Underactuated Ships Research Articles

Path tracking of underactuated ships with general form of dynamics

ABSTRACTThis article considers the path tracking problem for underactuated ships with general form of dynamics including uncertainties. By introducing certain two polar coordinate transformations, the ship's tracking kinematics and dynamics can be transformed into certain two-inputs–two-outputs nonlinear strict-feedback form. To avoid possible singularity problem in the backstepping control design, we introduce an asymptotic modification of orientation concept. Presented tracking scheme can guarantee the uniformly ultimately boundedness of closed-loop system in terms of polar coordinates. For the convenience of comparison with previous related works, where all tracking schemes were discussed in the Cartesian frame, we carry out some case studies to investigate the conditions under which the proposed tracking method can guarantee the same stability and convergence properties of tracking errors in the Cartesian frame. Numerical simulation studies are also carried out to demonstrate the effectiveness of presented tracking scheme.

Global stable tracking control of underactuated ships with input saturation

In this paper, tracking control of underactuated ship in the presence of input saturation is addressed. By dividing the tracking error dynamic system into a cascade of two subsystems, the torques in surge and yaw axes are designed separately using the backstepping technique. More specifically, we design the yaw axis torque in such a way that its corresponding subsystem is finite time stable, which makes it to be de-coupled from the second subsystem after a finite time. This enables us to design the torque in the surge axis independently. It is shown that the closed-loop system is stable and the mean-square tracking errors can be made arbitrarily small by choosing design parameters. Simulation results also verify the effectiveness of the proposed scheme.

Global Path-Following Control of Stochastic Underactuated Ships: A Level Curve Approach

A level curve approach is introduced to design global path-following controllers for an underactuated surface ship. The approach is based on the observation: if the position of the ship satisfies the equation of the reference path, then the ship will be on the path. Thus, the controllers are designed based on Lyapunov's direct and backstepping methods to force the position of the ship to satisfy the equation of the path and to move along the path tangentially. The approach does not require computation of the position from the ship to the path. Weak and strong nonlinear Lyapunov functions are introduced in the control design to overcome difficulties caused by underactuation and to guarantee boundedness of the sway velocity. Simulations are included to illustrate the effectiveness of the proposed results.

Adaptive neural path-following control for underactuated ships in fields of marine practice

In this note, one concerns with the problem of robust adaptive path-following control for uncertain underactuated ships in fields of marine practice: waypoints based navigation. A novel “logical virtual ship (LVS)” based steering law is developed to programme the rational reference route, which is to guidance the underactuated ship in the practical engineering. Furthermore, a practical adaptive neural control algorithm is proposed by virtue of the dynamic surface control (DSC) technique, neural networks approximation and polar coordinates scheme. And much effort are made to obtain semi-global uniform ultimate bounded stability for the closed-loop control system, using the Lyapunov synthesis. The advantages of the developed control scheme are that first, it could tackle the practical condition “waypoints based navigation”, which is very meaningful for applying the existed theoretical algorithm in control engineering; second, the developed neural controller is able to capture the vehicle uncertainties without the exact information of hydrodynamic damping structure and the sea disturbances. These characteristics would facilitate the implementation of the algorithm in the marine practice. Two numerical examples have been given to illustrate the performance and effectiveness of the proposed scheme.

Switching‐based asymptotic stabilisation of underactuated ships with non‐diagonal terms in their system matrices

Stabilisation is an issue of great practical importance to the ship industry. This study considers the global asymptotic stability controller for a class of underactuated surface vessel possessing non-diagonal inertia and damping matrices. For the synthesis of controller, the investigated underactuated model is first converted into two cascade connected subsystems using input and state transformations. For these subsystems, it is shown that the stabilisation problem of this study can be reduced to the one of the second subsystem. By combining the method of adding a power integrator and the direct Lyapunov approach, a finite time switching control strategy is developed guaranteeing global asymptotic convergence of the full states to origin. The simulation results testify to the effectiveness of the presented control approach.

Global path-following control of underactuated ships under deterministic and stochastic sea loads

SUMMARYThis paper presents a new method to design global path-following controllers for underactuated ships under both deterministic and stochastic sea loads. The path-following errors are first interpreted in a moving frame attached to the path. These errors are then to be stabilized at the origin by a design of controllers based on backstepping and Lyapunov's direct methods. Weak and strong nonlinear Lyapunov functions are introduced to overcome difficulties caused by underactuation and Hessian terms induced by stochastic differentiation rule, and to guarantee boundedness of the sway velocity. Potential projection functions are introduced to design update laws that provide bounded estimates of the mean values and covariances of the disturbances. Simulations are included to illustrate the effectiveness of the proposed approach.

Further results on global stabilisation and tracking control for underactuated surface vessels with non-diagonal inertia and damping matrices

This paper studies the global uniform stabilisation and exponential tracking problems for an underactuated ship with non-diagonal inertia and damping matrices. For the synthesis of the controller, first, the underactuated ship in question is converted into two cascade connected subsystems by using state and input transformations. Two constructive backstepping design schemes are developed, respectively, to get around the stabilisation burden and tracking burden. Along the way of proving stability analysis, it is shown that the designed control strategies can guarantee the global uniform asymptotic convergence of the state to the origin and global exponential convergence to the desired reference trajectory. Simulation results are provided to demonstrate the effectiveness of the proposed control methodologies.

A novel DVS guidance principle and robust adaptive path-following control for underactuated ships using low frequency gain-learning

Around the waypoint-based path-following control for marine ships, a novel dynamic virtual ship (DVS) guidance principle is developed to implement the assumption “the reference path is generated using a virtual ship”, which is critical for applying the current theoretical studies in practice. Taking two steerable variables as control inputs, the robust adaptive scheme is proposed by virtue of the robust neural damping and dynamic surface control (DSC) techniques. The derived controller is with the advantages of concise structure and being easy-to-implement for its burdensome superiority. Furthermore, the low frequency learning method improves the applicability of the algorithm. Finally, the comparison experiments with the line-of-sight (LOS) based fuzzy scheme are presented to demonstrate the effectiveness of our results.

Formation tracking and attitude synchronization control of underactuated ships along closed orbits

SummaryThis article considers the problem of directing a family of underactuated ships to formation tracking a set of closed orbits and achieve attitude synchronization. It shows that our previous concentric compression design can be extended to deal with a general kind of non‐convex, closed curves and the coordinated motion of underactuated ships. The condition of nonzero total linear speed of each ship is ensured by a potential function. Under the bidirectional communication topology, asymptotical stabilization is proved with the help of the invariance‐like theorem and the extension of Barbalat's lemma. Theoretical results are proved by the numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.

Concise Robust Adaptive Path-Following Control of Underactuated Ships Using DSC and MLP

<?Pub Dtl=""?> In this paper, the authors study the problem of robust adaptive path-following control for underactuated ships with model uncertainties and nonzero-mean time-varying disturbance. A concise adaptive neural network (NN)-based control scheme is proposed using backstepping, feedforward approximations, dynamic surface control, and minimal learning parameter techniques. In addition, to tackle the strong couplings among state variables (including the underactuated state variable) and underactuated characteristics, much effort is put into guaranteeing semiglobal uniform ultimate boundedness of the ship motion control system. The outstanding advantage of this scheme is that the control law has a concise form and is easy to implement in practice due to a smaller computational burden, with only two online parameters being tuned to tackle the uncertainties. The simulation results demonstrate the effectiveness of the proposed algorithm, especially including the experiment in the simulated marine environment.

Global Tracking Controller for Underactuated Ship via Switching Design

This paper studies the complete state tracking control of an underactuated ship with only two controls, namely, surge force and yaw moment. A novel finite-time switching controller is developed guaranteeing that the ship can track a reference trajectory generated by a virtual ship. The solution is based on the inherent cascaded interconnected structure of the ship dynamics. As opposed to the previous works, the assumptions used in this work are more relaxed in the sense that the reference surge and yaw velocities are allowed to be zero at the same time. Simulation results are given to serve the purpose of demonstrating and validating the proposed tracking methodology.

Straight-Line Trajectory Tracking Control for Sampled-Data Underactuated Ships

Straight-line trajectory tracking control of sampled-data underactuated ships with both state and output feedback controllers is considered and analyzed by resorting to a nonlinear sampled-data control theory. State feedback controllers and reduced-order observers are designed on the basis of the Euler approximate models. Then they are combined to obtain output feedback controllers that semiglobally practically uniformly asymptotically stabilize the tracking error dynamics. Both simulation and experimental results are given to show the efficiency of the designed controllers.

Global tracking for underactuated ships with bounded feedback controllers

In this paper, we present a global state feedback tracking controller for underactuated surface marine vessels. This controller is based on saturated control inputs and, under an assumption on the reference trajectory, the closed-loop system is globally asymptotically stable. It has been designed using a 3 degrees of freedom benchmark vessel model used in marine engineering. The main feature of our controller is the boundedness of the control inputs, which is an essential consideration in real life. In absence of velocity measurements, the controller works and remains stable with observers and can be used as an output feedback controller. Simulation results demonstrate the effectiveness of this method.

Global Asymptotic Trajectory Tracking and Point Stabilization of Asymmetric Underactuated Ships with Non-Diagonal Inertia/Damping Matrices

In this work, we investigate the trajectory tracking and point stabilization problems of asymmetric underactuated surface ships with non-diagonal inertia and damping matrices. By combining the novel state and input transformations, the direct Lyapunov approach, and the nonlinear time-varying tools, the trajectory tracking controller is derived, guaranteeing global κ-exponential convergence of state trajectory to the reference one satisfying mild persistent exciting conditions. By properly designing the reference trajectory, the proposed tracking scheme is also generalized to achieve global uniform asymptotic point stabilization. Simulation examples are given to illustrate the effectiveness of the proposed control schemes.

Adaptive robust sliding mode control for ship straight-line tracking in random waves

Since complex controllers do not suit for application, we design a simple controller with robustness in changeable sea state. The characteristics of ship motion are large inertia, strong nonlinearity and large time delay. This paper employs adaptive sliding mode technique. We focus on a class of underactuated ship systems with parametric uncertainties and wave effects. Random wave effects are seldom considered in former studies. Various simulations validate the adaptive characteristics and robustness of the proposed controller. The closed-loop system is stable and tracking error can be arbitrarily small by Lyapunov approach.

Strait-line Tracking Control of Under-actuated Ship

High performance path following control, especially straight line path tracking, is one of the most difficult problems in autonomous control of under-actuated ship. In this paper, we propose a straight line path following control algorithm by combining adaptive yaw angle feedback, back-stepping and acceleration feedback technique together. The most absorbing advantage of the proposed controller is that it not only reserves the good performance of back-stepping controller and bring much faster convergent rate, but also eliminates the disturbance impacts, which is very important in real applications. The simulation results with respect to a training ship model have shown the feasibility and validity of the proposed method.

Formation control of underactuated ships with elliptical shape approximation and limited communication ranges

Based on the recent theoretical development for formation control of multiple fully actuated agents with an elliptical shape in Do (2012), this paper develops distributed controllers that force a group of N underactuated ships with limited communication ranges to perform a desired formation, and guarantee no collisions between any ships in the group. The ships are first fitted to elliptical disks for solving collision avoidance. A coordinate transformation is then proposed to introduce an additional control input, which overcomes difficulties caused by underactuation and off-diagonal terms in the system matrices. The control design relies on potential functions with the separation condition between elliptical disks and the smooth or p-times differentiable step functions embedded in.

Adaptive Fuzzy Control for Path Tracking of Underactuated Ships Based on Dynamic Equilibrium State Theory

This paper presents an adaptive fuzzy backstepping control method that incorporates the dynamic equilibrium state (DES) theory to carry out path tracking for underactuated ships in presence of parameter variations and external disturbances induced by wind, wave and current. First, the optimal DES reference trajectories are designed for the sway displacement and the yaw angle. Then, by combining the DES theory with backstepping technology and using fuzzy logic systems to approximate unknown nonlinear functions in the system, a robust adaptive fuzzy controller is designed to track the prescribed trajectories. Theoretical analysis and simulation results show that the proposed method performs path tracking of underactuated ships with high precision, eliminates the influence of the uncertainties, and guarantees global stability and robustness of the system.

Global Tracking Control of Underactuated Ships With Input and Velocity Constraints Using Dynamic Surface Control Method

This paper proposes a global tracking control method for underactuated ships with input and velocity constraints using the dynamic surface control (DSC) method, where the control structure is formed in a modular way that cascaded kinematic and dynamic linearizations can be achieved similarly as in the backstepping method. First, the first step linearization of the kinematics determines the pseudo (or auxiliary) surge velocity and yaw angle, which are used as the commands for the second-step linearization. Then, in the second-step linearization of dynamics, the actual torque inputs are designed to make the actual surge velocity and yaw angle follow these pseudo commands to achieve the position and yaw angle tracking. By employing the dynamic surface control method in the design of each kinematic and dynamic linearization law, we can obtain a control structure that is much simpler than the previous backstepping-based controllers such that it is beneficial from the practical application viewpoint. In addition, it is possible to track general reference trajectories, i.e., the reference yaw velocity need not be persistently exciting and there is no restriction on the initial yaw tracking error. In particular, global tracking control is achieved even in the presence of input and velocity constraints, unlike the DSC method which introduces the several filters in the backstepping design procedure to avoid the model differentiation and make it easier to be implemented and usually has semiglobal tracking performance. Finally, the stability analysis and numerical simulations are performed to confirm the effectiveness of the proposed scheme.

Formation control of underactuated ships with elliptical shape approximation and limited communication ranges

A method is presented to design distributed controllers that force a group of N underactuated ships with limited communication ranges to perform a desired formation, and guarantee no collisions between any ships in the group. The ships are first fitted to elliptical disks for solving collision avoidance. A separation condition for elliptical disks is then derived. Smooth or p -times differentiable step functions are next introduced to deal with the ships’ limited communication ranges. A coordinate transformation is then proposed to introduce an additional control input, which overcomes difficulties caused by underactuation and off-diagonal terms in the system matrices. The control design is based on novel potential functions with the separation condition between elliptical disks and the smooth or p -times differentiable step functions embedded in.