Underwater vehicles present some difficult and very particular control system design problems. These are often the result of nonlinear dynamics and uncertain models, as well as the presence of sometimes unforeseeable environmental disturbances that are difficult to measure or estimate.
Autonomous Underwater Vehicles: Modeling, Control Design, and Simulation outlines a novel approach to help readers develop models to simulate feedback controllers for motion planning and design. The book combines useful information on both kinematic and dynamic nonlinear feedback control models, providing simulation results and other essential information, giving readers a truly unique and all-encompassing new perspective on design.
Includes MATLAB® Simulations to Illustrate Concepts and Enhance Understanding
Starting with an introductory overview, the book offers examples of underwater vehicle construction, exploring kinematic fundamentals, problem formulation, and controllability, among other key topics. Particularly valuable to researchers is the books detailed coverage of mathematical analysis as it applies to controllability, motion planning, feedback, modeling, and other concepts involved in nonlinear control design. Throughout, the authors reinforce the implicit goal in underwater vehicle designto stabilize and make the vehicle follow a trajectory precisely.
Fundamentally nonlinear in nature, the dynamics of AUVs present a difficult control system design problem which cannot be easily accommodated by traditional linear design methodologies. The results presented here can be extended to obtain advanced control strategies and design schemes not only for autonomous underwater vehicles but also for other similar problems in the area of nonlinear control.
| Preface |
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xi | |
| About the Authors |
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xiii | |
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1 | (28) |
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1 | (3) |
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1.2 Examples of Underwater Vehicle Construction |
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4 | (8) |
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1.2.1 Propeller Principle |
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6 | (1) |
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6 | (2) |
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8 | (3) |
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1.2.2 Commercially Available Underwater Vehicles |
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11 | (1) |
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1.3 Vehicle Kinematics Fundamentals |
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12 | (11) |
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1.3.1 Frenet-Serret Equations for Cartan Moving Frame |
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12 | (6) |
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1.3.2 Mathematical Background for Rigid Motion in a Plane |
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18 | (1) |
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1.3.2.1 Rotation of a Vector |
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18 | (1) |
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1.3.2.2 Vector Represented in a Rotated Frame |
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19 | (1) |
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1.3.2.3 Representation of a Rotated Frame |
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19 | (1) |
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1.3.2.4 Group Representation |
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20 | (2) |
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1.3.2.5 Homogeneous Representation |
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22 | (1) |
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1.4 Lie Groups and Lie Algebras |
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23 | (6) |
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23 | (3) |
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26 | (3) |
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Chapter 2 Problem Formulation and Examples |
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29 | (12) |
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2.1 Motion Planning of Nonholonomic Systems |
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29 | (1) |
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2.2 Nonholonomic Constraints |
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30 | (1) |
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31 | (2) |
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2.4 Control Model Formulation |
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33 | (1) |
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2.5 Controllability Issues |
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34 | (1) |
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35 | (3) |
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2.6.1 Controllability and Stabilization at a Point |
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35 | (1) |
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2.6.2 Controllability and Stabilization about Trajectory |
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36 | (1) |
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2.6.3 Approximate Linearization |
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36 | (1) |
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2.6.4 Exact Feedback Linearization |
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36 | (1) |
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2.6.5 Static Feedback Linearization |
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37 | (1) |
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2.6.6 Dynamic Feedback Linearization |
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37 | (1) |
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2.7 Examples of Nonholonomic Systems |
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38 | (3) |
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Chapter 3 Mathematical Modeling and Controllability Analysis |
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41 | (14) |
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3.1 Mathematical Modeling |
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41 | (5) |
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3.1.1 Kinematic Modeling and Nonholonomic Constraints |
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41 | (1) |
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3.1.2 Kinematic Model with Respect to Global Coordinates |
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42 | (4) |
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3.2 Controllability Analysis |
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46 | (4) |
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3.2.1 Controllability about a Point |
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46 | (2) |
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3.2.2 Controllability about a Trajectory |
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48 | (2) |
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50 | (5) |
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Chapter 4 Control Design Using the Kinematic Model |
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55 | (62) |
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4.1 Trajectory Tracking and Controller Design for the Chained Form |
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55 | (1) |
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4.2 Reference Trajectory Generation |
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55 | (3) |
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4.3 Control Using Approximate Linearization |
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58 | (19) |
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4.3.1 Simulation of the Controller |
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61 | (7) |
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4.3.2 MATLAB® Program Code for the Approximate Linearization |
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68 | (9) |
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4.4 Control Using Exact Feedback Linearization via State and Input Transformations |
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77 | (21) |
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4.4.1 Control Using Exact Feedback Linearization via Static Feedback |
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78 | (1) |
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4.4.2 Control Using Exact Feedback Linearization via Dynamic Feedback |
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79 | (2) |
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4.4.3 Simulation of the Controller |
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81 | (7) |
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4.4.4 MATLAB Program Code for Dynamic Extension |
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88 | (10) |
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4.5 Point-to-Point Stabilization |
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98 | (19) |
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4.5.1 Control with Smooth Time-Varying Feedback |
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99 | (1) |
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99 | (1) |
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4.5.3 Control Design with Smooth Time-Varying Feedback |
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100 | (1) |
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4.5.4 Simulation of the Controller |
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101 | (6) |
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4.5.5 MATLAB Program Code for Point Stabilization |
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107 | (10) |
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Chapter 5 Control Design Using the Dynamic Model |
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117 | (10) |
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117 | (1) |
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5.2 Point-to-Point Stabilization Control Design |
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118 | (9) |
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5.2.1 State Feedback Control Using Backstepping |
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119 | (1) |
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5.2.2 Control with Smooth Time-Varying Feedback |
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120 | (1) |
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5.2.3 Lyapunov Stability Analysis |
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121 | (1) |
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5.2.4 Control of the Dynamic Model |
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122 | (5) |
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Chapter 6 Robust Feedback Control Design |
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127 | (16) |
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6.1 Robust Control Using the Kinematic Model |
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127 | (6) |
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6.1.1 Input Uncertain Control Model |
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128 | (2) |
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6.1.2 Robust Control by the Lyapunov Redesign Method |
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130 | (3) |
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6.2 Robust Control Using the Dynamic Model |
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133 | (10) |
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6.2.1 Robust Backstepping: Unmatched Uncertainty |
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134 | (3) |
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6.2.2 Robust Control: Matched Uncertainty |
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137 | (3) |
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6.2.3 Robust Control: Both Matched and Unmatched Uncertainties |
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140 | (3) |
| References |
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143 | (2) |
| Index |
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145 | |
Sabiha Wadoo, Ph.D, received a BE degree in electrical engineering from the Regional Engineering College, Kashmir, India, in 2001, and an MS degree in electrical engineering, an MS degree in mathematics, and a Ph.D degree in electrical engineering from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, in 2003, 2005, and 2007, respectively. Since 2007, she has been with the New York Institute of Technology, Old Westbury, New York, where she is an assistant professor with the Department of Electrical and Computer Engineering. Her research interests are in the areas of feedback control of nonlinear control systems, nonlinear control system abstraction, and feedback control of distributed parameter systems.
Pushkin Kachroo, Ph.D, received a BTech degree in civil engineering from the Indian Institute of Technology, Bombay, India, in 1988, an MS degree in mechanical engineering from Rice University, Houston, Texas, in 1990, a Ph.D degree in mechanical engineering from the University of California, Berkeley, in 1993, and MS and Ph.D degrees in mathematics from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, in 2004 and 2007, respectively. He is the director of the Transportation Research Center, Harry Reid Center for Environmental Studies, Las Vegas, Nevada, and a professor with the Department of Electrical and Computer Engineering, University of Nevada, Las Vegas.
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