NONLINEAR ADAPTIVE HEADING CONTROL FOR AN UNDERACTUATED SURFACE VESSEL WITH CONSTRAINED INPUT AND SIDESLIP ANGLE COMPENSATION

In this paper, a nonlinear adaptive heading controller is developed for an underactuated surface vessel with constrained input and sideslip angle compensation. The controller design is accomplished in a framework of backstepping technique. First, to amend the irrationality of the traditional definition of the desired heading, the desired heading is compensated by the sideslip angle. Considering the actuator physical constrain, a hyperbolic tangent function and a Nussbaum function are introduced to handle the nonlinear part of control input. The error and the disturbance are estimated and compensated by an adaptive control law. In addition, to avoid the complicated calculation of time derivatives of the virtual control, the command filter is introduced to integrate with the control law. It is analysed by the Lyapunov theory that the closed loop system is guaranteed to be uniformly ultimately bounded stability. Finally, the simulation studies illustrate the effectiveness of the proposed control method

Robust trajectory tracking control for unmanned surface vessels under motion constraints and environmental disturbances

To achieve a fully autonomous navigation for unmanned surface vessels (USVs), a robust control capability is essential. The control of USVs in complex maritime environments is rather challenging as numerous system uncertainties and environmental influences affect the control performance. This paper therefore investigates the trajectory tracking control problem for USVs with motion constraints and environmental disturbances. Two different controllers are proposed to achieve the task. The first approach is mainly based on the backstepping technique augmented by a virtual system to compensate for the disturbance and an auxiliary system to bound the input in the saturation limit. The second control scheme is mainly based on the normalisation technique, with which the bound of the input can be limited in the constraints by tuning the control parameters. The stability of the two control schemes is demonstrated by the Lyapunov theory. Finally, simulations are conducted to verify the effectiveness of the proposed controllers. The introduced solutions enable USVs to follow complex trajectories in an adverse environment with varying ocean currents

Upravljanje pozicijom električki pokretanog brzog površinskog vozila korištenjem unaprijedne projekcije izlazne povratne veze

Robust tracking is an issue of vital practical importance to the ship This paper addresses the design of a trajectory tracking controller for fast underactuated ships in the presence of model uncertainties without velocity measurements in the yaw and surge directions. An observer-based trajectory tracking controller is proposed for the fast underactuated ship model. Then, the dynamic surface control approach is effectively exploited to propose a tracking controller considering the actuator dynamics. Adaptive robust techniques are also adopted to cope with the parametric and non-parametric uncertainties in the fast underactuated ship model. A Lyapunov-based stability analysis is utilised to guarantee that tracking and state estimation errors are uniformly ultimately bounded. Simulation results are presented to illustrate the feasibility and efficiency of the proposed controller.Robusno praćenje je pitanje od vitalnog praktičnog značaja za brod. Ovaj se rad bavi projektiranjem regulatora za praćenje trajektorije za brze podaktuirane brodove s modelima nesigurnosti bez mjerenja brzine u smjerovima zaošijanja i uzdužnog napredovanja. Regulator za praćenje putanje zasnovan na observeru predložen je za brz podaktuiran model broda. Upravljanje površinskom dinamikom je učinkovito iskorišteno kako bi se predložio regulatora za praćenje trajektorije s obzirom na dinamiku aktuatora. Također su primjenjene adaptivne robusne tehnike kako bi se nosile sa parametarskim i neparametarskim nesigurnostima u modelu brzog podaktuiranoga broda. Analiza stabilnosti temeljena na Lyapunovu se koristi kako bi se zajamčilo da se pogreške praćenja i estimacije stanja adaptivne robusne tehnike također usvajaju kako bi se nosile s parametarskim i neparametarskim nesigurnostima u brzom neaktivnom brodskom modelu. Analiza stabilnosti temeljena na Lyapunovu se koristi kako bi se zajamčilo da su pogreške praćenja i procjene stanja jednoliko konačno ograničene. Prikazani su simulacijski rezultati koji ilustriraju izvedivost i učinkovitost predloženog regulatora

Adaptive neural network control of underactuated surface vessels with guaranteed transient performance: Theory and experimental results

In this paper, an adaptive trajectory trackingcontrol algorithm for underactuated unmanned surfacevessels (USVs) with guaranteed transient performance isproposed. To meet the realistic dynamical model of USVs,we consider that the mass and damping matrices are notdiagonal and the input saturation problem. Neural Networks(NNs) are employed to approximate the unknown externaldisturbances and uncertain hydrodynamics of USVs. Moreover,both full state feedback control and output feedbackcontrol are presented, and the unmeasurable velocities ofthe output feedback controller are estimated via a highgainobserver. Unlike the conventional control methods,we employ the error transformation function to guaranteethe transient tracking performance. Both simulation andexperimental results are carried out to validate the superiorperformance via comparing with traditional potential integral(PI) control approaches

Robust optimal control of a nonlinear surface vessel model with parametric uncertainties

This paper presents a fast alternative optimization method for developing a reliable optimal controller that can handle system model parameter uncertainties. The source of uncertainty in this study is identified as hydrodynamic coefficients, which are prone to errors due to the challenges involved in obtaining accurate values. The proposed optimization method utilizes a complex nonlinear ship model provided by Maneuver Modelling Group (MMG) as the reference for the ship motion model. The optimization process is divided into two stages: a blind search followed by bisection optimization, to obtain a robust optimal controller. To demonstrate the effectiveness of the proposed approach, system response analysis and practical tests were performed on Step, M-Turn, and Doublet maneuvers. The results show that the controller parameters obtained from the proposed optimization method are capable of achieving high success rates in controlling a system with uncertain parameters

An environmental disturbance observer framework for autonomous surface vessels

This paper proposes a robust disturbance observer framework for maritime autonomous surface vessels considering model and measurement uncertainties. The core contribution lies in a nonlinear disturbance observer, reconstructing the forces on a vessel impacted by the environment. For this purpose, mappings are found leading to synchronized global exponentially stable error dynamics. With the stability theory of Lyapunov, it is proven that the error converges exponentially into a ball, even if the disturbances are highly dynamic. Since measurements are affected by noise and physical models can be erroneous, an unscented Kalman filter (UKF) is used to generate more reliable state estimations. In addition, a noise estimator is introduced, which approximates the noise strength. Depending on the severity of the measurement noise, the observed disturbances are filtered through a cascaded structure consisting of a weighted moving average (WMA) filter, a UKF, and the proposed disturbance observer. To investigate the capability of this observer framework, the environmental disturbances are simulated dynamically under consideration of different model and measurement uncertainties. It can be seen that the observer framework can approximate dynamical forces on a vessel impacted by the environment despite using a low measurement sampling rate, an erroneous model, and noisy measurements.publishedVersio

A path planning control for a vessel dynamic positioning system based on robust adaptive fuzzy strategy

The thrusters and propulsion propellers systems, as well as the operating situations, are all well-known nonlinearities which are caused less accuracy of the dynamic positioning system (DPS) of vessels in the path planning control process. In this study, to enhance the robust performance of the DPS, we proposed a robust adaptive fuzzy control model to reduce the effect of uncertainty problems and disturbances on the DPS. Firstly, the adaptive fuzzy controller with adaptive law is designed to adjust the membership function of the fuzzy controller to minimize the error in path planning control of the vessel. Secondly, the H∞ performance of robust tracking is proved by the Lyapunov theory. Moreover, compared to the other controller, a simulation experiment comprising two case studies confirmed the efficiency of the approach. Finally, the results showed that the proposed controller reaches control quality, performance and stability

통합형 무인 수상선-케이블-수중선 시스템의 다물체동역학 거동 및 제어

Underwater exploration is becoming more and more important, since a vast range of unknown resources in the deep ocean remain undeveloped. This dissertation thus presents a modeling of the coupled dynamics of an Unmanned Surface Vehicle (USV) system with an Underwater Vehicles (UV) connected by an underwater cable (UC). The complexity of this multi-body dynamics system and ocean environments is very difficult to model. First, for modeling this, dynamics analysis was performed on each subsystem and further total coupled system dynamics were studied. The UV which is towed by a UC is modeled with 6-DOF equations of motion that reflects its hydrodynamic characteristic was studied. The 4th-order Runge–Kutta numerical method was used to analyze the motion of the USV with its hydrodynamic coefficients which were obtained through experiments and from the literature. To analyze the effect of the UC, the complicated nonlinear and coupled UC dynamics under currents forces, the governing equations of the UC dynamics are established based on the catenary equation method, then it is solved by applying the shooting method. The new formulation and solution of the UC dynamics yields the three dimensional position and forces of the UC end point under the current forces. Also, the advantage of the proposed method is that the catenary equations using shooting method can be solved in real time such that the calculated position and forces of UC according to time can be directly utilized to calculate the UV motion. The proposed method offers advantages of simple formulation, convenient use, and fast calculation time with exact result. Some simple numerical simulations were conducted to observe the dynamic behaviors of AUV with cable effects. The simulations results clearly reveal that the UC can greatly influence the motions of the vehicles, especially on the UV motions. Based on both the numerical model and simulation results developed in the dissertation, we may offer some valuable information for the operation of the UV and USV. Secondly, for the design controller, a PD controller and its application to automatic berthing control of USV are also studied. For this, a nonlinear mathematical model for the maneuvering of USV in the presence of environmental forces was firstly established. Then, in order to control rudder and propeller during automatic berthing process, a PD control algorithm is applied. The algorithm consists of two parts, the forward velocity control and heading angle control. The control algorithm was designed based on the longitudinal and yaw dynamic models of USV. The desired heading angle was obtained by the so-called “Line of Sight” method. To support the validity of the proposed method, the computer simulations of automatic USV berthing are carried out. The results of simulation showed good performance of the developed berthing control system. Also, a hovering-type AUV equipped with multiple thrusters should maintain the specified position and orientation in order to perform given tasks by applying a dynamic positioning (DP) system. Besides, the control allocation algorithm based on a scaling factor is presented for distributing the forces required by the control law onto the available set of actuators in the most effective and energy efficient way. Thus, it is necessary for the robust control algorithm to conduct successfully given missions in spite of a model uncertainty and a disturbance. In this dissertation, the robust DP control algorithm based on a sliding mode theory is also addressed to guarantee the stability and better performance despite the model uncertainty and disturbance of current and cable effects. Finally, a series of simulations are conducted to verify the availability of the generated trajectories and performance of the designed robust controller. Thirdly, for the navigation of UV, a method for designing the path tracking controller using a Rapidly-exploring Random Trees (RRT) algorithm is proposed. The RRT algorithm is firstly used for the generation of collision free waypoints. Next, the unnecessary waypoints are removed by a simple path pruning algorithm generating a piecewise linear path. After that, a path smoothing algorithm utilizing cubic Bezier spiral curves to generate a continuous curvature path that satisfies the minimum radius of curvature constraint of underwater is implemented. The angle between two waypoints is the only information required for the generation of the continuous curvature path. In order to underwater vehicle follow the reference path, the path tracking controller using the global Sliding Mode Control (SMC) approach is designed. To verify the performance of the proposed algorithm, some simulation results are performed. Simulation results showed that the RRT algorithm could be applied to generate an optimal path in a complex ocean environment with multiple obstacles.Acknowledgement .................................................................................................. vi Abstract……. ....................................................................................... ………….viii Nomenclature ....................................................................................................... xvi List of Abbreviations ........................................................................................... xxi List of Tables ...................................................................................................... xxiii List of Figures ..................................................................................................... xxiv Chapter 1: Introduction ......................................................................................... 1 1.1 Background .................................................................................................. 1 1.1.1 Unmanned Surface Vehicles (USVs) ...................................................... 1 1.1.2 Umbilical Cable ....................................................................................... 4 1.1.3 Unmanned Underwater Vehicles (UUVs) ............................................... 5 1.1.4 Literature on Modeling of Marine Vehicles ............................................ 9 1.1.5 Literature on Control and Guidance of Marine Vehicles ...................... 11 1.2 Our System Architecture ........................................................................... 12 1.3 Motivation ................................................................................................. 13 1.4 Contribution ............................................................................................... 16 1.5 Publications Associated to the Dissertation .............................................. 17 1.6 Structure of the Dissertation ...................................................................... 18 Chapter 2: Mathematical Model of Unmanned Surface Vehicle (USV) ......... 20 2.1 Basic Assumptions .................................................................................... 20 2.2 Three Coordinate Systems ......................................................................... 20 2.3 Variable Notation ...................................................................................... 22 2.4 Kinematics ................................................................................................. 23 2.5 Kinetics ...................................................................................................... 26 2.5.1 Rigid Body Equations of Motion ........................................................... 26 2.5.2 Hydrodynamic Forces and Moments ..................................................... 28 2.5.3 Restoring Forces and Moments ............................................................. 31 2.5.4 Environmental Disturbances .................................................................. 32 2.5.5 Propulsion Forces and Moments ........................................................... 35 2.6 Nonlinear 6DOF Dynamics ....................................................................... 35 2.7 Mathematical Model of USV in 3 DOF .................................................... 36 2.7.1 Planar Kinematics .................................................................................. 36 2.7.2 Planar Nonlinear 3 DOF Dynamics ....................................................... 38 2.8 Configuration of Thrusters ........................................................................ 40 2.9 General Structure and Model Parameters .................................................. 41 2.9.1 Structure of USV ................................................................................... 41 2.9.2 Control System of USV ......................................................................... 42 2.9.3 Winch Control System ........................................................................... 43 Chapter 3: Mathematical Model of the Umbilical Cable (UC) ........................ 45 3.1 Basic Assumptions for UC ........................................................................ 45 3.2 Analysis on Forces of UV ......................................................................... 47 3.3 Relation for UC Equilibrium ..................................................................... 50 3.4 Catenary Equation in the Space Case ........................................................ 51 3.5 Shooting Method ....................................................................................... 55 3.6 Boundary Conditions ................................................................................. 57 3.7 Cable Effects ............................................................................................. 58 3.8 Model Parameters and Simulation ............................................................. 59 Chapter 4: Mathematical Model of Underwater Vehicle (UV) ........................ 63 4.1 Background ................................................................................................ 63 4.1.1 Basic Assumptions................................................................................. 63 4.1.2 Reference Frames .................................................................................. 64 4.1.3 Notations ................................................................................................ 65 4.2 Kinematics Equations ................................................................................ 66 4.3 Kinetic Equations ...................................................................................... 67 4.3.1 Rigid-Body Kinetics .............................................................................. 67 4.3.2 Hydrostatic Terms ................................................................................. 69 4.3.3 Hydrodynamic Terms ............................................................................ 70 4.3.4 Actuator Modeling ................................................................................. 75 4.3.5 Umbilical Cable Forces ......................................................................... 75 4.4 Nonlinear Equations of Motion (6DOF) ................................................... 76 4.5 Simplification of UV Dynamic Model ...................................................... 77 4.5.1 Simplifying the Mass and Inertia Matrix ............................................... 78 4.5.2 Simplifying the Hydrodynamic Damping Matrix.................................. 79 4.5.3 Simplifying the Gravitational and Buoyancy Vector ............................ 80 4.6 Thruster Modeling ..................................................................................... 80 4.7 Current Modeling ...................................................................................... 83 4.8 Dynamic Model Including Ocean Currents ............................................... 84 4.9 Complete Motion Equations of AUV (6DOF) .......................................... 89 4.10 Dynamics Model Parameter Identification ................................................ 91 4.11 Numerical Solution for Equations of Motion ............................................ 93 4.12 General Structure and Model Parameters .................................................. 94 4.12.1 Structure of AUV ............................................................................... 94 4.12.2 Control System of AUV ..................................................................... 96 Chapter 5: Guidance Theory ............................................................................... 97 5.1 Configuration of GNC System .................................................................. 97 5.1.1 Guidance ................................................................................................ 98 5.1.2 Navigation .............................................................................................. 98 5.1.3 Control ................................................................................................... 98 5.2 Maneuvering Problem Statement .............................................................. 99 5.3 Guidance Objectives ................................................................................ 100 5.3.1 Target Tracking ................................................................................... 100 5.3.2 Trajectory Tracking ............................................................................. 100 5.4 Waypoint Representation ........................................................................ 101 5.5 Path Following ......................................................................................... 102 5.6 Line of Sight (LOS) Waypoint Guidance ................................................ 102 5.6.1 Enclosure-Based Steering .................................................................... 104 5.6.2 Look-ahead Based Steering ................................................................. 105 5.6.3 LOS Control......................................................................................... 106 5.7 Cubic Polynomial for Path-Following ..................................................... 107 Chapter 6: Control Algorithm Design and Analysis ....................................... 110 6.1 Proportional Integral Differential (PID) Controller ................................ 110 6.1.1 General Theory .................................................................................... 110 6.1.2 Stability of General PID Controller ..................................................... 112 6.1.3 PID Tuning .......................................................................................... 114 6.1.4 Nonlinear PID for Marine Vehicles ..................................................... 116 6.1.5 Nonlinear PD for Marine Vehicles ...................................................... 117 6.1.6 Stability of Designed PD Controller .................................................... 117 6.2 Sliding Mode Controller .......................................................................... 118 6.2.1 Tracking Error and Sliding Surface ..................................................... 119 6.2.2 Chattering Situation ............................................................................. 120 6.2.3 Control Law and Stability .................................................................... 121 6.3 Allocation Control ................................................................................... 124 6.3.1 Linear Quadratic Unconstrained Control Allocation Using Lagrange Multipliers ................................................................................................ 125 6.3.2 Thruster Allocation with a Constrained Linear Model ........................ 127 6.4 Simulation Results and Discussion ......................................................... 131 6.4.1 Berthing (parking) Control of USV ..................................................... 133 6.4.2 Motion Control of UV ......................................................................... 136 Chapter 7: Obstacle Avoidance and Path Planning for Vehicle Using Rapidly-Exploring Random Trees Algorithm.................................................................. 168 7.1 Path Planning and Guidance: Two Interrelated Problems ....................... 168 7.2 RRT Algorithm for Exploration .............................................................. 171 7.2.1 Random Node Selection ...................................................................... 172 7.2.2 Nearest Neighbor Node Selection ....................................................... 173 7.2.3 RRT Exploration with Obstacles ......................................................... 174 7.3 RRT Algorithm for Navigation of AUV ................................................. 176 7.3.1 Basic RRT Algorithm .......................................................................... 176 7.3.2 Biased-Greedy RRT Algorithm ........................................................... 178 7.3.3 Synchronized Biased-Greedy RRT Algorithm .................................... 179 7.4 Path Pruning ............................................................................................ 182 7.4.1 Path Pruning Using LOS ..................................................................... 182 7.4.2 Global Path Pruning ............................................................................. 183 7.5 Summarize the Proposed RRT Algorithm ............................................... 185 7.6 Simulation for Path Following of AUV .................................................. 187 Chapter 8: Simulation of Complete USV-UC-UV Systems ............................ 196 8.1 Simulation Procedure .............................................................................. 196 8.2 Simulation Results and Discussion ......................................................... 201 8.2.1 Dynamic Behaviors of Complete USV (Stable)-Cable- AUV (Turning Motion) ..................................................................................................... 201 8.2.2 Dynamic Behaviors of Complete USV (Forward motion)-Cable- AUV (Turning Motion) ...................................................................................... 207 8.2.3 Applied Controller to Complete USV -Cable- AUV ........................... 215 Chapter 9: Conclusions and Future Works ..................................................... 238 9.1 Modeling of Complete USV-Cable-AUV System .................................. 238 9.2 Motion Control ........................................................................................ 239 9.3 Cable Force and Moment at the Tow Points ........................................... 239 9.4 Path Planning ........................................................................................... 239 9.5 Future Works ........................................................................................... 240Docto

Non-Linear Robust Observers For Systems With Non-Collocated Sensors And Actuators

Challenges in controlling highly nonlinear systems are not limited to the development of sophisticated control algorithms that are tolerant to significant modeling imprecision and external disturbances. Additional challenges stem from the implementation of the control algorithm such as the availability of the state variables needed for the computation of the control signals, and the adverse effects induced by non-collocated sensors and actuators. The present work investigates the adverse effects of non-collocated sensors and actuators on the phase characteristics of flexible structures and the ensuing implications on the performance of structural controllers. Two closed-loop systems are considered and their phase angle contours have been generated as functions of the normalized sensor location and the excitation frequency. These contours were instrumental in the development of remedial actions for rendering structural controllers immune to the detrimental effects of non-collocated sensors and actuators. Moreover, the current work has focused on providing experimental validation for the robust performances of a self-tuning observer and a sliding mode observer. The observers are designed based on the variable structure systems theory and the self-tuning fuzzy logic scheme. Their robustness and self-tuning characteristics allow one to use an imprecise model of the system and eliminate the need for the extensive tuning associated with a fixed rule-based expert fuzzy inference system. The first phase of the experimental work was conducted in a controlled environment on a flexible spherical robotic manipulator whose natural frequencies are configuration-dependent. Both controllers have yielded accurate estimates of the required state variables in spite of significant modeling imprecision. The observers were also tested under a completely uncontrolled environment, which involves a 16-ft boat operating in open-water under different sea states. Such an experimental work necessitates the development of a supervisory control algorithm to perform PTP tasks, prescribed throttle arm and steering tasks, surge speed and heading tracking tasks, or recovery maneuvers. This system has been implemented herein to perform prescribed throttle arm and steering control tasks based on estimated rather than measured state variables. These experiments served to validate the observers in a completely uncontrolled environment and proved their viability as reliable techniques for providing accurate estimates for the required state variables