Underactuated Ships Research Articles

Optimal Path Following Controller Design Based on Linear Quadratic Regulator for Underactuated Ships in Varying Wave and Wind Conditions

Optimal Path Following Controller Design Based on Linear Quadratic Regulator for Underactuated Ships in Varying Wave and Wind Conditions

Improved Stanley guidance law–based adaptive path-following control of underactuated ship with state-constrained and time-varying drift angle

To improve the following performance in large curve path and time-varying drift angle, a reduced-order extended state observer is added to the Improved Stanley Guidance Law (EISGL). Combining with the dynamic surface control (DSC), an adaptive auxiliary system is simultaneously built to compensate for the effect of the state constraints on the system. A barrier Lyapunov function combined with a prescribed performance function is designed to constrain the heading angle error of path following. Adaptive laws are also designed to approximate errors, estimating perturbation in poor sea condition. Lyapunov stability analysis shows that all signals are semi-global coherent and eventually bounded. In conclusion, the numerical comparison simulation experiments verify that the scheme has a strong anti-jamming capability and achieves good path following in large curve path.

Adaptive output-feedback event-triggered formation control for underactuated ships with obstacle avoidance mechanism

This paper focuses on the adaptive output-feedback event-triggered control strategy for the formation tracking and obstacle avoidance activity of unmanned surface vessels (USVs) with unmeasurable velocity, constrained communication and actuator fault. By using the neural networks and minimal learning parameter, a novel output-feedback event-triggered controller is deigned, effectively alleviates constraints related to continuous feedback signal acquisition in dynamic systems. Subsequently, by incorporating an adjustable threshold, the event-triggered condition is established, thus facilitating updates to the state and adaptive law solely within the discrete-time domain. Then, only two aperiodic adaptive laws are derived to mitigate actuator faults and system uncertainties. As for the path planning, benefiting from the artificial potential field method, a novel obstacle avoidance mechanism is developed for obstacle avoidance and waypoint-based path navigation. Considerable effort has been made to guarantee the semi-globally uniformly ultimately bounded stability. Finally, two numerical simulations are illustrated to demonstrate the remarkable performance of the proposed control strategy.

Cooperative Maritime Search of Multi-Ship Based on Improved Robust Line-of-Sight Guidance

In this paper, an improved robust line-of-sight (RLOS) guidance-based fuzzy sliding mode controller is presented to control underactuated ships to conduct the cooperative maritime search operation under the presented improved creeping line search method. First, considering that the ship cannot perform turning with corners, an improved creeping line search method is presented by integrating the Bezier method into the traditional creeping line search method to smooth the transition points with corners and employing the cubic spline interpolation method to generate continuous reference paths. Second, an improved RLOS guidance method is presented for the first time by exploring the idea of robust adaptive control to mitigate the chattering effect of the RLOS guidance. Third, the fuzzy logic system with approximate ability is integrated into the design of sliding mode controller to handle unknown nonlinear model dynamics and environmental disturbances. Finally, an improved RLOS guidance-based fuzzy sliding mode controller is presented. The closed-loop stability is guaranteed by the Lyapunov theorem. Comparative simulations are conducted to illustrate the advantages and verify the effectiveness of the presented method.

Integrated trajectory planning into automatic berthing control of underactuated ship based on fuzzy-backstepping method

The trajectory planning and automatic berthing control are traditionally studied separately; however, the planned trajectory is indeed required to be the reference trajectory for the automatic berthing control system. In this paper, a novel trajectory planning strategy is presented and integrated into the automatic berthing control of underactuated ship. First, a novel trajectory planning strategy, including the Bezier curve planning, the least square fitting, and the speed assignment mechanism, is presented for the first time herein to provide the differentiable reference trajectory for the automatic berthing control system based on backstepping method. Second, a novel coordinate transformation between the Earth-fixed frame and the berth-fixed frame is established for the first time herein for the arbitrary berth position. Third, the fuzzy logic system is incorporated into backstepping controller to alleviate the influence of the model uncertainty, which is probably introduced by the shallow water and bank effects. The closed-loop signals are proved to be stable based on Lyapunov theorem. Two simulations are conducted to illustrate the effectiveness and advantages of the presented fuzzy-backstepping-based automatic berthing control methodology.

Event-Triggered Adaptive Neural Network Trajectory Tracking Control For Underactuated Ships Under Uncertain Disturbance

Abstract An adaptive neural network (NN) event-triggered trajectory tracking control scheme based on finite time convergence is proposed to address the problem of trajectory tracking control of underdriven surface ships. In this scheme, both NNs and minimum learning parameters (MLPS) are applied. The internal and external uncertainties are approximated by NNs. To reduce the computational complexity, MLPs are used in the proposed controller. An event-triggered technique is then incorporated into the control design to synthesise an adaptive NN-based event-triggered controller with finite-time convergence. Lyapunov theory is applied to prove that all signals are bounded in the tracking system of underactuated vessels, and to show that Zeno behavior can be avoided. The validity of this control scheme is determined based on simulation results, and comparisons with some alternative schemes are presented.

Global fast terminal sliding mode control for path following of ultra large underactuated ship based on predictive LOS guidance

This study proposes a new line-of-sight guidance method based on position prediction that constructs the total path deviation by predicting the future time position of ships. This method can solve the problem of overshoot, which is prone to occur in the path following process of ultra large underactuated ships. A global fast terminal sliding mode method is used to design controllers that allow path deviations to converge in a finite time. To solve the problems of unknown velocity, disturbances, and sideslip angle during navigation, a high-order nonlinear observer is designed to estimate the system states and obtain the velocity values and external disturbances. The sideslip angle of the ship during navigation is obtained by estimating its velocity. Therefore, the problem of an unknown sideslip angle is solved, and the effectiveness of the proposed algorithm is verified through simulation experiments.

Path following of under-actuated ships based on backstepping and predictive control method.

To deal with the sideslip angle caused by the current disturbances or transverse motion for path following of under-actuated ships, a nonlinear observer established by an exponential function is introduced in the backstepping approach which converts the path following into heading control. Then, the model predictive control (MPC) method is used as a heading controller, addressing the rudder optimization. A linear extended state observer technology was exploited to estimate yaw rate, external disturbances, and internal uncertainties, which could avoid measuring the high-order state used in the MPC controller and promote the accuracy of the MPC internal model. Moreover, an inverse tangent function is applied to develop a new method for switching the reference heading angle to reduce rudder amplitude when the ship is choosing the next waypoint. Finally, the validity and reliability of the design method were verified through comparative computer simulation experiments.

Event-triggered adaptive finite time trajectory tracking control for Underactuated Vessel considering unknown time-varying disturbances

Abstract This paper aims to solve the finite-time trajectory tracking problem of underactuated surface ships under the influence of dynamic uncertainty, unknown external time-varying interference and limited communication resources, an event-triggered robust adaptive finite-time trajectory tracking control method for underactuated ships is designed by combing the existing trajectory tracking control methods and engineering needs in actual navigation. It can obviously improve the tracking accuracy of the ship, and complete the tracking task safely and efficiently. This scheme transforms the composite uncertain vector synthesized by uncertain parameters and external disturbances into a linear parameterized form. Next, considering the limitation of communication resources, a relative threshold event triggering mechanism is introduced to further extend the triggering time interval on the basis of the fixed threshold triggering scheme. Then, an event-triggered robust adaptive finite-time trajectory tracking control scheme is designed for underactuated ships, and a rigorous stability proof is provided for the finite-time trajectory tracking control scheme designed above through Lyapunov stability theory. Simulation experiment is carried out in MATLAB and the results show that the finite-time trajectory tracking control scheme proposed in this paper can effectively solve the problems of dynamic uncertainty, unknown time-varying interference from the outside world, and limitation of communication resources. This paper can provide theoretical support for the autonomous navigation of intelligent ships.

Nonlinear control of decarbonization path following underactuated ships

Decarbonizing shipping is one of the most critical challenges in controlling global carbon emissions. Therefore, from the point of view of general shipping control, it is essential to control carbon dioxide emissions from underactuated ships, the primary mode of transport in the shipping industry. In this paper, we proposed an extended state observer to deal with the uncertainty of the ship model and the estimation of external disturbances. Then, we developed an improved " dynamic virtual ship” guidance algorithm and an energy-saving ship path following controller by combining nonlinear feedback and adaptive backstepping. Finally, it is found that the proposed nonlinear control algorithms result in improved path following control where the average ship output rudder angle is reduced by 17%, the average steering power is reduced by 10%, the Energy Efficiency Design Index (EEDI) of the ship is reduced by 2%, the average ship speed is increased by 0.3 knots, and the carbon dioxide emissions during general shipping are reduced by 32.45%. We anticipate that the proposed algorithm will play an essential role in the process of decarbonization in shipping.

RLOS-based path following with event-triggered roll motion control for underactuated ship using rudder

Path following with event-triggered roll motion control of underactuated ship is presented herein. First, the robust line-of-sight (RLOS) is presented for the first time herein by exploring the idea of sliding mode. Second, the model predictive control, which is known as the optimization control method for multi-objective, is introduced to achieve path following with event-triggered roll stabilization. Third, instead of traditional time-triggered mechanism, the objective of roll motion control in the presented methodology is activated based on event-triggered mechanism, i.e., the roll motion control is only activated when the roll motion exceeds the triggering condition; consequently, the rudder abrasion is correspondingly mitigated. Numerical simulations are conducted to illustrate the advantages of path following with event-triggered roll motion control of underactuated ship by rudder.

Event-Triggered Asymptotic Tracking Control of Underactuated Ships With Prescribed Performance

Adapting to the navigational high-precision tracking tasks, this paper develops an event-triggered adaptive neural asymptotic tracking control framework for underactuated ships. The prescribed performance control (PPC) technique is employed to address spatial constraints in navigation, where the positional tracking errors are transformed via the transformation functions. By using the approximation of radial basis function neural networks (RBF NNs) in the form of minimum learning parameters (MLPs), the uncertainties coming from the unknown model dynamics, the environmental disturbances and the derivation of virtual control laws are offset all together, and a succinct computation is guaranteed. Assisted by the property of neural basis function, the “algebraic loop” problem in the backstepping design is released. To achieve the asymptotic tracking performance, the hyperbolic tangent functions are incorporated into the control laws, which are characterized by the integral-bounded terms. The event-triggered control (ETC) is designed in the controller-to-actuator (CA) channel. Two separate triggering conditions are constructed for the surge and the yaw motions respectively, which are characterized by the compound thresholds composed of a variable and a constant. The “Zeno” behaviors can thereby be avoided. The proposed scheme has three notable characteristics: 1) the computational complexity is reduced by using the MLP technique with lumped uncertainties; 2) the high-precision tracking performance can be achieved through the asymptotic tracking control; 3) the practical problems of spatial constraints and communication burdens can be solved by fabricating a uniform control framework including PPC and ETC. With the aid of direct Lyapunov candidates and the Barbalat’s lemma, the asymptotic convergence of all the tracking errors is proved. Finally, a numerical experiment corroborates the feasibility of the proposed scheme.

Data-driven model predictive control for ships with Gaussian process

Nonlinear and underactuated ship maneuvering model is the main difficulty in ship motion control, and model predictive control (MPC) offers a great choice to handle this problem. However, most of the research on MPC adopts traditional parametric models based on physical prior knowledge, which limits its control performance and further application for various USVs. Recent success of machine learning has aroused a growing interest in data-driven and learning-based controller. Here, we present a data-driven ship heading controller, which combines the Gaussian process (GP) and MPC. The proposed method can identify the ship maneuvering model without any prior knowledge, and realize the heading control and waypoints following based on the learned nonparametric model. The similarity-based sparse GP algorithm is presented to reduce the computational complexity. Evaluated by both heading control and waypoints following in a real container ship data-driven simulation under environmental disturbances, the developed scheme is a powerful data-driven controller with good generalization ability and robustness to unknown disturbance.

A Novel Guidance Algorithm for Underactuated Ship Path-Following Control Based on Marine Practice

A Novel Guidance Algorithm for Underactuated Ship Path-Following Control Based on Marine Practice

Stabilization of Asymmetric Underactuated Ships With Full-State Constraints: From Underactuated to Nonholonomic Configuration

Dear Editor, This letter addresses the stabilization control of an asymmetric underactuated surface ship with full-state constraints. To simplify the design of controller, the original ship model is transformed into a nonlinear cascade system with a minimum phase. Then, the stabilization of the cascade system is further processed into an equivalent stabilization of a reduced-order nonholonomic-like system. A discontinuous stabilization control method is proposed through a combination of state-scaling and state-dependent function transformations, nonlin-ear filters, and switching technologies. Stability analysis demon-strates that under the newly designed stabilization controller, the closed-loop system states are bounded and the desired state constraints are not violated.

Adaptive neural network asymptotic path-following control of underactuated ships with stochastic sea loads

This paper investigates the high-precision path following of underactuated ships suffering from stochastic sea loads, where a novel adaptive neural network asymptotic control framework is fabricated. Based on the nonlinear 3-degree-of-freedom (3-DOF) motion model of the underactuated ship, the stochastic ship motion model is established by involving both unknown deterministic and stochastic disturbances, which is chosen as the control objective. To transform path following to tracking control, a novel virtual ship guidance approach is fabricated with generating smooth reference signals. Through the control scheme, the radial-basis-function neural networks (RBF NNs) are employed to approximate the total marine uncertainties. By introducing integral-bounded functions to control laws and adaptive laws, the asymptotic convergence of positional tracking errors is guaranteed with the aid of adaptive backstepping control. To ensure the computational simplicity, the adaptive laws are fabricated with the minimum learning parameters (MLPs). Via the important inequality of the neural basis function, the “algebraic loop” problem is successfully solved, such that the control logicality is guaranteed. Finally, the numerical experiments validate the high-precision tracking performance of the proposed scheme.

Guidance-Based Path Following of an Underactuated Ship Based on Event-Triggered Sliding Mode Control

In this paper, the path following of an underactuated ship as a fundamental application for autonomous sailing in seaways is studied. First, the guidance system based on the line of sight (LOS) method is established to handle underactuated dynamics of ship motion. Then, path following control is converted to heading control with fewer dimensions. Second, the extended state observer (ESO) is used to observe unknown dynamics of ship motion. Third, the sliding mode control method is highly robust to external disturbance and is employed to design the controller. Fourth, the event-triggered mechanism (ETM) is included to reduce the trigger time. All the closed-loop signals are shown to be bounded by the Lyapunov theory. Simulations are carried out to verify the effectiveness of the proposed method.

Data-driven model predictive control of underactuated ships with unknown dynamics in confined waterways

AbstractInland waterway transportation is one of the most important means to transport cargo in rivers and canals. To facilitate autonomous navigation for ships in inland waterways, this paper proposes a data-driven approach for predictions and control of underactuated ships with unknown dynamics, which integrates model predictive control (MPC) with an iterative learning control (ILC) scheme. In each iteration, kernel-based linear regressors are used to identify the relations between the evolution of ship states and control inputs based on the stored data from previous iterations and the collected data during operation, so as to build the system prediction model. The data are dynamically used to fix the prediction model over iterations, as well as to improve the controller performance until it converges. The proposed approach does not require prior knowledge regarding the hydrodynamic coefficients and ship parameters, but learns from the data instead. In addition, it exploits the advantages of MPC in handling constraints with minimised overall cost. Simulation results show that the controller could start from a nominal, linear data-driven ship model and then learn to reduce the path-following errors based on the data obtained over iterations.

Autonomous piloting and berthing based on Long Short Time Memory neural networks and nonlinear model predictive control algorithm

Autonomous berthing of large underactuated ships is one of challenge tasks in the development of intelligent and autonomous ships, especially under hybrid disturbances of wind and currents, both trajectory prediction and tracking control are difficult issues due to the complexity of the ship motion. In this paper, a low-speed underactuated ship-handling and motion model which fully consider the disturbances of wind and currents is proposed to support the trajectory prediction and tracking control. In addition, a novel trajectory prediction model base on Long Short Time Memory (LSTM) neural network is presented by exploiting the time series features of the berthing trajectories, in which the proposed accurate ship motion model is used to create teaching data that help improve the data consistent and the accuracy of the trajectory prediction. Furthermore, nonlinear Model Predictive Control (MPC) model based on accurate ship motion model is employed to control the trajectory tracking, which efficiently improves the capability of the anti-disturbance. Experiments were designed to validate the reliability and accuracy of the proposed approach under various disturbances of wind and currents. Experimental results have demonstrated that the proposed approach has outstanding performance and effectiveness under the hybrid disturbances of wind and currents.

Distributed formation control of underactuated ships with connectivity preservation and collision avoidance

Formation control of ship has distinct advantages in ocean exploration, environment monitoring, patrol surveillance, and maritime rescue with efficiency and flexibility. In this paper, the distributed formation control of underactuated ships, the connectivity preservation, the collision avoidance among formation members, and the collision avoidance with external obstacles are achieved for the first time under the consideration of control input constraints. Taking advantage of nonlinear model predictive control (NMPC), the problem of distributed formation control of underactuated ships with connectivity preservation and collision avoidance is formulated as the quadratic optimization problem with input and output constraints. The periodic event-triggered mechanism is included to solve the optimization problem efficiently. The Floyd method is employed to obtain the optimal communication topology. Multiple studies are conducted to illustrate the advantages of presented methodology.