to successfully identify the required states and parameters
when compared to the full state model in vessel steering under persistent excitation maneuvers. Therefore, the proposed approach can be used in a wide range of system identification applications.
An approximate method based on the steady state linearized sway-yaw equations is proposed to estimate the pivot point of a turning ship. The location of the pivot point is directly related to the ratio of the `sway-rudder' and `yaw-rudder' gain coefficients, which can be readily computed from six linear hydrodynamic coefficients. Hence, estimation of the pivot point for a ship at the design stage is made possible with minimum hydrodynamic coefficients information required. Numerical results indicate that based on the proposed method, the estimated pivot point position for a turning ship correlates well with the solution obtained from a full nonlinear differential equations of motion-based analysis, where some forty hydrodynamic coefficients are involved. Existence of similar pattern in the sway speed v and yaw rate r, known as the cancellation effect in a turning maneuver significantly extends the applicability of the proposed steady condition-based approach. Specifically, the ratio v/r that defines the pivot point reaches a steady value long before the ship reaches the steady state phase of the turning.
This study focuses on a collision detection methodology (i.e. collision risk assessment) in an integrated bridge system accounting for vessel state uncertainties in complex ship maneuvers. Modern technology solutions in integrated bridge systems (IBSs) to improve the navigation safety under vessel close encounters are discussed and ship navigation tools that would detect potential collision situations ahead of time are presented. The proposed vessel relative distance based collision risk detection and quantification methodology is simulated and evaluated under a two vessel encounter in a collision or near-collision situation. Furthermore, the relative navigation trajectory, the relative course-speed vector and the relative bearing vector of one vessel with respect to the other vessel are estimated by an extended Kalman filter. Then, the respective course-speed and relative bearing vectors are used to detect and quantify the collision risk between the vessels. Hence, the proposed collision risk detection and quantification methodology can be implemented in modem integrated bridge system (IBSs), where the potential risk among vessels ahead of a collision situation can be detected and that is also an important part of e-navigation.
A kinematic modeling convention for robot manipulators is proposed. The kinematic model has complete and parametrically continuous (CPC) properties. The parametric continuity of the CPC model is achieved by adopting a singularity-free line representation. Completeness is achieved through adding two link parameters which allow arbitrary placement of link coordinate frames. The transformations from the base frame to the world frame and from the tool frame to the last link frame can be modeled with the same convention as that used for internal link transformations. These parameters make the CPC model particularly useful for robot calibration.
Experimental evaluations on autonomous navigation and collision avoidance of ship maneuvers by intelligent guidance are presented in this paper. These ship maneuvers are conducted on an experimental setup that consists of a navigation and control platform and a vessel model, in which the mathematical formulation presented is actually implemented. The mathematical formulation of the experimental setup is presented under three main sections: vessel traffic monitoring and information system, collision avoidance system and vessel control system.
The physical system of the experimental setup is presented under two main sections: vessel model and navigation and control platform. The vessel model consists of a scaled ship that has been used in this study. The navigation and control platform has been used to control the vessel model and that has been further divided under two sections: hardware structure and software architecture. Therefore, the physical system has been used to conduct ship maneuvers in autonomous navigation and collision avoidance experiments.
Finally, several collision avoidance situations with two vessels are considered in this study. The vessel model is considered as the vessel (i.e. own vessel) that makes collision avoidance decisions/actions and the second vessel (i.e. target vessel) that does not take any collision avoidance actions is simulated. Finally, successful experimental results on several collision avoidance situations with two vessels are also presented in this study.
This paper proposes a methodology to overcome
Mamdani type inference failures on a Fuzzy logic based decision
making process applied to collision avoidance in ship navigation.
The Fuzzy inference failures are observed in three distinct
situations: intersected contradictory decision boundaries; an
improper transition region between the inference boundaries of
non-intersected contradictory decisions; contradictory decision
accumulation under multiple obstacle scenarios. The solutions to
overcome the above Fuzzy inference failures and their limitations
are also discussed in this study. The proposed solutions consist of:
insertion of smooth transition regions; determination of the
proper size of the smooth transition regions; use of multi-level
decision/action formulations. Furthermore, this study analyzes a
decision making process for ship navigation, derives input and
output Fuzzy membership functions, formulates an If-Then rule
based Fuzzy inference system, and presents simulation results
that support to recovery from rule inference failures in several
contradictory decision boundary conditions.
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.
This work presents a contribution to solving the problem of identification of ship model parameters using the experimental results from a particular trial test. The innovation of this paper lies in the fact that for this identification purpose it is necessary to know only the turning radius that describes the ship during the performance of the turning test trial. A relatively complex nonlinear model of Norrbin has been chosen as a basis because it represents the ship's dynamics appropriately, as proven through experimental measurements obtained during the course change test. The proposed algorithm of identification of the four ship model parameters is based on an adaptive procedure and the backstepping theory. Another additional coefficient can be determined by an alternative procedure. The knowledge of the true values that characterize the dynamic of a ship is fundamental in the ship steering control that is carried out by autopilots. The simulation results show the suitability of the proposed procedure.
Maneuvering vessel detection and tracking (VDT), incorporated with state estimation and trajectory prediction, are important tasks for vessel navigational systems (VNSs), as well as vessel traffic monitoring and information systems (VTMISs) to improve maritime safety and security in ocean navigation. Although conventional VNSs and VTMISs are equipped with maritime surveillance systems for the same purpose, intelligent capabilities for vessel detection, tracking, state estimation, and navigational trajectory prediction are underdeveloped. Therefore, the integration of intelligent features into VTMISs is proposed in this paper. The first part of this paper is focused on detecting and tracking of a multiple-vessel situation. An artificial neural network (ANN) is proposed as the mechanism for detecting and tracking multiple vessels. In the second part of this paper, vessel state estimation and navigational trajectory prediction of a single-vessel situation are considered. An extended Kalman filter (EKF) is proposed for the estimation of vessel states and further used for the prediction of vessel trajectories. Finally, the proposed VTMIS is simulated, and successful simulation results are presented in this paper.
Ship berthing plans reserve a location for inbound U.S. Navy surface vessels prior to their port entrance, or reassign ships once in port to allow them to complete, in a timely manner, reprovisioning, repair, maintenance, training, and certification tests prior to redeploying for future operational commitments. Each ship requires different services when in port, such as shore power, crane, ordnance, and fuel. Unfortunately, not all services are offered at all piers, and berth shifting is disruptive and expensive: A port operations scheduler strives to reduce unnecessary berth shifts. We present an optimization model for berth planning and demonstrate it for Norfolk Naval Station, which exhibits all the richness of berthing problems the Navy faces. ® 1994 John Wiley & Sons, Inc.
This paper deals with the identification of linear discrete-time multivariable models of an autonomous underwater vehicle (AUV). The observer Kalman filter identification (OKID) method is applied with the main objective of evaluating its effectiveness to the experimental identification of the dynamic behaviour of an AUV. After presenting the mathematical background of the OKID algorithm, the proposed method is first validated on the basis of simulated data of both the linearized and nonlinear yaw dynamics of an AUV. Subsequently, the identification algorithm is applied to a set of experimental data. Results suggest that the method can be an efficient tool for the experimental identification of AUV dynamics.
According to the high-order nonlinearity and parameter uncertainty of the ship steering dynamics, it is difficult to establish the accurate mathematical model by using normal identification methods. To solve this problem, a new kind of support vector regression based on the ant colony algorithm (ACA-SVR) is proposed. This method can select the parameters of SVR automatically without trial and error, thus ensure the accuracy of parameters optimization. Applying this method in the model identification of the ship steering dynamics, and comparing the identification effect with the experimental reference data. The SVR obtained by this method is able to establish the system model effectively, the structure is simple and generalization ability is well.
System identification techniques are applied to determine ship steering dynamics. The parameters of a linear continuous time model are determined using discrete time measurements. The parameters are estimated using the maximum likelihood method. Applications to measurements on a freighter and a tanker are given.
In this paper, a model-predictive trajectory-tracking control applied to a mobile robot is presented. Linearized tracking-error dynamics is used to predict future system behavior and a control law is derived from a quadratic cost function penalizing the system tracking error and the control effort. Experimental results on a real mobile robot are presented and a comparison of the control obtained with that of a time-varying state- feedback controller is given. The proposed controller includes velocity and acceleration constraints to prevent the mobile robot from slipping and a Smith predictor is used to compensate for the vision-system dead-time. Some ideas for future work are also discussed. c 2007 Elsevier B.V. All rights reserved.
Metabolic control analysis is adapted as a method for describing and analysing the control by organs in the body over the fluxes and concentrations of substances carried in the blood. This physiological control analysis can most usefully be applied to substances with fluxes into and out of organs that are uniquely dependent only on their plasma concentrations. The organ flux of a substance is defined as the steady-state net flux of a substance into a particular organ. The organ flux control coefficients quantify the extent to which a particular organ controls the flux of a substance into the same or another particular organ. Organ concentration control coefficients quantify the extent to which an organ controls the steady-state concentration of a substance in the blood. The control coefficients are additive and obey summation, connectivity and branching theorems. Thus the control coefficients can be determined experimentally by measuring the sensitivities (elasticities) of organ fluxes to the plasma concentration of the substance. As an example of the application of these concepts, the control of ketone-body metabolism in vivo is analysed using data from the literature.
We consider the techniques of on-line parameter identification for a simplified model of ship dynamic. In the past two decades, there is an increase in the use of the extended Kalman filter (EKF) algorithm in estimating parameters from noisy data; this algorithm and an improved EKF the second order filter (SOF), will be used in this paper. The parameters, which are generated theoretically from a ship dynamic model with one propeller moving in the forward direction, are identified via computer simulation under differential scenarios.
A sensor failure detection and identification scheme for a closed
loop nonlinear system is described. Detection and identification tasks
are performed by estimating parameters directly related to potential
failures. An extended Kalman filter is used to estimate the
fault-related parameters, while a decision algorithm based on threshold
logic processes the parameter estimates to detect possible failures. For
a realistic evaluation of its performance, the detection scheme has been
implemented on an inverted pendulum controlled by real-time control
software. The failure detection and identification scheme is tested by
applying different types of failures on the sensors of the inverted
pendulum. Experimental results are presented to validate the
effectiveness of the approach
A mobile robot is one of the well-known nonholonomic systems. The
integration of a kinematic controller and a torque controller for the
dynamic model of a nonholonomic mobile robot has been presented (Fierro
and Lewis, 1995). In this paper, an adaptive extension of the controller
is proposed. If an adaptive tracking controller for the kinematic model
with unknown parameters exists, an adaptive tracking controller for the
dynamic model with unknown parameters can be designed by using an
adaptive backstepping approach. A design example for a mobile robot with
two actuated wheels is provided. In this design, a new kinematic
adaptive controller is proposed, then a torque adaptive controller is
derived by using the kinematic controller
A kinematic modeling convention for robot manipulators is
proposed. The kinematic model is named for its completeness and
parametric continuity (CPC) properties. Parametric continuity of the CPC
model is achieved by adopting a singularity-free line representation
consisting of four line parameters. Completeness is achieved through
adding two link parameters to allow arbitrary placement of link
coordinate frames. The transformations from the world frame to the base
frame and from the last link frame to the tool frame can be modeled with
the same modeling convention used for internal link transformations.
Since all the redundant parameters in the CPC model can be
systematically eliminated, a linearized robot error model can be
constructed in which all error parameters are independent and span the
entire geometric error space. The focus is on model construction,
mappings between the CPC model and the Denavit-Hartenberg model, the
study of the model properties, and its application to robot kinematic
calibration
Identification of ship steering dynamics
- K J Astrom
- C G Kalstrom
Astrom, K.J., Kalstrom, C.G., 1976. Identification of ship steering dynamics. Automatica
12, 9-12.
Real time prediction of ship motions and attitude using advanced prediction techniques
- A Khan
- C Bil
- K Marion
- M Crozier
Khan, A., Bil, C., Marion, K., Crozier, M., 2004. Real time prediction of ship motions and
attitude using advanced prediction techniques. In: Proceedings of the 24th
International conference of the Aeronautical Sciences.
Advanced Ship Autopilot System
- M El-Tahan
- H El-Tahan
- K Tuer
- M Rossi
El-Tahan, M., El-tahan, H., Tuer, K., Rossi, M., Advanced Ship Autopilot System. Patent
US 6 611 737 B1.