A survey of fuzzy control for stabilized platforms

This paper focusses on the application of fuzzy control techniques (fuzzy type-1 and type-2) and their hybrid forms (Hybrid adaptive fuzzy controller and fuzzy-PID controller) in the area of stabilized platforms. It represents an attempt to cover the basic principles and concepts of fuzzy control in stabilization and position control, with an outline of a number of recent applications used in advanced control of stabilized platform. Overall, in this survey we will make some comparisons with the classical control techniques such us PID control to demonstrate the advantages and disadvantages of the application of fuzzy control techniques

Design and Optimization of PID Controller using Various Algorithms for Micro-Robotics System

Microparticles have the potentials to be used for many medical purposes in-side the human body such as drug delivery and other operations. This paper attempts to provide a thorough comparison between five meta-heuristic search algorithms:  Sparrow Search Algorithm (SSA), Flower Pollination Algorithm (FPA), Slime Mould Algorithm (SMA), Marine Predator Algorithm (MPA), and Multi-Verse Optimizer (MVO). These approaches were used to calculate the PID controller optimal indicators with the application of different functions, including Integral Absolute Error (IAE), Integral of Time Multiplied by Square Error (ITSE), Integral Square Time multiplied square Error (ISTES), Integral Square Error (ISE), Integral of Square Time multiplied by square Error (ISTSE), and Integral of Time multiplied by Absolute Error (ITAE). Every method of controlling was presented in a MATLAB Simulink numerical model, and LABVIEW software was used to run the experimental tests. It is observed that the MPA technique achieves the highest values of settling error for both simulation and experimental results among other control approaches, while the SSA approach reduces the settling error by 50% compared to former experiments. The results indicate that SSA is the best method among all approaches and that ISTES is the best choice of PID for optimizing the controlling parameters

A Predictive Fuzzy-Neural Autopilot for the Guidance of Small Motorised Marine Craft

This thesis investigates the design and evaluation of a control system, that is able to adapt quickly to changes in environment and steering characteristics. This type of controller is particularly suited for applications with wide-ranging working conditions such as those experienced by small motorised craft. A small motorised craft is assumed to be highly agile and prone to disturbances, being thrown off-course very easily when travelling at high speed 'but rather heavy and sluggish at low speeds. Unlike large vessels, the steering characteristics of the craft will change tremendously with a change in forward speed. Any new design of autopilot needs to be to compensate for these changes in dynamic characteristics to maintain near optimal levels of performance. This study identities the problems that need to be overcome and the variables involved. A self-organising fuzzy logic controller is developed and tested in simulation. This type of controller learns on-line but has certain performance limitations. The major original contribution of this research investigation is the development of an improved self-adaptive and predictive control concept, the Predictive Self-organising Fuzzy Logic Controller (PSoFLC). The novel feature of the control algorithm is that is uses a neural network as a predictive simulator of the boat's future response and this network is then incorporated into the control loop to improve the course changing, as well as course keeping capabilities of the autopilot investigated. The autopilot is tested in simulation to validate the working principle of the concept and to demonstrate the self-tuning of the control parameters. Further work is required to establish the suitability of the proposed novel concept to other control

Review of dynamic positioning control in maritime microgrid systems

For many offshore activities, including offshore oil and gas exploration and offshore wind farm construction, it is essential to keep the position and heading of the vessel stable. The dynamic positioning system is a progressive technology, which is extensively used in shipping and other maritime structures. To maintain the vessels or platforms from displacement, its thrusters are used automatically to control and stabilize the position and heading of vessels in sea state disturbances. The theory of dynamic positioning has been studied and developed in terms of control techniques to achieve greater accuracy and reduce ship movement caused by environmental disturbance for more than 30 years. This paper reviews the control strategies and architecture of the DPS in marine vessels. In addition, it suggests possible control principles and makes a comparison between the advantages and disadvantages of existing literature. Some details for future research on DP control challenges are discussed in this paper

Development of Robust Control Strategies for Autonomous Underwater Vehicles

The resources of the energy and chemical balance in the ocean sustain mankind in many ways. Therefore, ocean exploration is an essential task that is accomplished by deploying Underwater Vehicles. An Underwater Vehicle with autonomy feature for its navigation and control is called Autonomous Underwater Vehicle (AUV). Among the task handled by an AUV, accurately positioning itself at a desired position with respect to the reference objects is called set-point control. Similarly, tracking of the reference trajectory is also another important task. Battery recharging of AUV, positioning with respect to underwater structure, cable, seabed, tracking of reference trajectory with desired accuracy and speed to avoid collision with the guiding vehicle in the last phase of docking are some significant applications where an AUV needs to perform the above tasks. Parametric uncertainties in AUV dynamics and actuator torque limitation necessitate to design robust control algorithms to achieve motion control objectives in the face of uncertainties. Sliding Mode Controller (SMC), H / μ synthesis, model based PID group controllers are some of the robust controllers which have been applied to AUV. But SMC suffers from less efficient tuning of its switching gains due to model parameters and noisy estimated acceleration states appearing in its control law. In addition, demand of high control effort due to high frequency chattering is another drawback of SMC. Furthermore, real-time implementation of H / μ synthesis controller based on its stability study is restricted due to use of linearly approximated dynamic model of an AUV, which hinders achieving robustness. Moreover, model based PID group controllers suffer from implementation complexities and exhibit poor transient and steady-state performances under parametric uncertainties. On the other hand model free Linear PID (LPID) has inherent problem of narrow convergence region, i.e.it can not ensure convergence of large initial error to zero. Additionally, it suffers from integrator-wind-up and subsequent saturation of actuator during the occurrence of large initial error. But LPID controller has inherent capability to cope up with the uncertainties. In view of addressing the above said problem, this work proposes wind-up free Nonlinear PID with Bounded Integral (BI) and Bounded Derivative (BD) for set-point control and combination of continuous SMC with Nonlinear PID with BI and BD namely SM-N-PID with BI and BD for trajectory tracking. Nonlinear functions are used for all P,I and D controllers (for both of set-point and tracking control) in addition to use of nonlinear tan hyperbolic function in SMC(for tracking only) such that torque demand from the controller can be kept within a limit. A direct Lyapunov analysis is pursued to prove stable motion of AUV. The efficacies of the proposed controllers are compared with other two controllers namely PD and N-PID without BI and BD for set-point control and PD plus Feedforward Compensation (FC) and SM-NPID without BI and BD for tracking control. Multiple AUVs cooperatively performing a mission offers several advantages over a single AUV in a non-cooperative manner; such as reliability and increased work efficiency, etc. Bandwidth limitation in acoustic medium possess challenges in designing cooperative motion control algorithm for multiple AUVs owing to the necessity of communication of sensors and actuator signals among AUVs. In literature, undirected graph based approach is used for control design under communication constraints and thus it is not suitable for large number of AUVs participating in a cooperative motion plan. Formation control is a popular cooperative motion control paradigm. This thesis models the formation as a minimally persistent directed graph and proposes control schemes for maintaining the distance constraints during the course of motion of entire formation. For formation control each AUV uses Sliding Mode Nonlinear PID controller with Bounded Integrator and Bounded Derivative. Direct Lyapunov stability analysis in the framework of input-to-state stability ensures the stable motion of formation while maintaining the desired distance constraints among the AUVs

Application of Machine and Deep Learning to Mooring, Dynamic Positioning, and Ship Berthing Systems

In recent years, there have been a surge of advances in machine and deep learning due to accessibility to a large amount of digital data, developments in computer hardware, and state-of-the-art machine and deep learning algorithms proposed. The robust performance of the recent machine and deep learning algorithms have been proven in many applications such as natural language processing, computer vision, market research, self-driving car, autonomous shipping, and so on. The application of machine and deep learning is very powerful in a sense that one does not need to build such a complex and hard-coded system to implement sophisticated functionality. Instead, a machine and deep learning-based system can be trained on a collected training dataset and the trained system can robustly perform as desired. There are two main advantages of the use of machine and deep learning-based systems over the traditional hard-coded systems. First, as mentioned, the machine and deep learning-based systems do not require such complex and hard-coded algorithms, therefore, such learning systems are less prone to errors and faster to implement without much debugging. Second, the machine and deep learning-based systems can adapt to varying circumstances through re-training based on collected data. An example of the varying circumstance can be a varying purchase trend impacted by the media. Therefore, even if the input distribution from the circumstance changes over time, the machine and deep learning-based systems can easily adapt. In this paper, the machine and deep learning algorithms are applied to various applications such as a mooring system, dynamic positioning system (DPS), and ship berthing system. Specifically, the machine and deep learning algorithms are utilized to build a mooring line tension prediction system, a feed-forward system for DPS, an adaptive proportional-integral-derivative (PID) controller for DPS, and an automatic ship berthing system.1. Introduction 1 2. Background of Machine and Deep Learning 4 2.1 Machine Learning 4 2.2 Deep Learning 9 2.2.1 Types of Deep Learning Layers 9 2.2.2 Activation Function and Weight Initialization Methods 18 2.2.3 Optimizers 19 2.2.4 Training Dataset Scaling 26 2.2.5 Transfer Learning 28 2.3 Reinforcement Learning 28 3. Machine Learning-Based Mooring Line Tension Prediction System 39 3.1 Introduction 39 3.2 Brief Comparison Between Conventional and Proposed Mooring Line Tension Prediction Systems 40 3.3 Proposed K-Means-Based Sea State Selection Method 41 3.3.1 Padding 42 3.3.2 K-Means 44 3.3.3 K-Means-Based Monte Carlo Method 45 3.3.4 Feature Vector Generation 47 3.3.5 Clustering of Relevant Sampled Sea States with K-Means 48 3.4 Proposed Hybrid Neural Network Architecture 50 3.4.1 Architecture 50 3.4.2 Training Procedure 54 3.5 Simulation and Result Discussion 55 3.5.1 Simulation Conditions 55 3.5.2 Overall Hs-focused NN model 56 3.5.3 Effectiveness of Batch Normalization 59 3.5.4 Low Hs-focused NN model 60 3.5.5 Proposed Hybrid Neural Network Architecture 61 4. Motion Predictive Control for DPS Using Predicted Drifted Ship Position Based on Deep Learning and Replay Buffer 65 4.1 Introduction 65 4.2 PID Feed-Back System and Wind Feed-Forward System 66 4.3 Proposed Motion Predictive Control 69 4.4 Numerical Modeling of Target Ship's Behavior 73 4.4.1 Target Ship and DPS 73 4.4.2 Equation of Motion of Target Ship 74 4.5 Effectiveness of Proposed Algorithms 76 4.5.1 Simulation Conditions 76 4.5.2 Types of Deep Learning Layers 77 4.5.3 Real-Time Normalization Method 78 4.5.4 Replay Buffer 80 4.6 Simulation and Result Discussion 81 4.6.1 Simulation Under One Environmental Condition 81 4.6.2 Simulation Under Two Different Sequential Environmental Conditions 84 5. Reinforcement Learning-Based Adaptive PID Controller for DPS 88 5.1 Introduction 88 5.2 Target Ship and DPS 90 5.2.1 PID Control in DPS 91 5.2.2 Hydrodynamics Associated with a Drifting Motion of a Ship 93 5.3 Proposed Adaptive Fine-Tuning System for PID Gains in DPS 95 5.4 Simulation Results 99 5.4.1 Effectiveness of the Proposed Adaptive Fine-Tuning System 99 5.4.2 Overall Performance Assessment 103 5.5 Discussion 107 6. Application of Recent Developments in Deep Learning To ANN-based Automatic Berthing System 111 6.1 Introduction 111 6.2 Mathematical Model of Ship Maneuvering 112 6.2.1 Mathematical Model for Ship-Maneuvering Problem 113 6.2.2 Modeling of Propeller and Rudder 114 6.3 Artificial Neural Network and Important Factors in Training the Network 115 6.3.1 Artificial Neural Network 115 6.3.2 Optimizer 117 6.3.3 Input Data Scaling 117 6.3.4 Number of Hidden Layers 118 6.3.5 Overfitting Prevention 118 6.4 Application of Recent Developments in Deep Learning to Automatic Berthing 119 6.5 Simulation and Result Discussion 125 7. Conclusion 131 7.1 Machine Learning-Based Mooring Line Tension Prediction System 131 7.2 Motion Predictive Control for DPS Using Predicted Drifted Ship Position Based on Deep Learning and Replay Buffer 132 7.3 Reinforcement Learning-Based Adaptive PID Controller for DPS 133 7.4 Application of Recent Developments in Deep Learning to ANN-Based Automatic Berthing System 134Maste

The Baseline Design of The UiS Subsea Glider for Cargo and Liquid Carbon Dioxide Transportation

This dissertation presents the baseline design of the UiS subsea-freight glider (USFG) for cargo and liquid carbon dioxide transportation. The USFG is a cutting-edge autonomous vessel developed to be an alternative to active transportation technologies and satisfy the demands of small-scale fields for CO2 transportation. Usually, these smaller fields fail to economically justify the costs of large tanker or cargo ships or underwater pipelines on the seabed, as the transport volume is nominal compared to larger fields. The USFG can travel underwater at an operational depth of 200 meters, allowing the glider to carry freight operations without considering ideal weather windows. The length of the USFG is 5.50 meters, along with a beam of 50.25 meters, which allows the vessel to carry 518 m3 of CO2 while serving the storage needs of the carbon capture and storage (CCS) ventures on the Norwegian continental shelf. It can maneuver itself underwater by monitoring the flow between the ballast tanks. During the entire mission of the USFG, from capturing to injection locations, it follows a pre-laid route while experiencing transient loads from the ocean current. A planar mathematical model for the analysis of equilibrium glide paths of the USFG is presented. The model is developed using Simscape Multibody in MATLAB/Simulink to study the volatile dynamics of the glider. Subsequently, the gliding paths of USFG in the vertical plane are analyzed along with the observability and controllability of the steady equilibrium glides. Along with the control gliding design of the USFG, the mechanical design is also presented in this work. The maneuvering model of the USFG is presented along with two operational case studies: the equilibrium glide and the -38° dive. The extreme motion along the surge direction affects the range of the glider (vital for battery design) and the dynamic controller parameters concerning maneuverability. Finally, the averaged conditional exceedance rate (ACER) is employed to scrutinize the extreme motion (surge direction) of the USFG while gliding to a defined depth. This analysis is done when the glider is exposed to an average current velocity of 0.5 m/s and 1.0 m/s. The presented ACER method efficiently uses the available data points and accurately predicts the extreme surge responses precisely and accurately

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