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DYNAMICS and CONTROL of AUTONOMOUS UNDERWATER VEHICLES with INTERNAL ACTUATORS by Bo Li

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DYNAMICS and CONTROL of AUTONOMOUS UNDERWATER VEHICLES with INTERNAL ACTUATORS by Bo Li DYNAMICS AND CONTROL OF AUTONOMOUS UNDERWATER VEHICLES WITH INTERNAL ACTUATORS by Bo Li A Dissertation Submitted to the Faculty of College of Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Florida Atlantic University Boca Raton, FL December 2016 Copyright 2016 by Bo Li ii ACKNOWLEDGEMENTS I want to express my deep gratitude to my advisor, Professor Tsung-Chow Su, for his tremendous support for my dissertation research at Florida Atlantic University in the past three years. I am blessed and honored to be his student. I also wish to thank Professors Karl von Ellenrieder, Manhar Dhanak, Yuan Wang, and Palaniswamy Ananthakrishnan for serving in my supervisory commit- tee and sharing their time and ideas. I owe special thanks to Professor Karl von Ellenrieder for supporting my research in Maritime Systems Laboratory at SeaT- ech in the past six months. I also want to thank Professor Lei Wang at Shanghai Jiao Tong University for opening up the opportunity for me to study in the United States. I gratefully thank my colleague Yanjun Li and his wife Guifang Tang for their invaluable friendship. I also thank all my friends in Boca Raton for their com- pany and friendship all these years. Thanks also to the students, faculty and staff members in my department who have helped me in the past three years. Finally, I thank my parents for their enduring love and support. I am so lucky to have them in my life. iv ABSTRACT Author: Bo Li Title: Dynamics and Control of Autonomous Underwater Vehicles with Internal Actuators Institution: Florida Atlantic University Dissertation Advisor: Dr. Tsung-Chow Su Degree: Doctor of Philosophy Year: 2016 This dissertation concerns the dynamics and control of an autonomous un- derwater vehicle (AUV) which uses internal actuators to stabilize its horizontal- plane motion. The demand for high-performance AUVs are growing in the field of ocean engineering due to increasing activities in ocean exploration and research. New generations of AUVs are expected to operate in harsh and complex ocean envi- ronments. We propose a hybrid design of an underwater vehicle which uses internal actuators instead of control surfaces to steer. When operating at low speeds or in relatively strong ocean currents, the performances of control surfaces will degrade. Internal actuators work independent of the relative flows, thus improving the ma- neuvering performance of the vehicle. We develop the mathematical model which describes the motion of an under- water vehicle in ocean currents from first principles. The equations of motion of a body-fluid dynamical system in an ideal fluid are derived using both Newton-Euler and Lagrangian formulations. The viscous effects of a real fluid are considered sepa- rately. We use a REMUS 100 AUV as the research model, and conduct CFD simu- v lations to compute the viscous hydrodynamic coefficients with ANSYS Fluent. The simulation results show that the horizontal-plane motion of the vehicle is inherently unstable. The yaw moment exerted by the relative flow is destabilizing. The open-loop stabilities of the horizontal-plane motion of the vehicle in both ideal and real fluid are analyzed. In particular, the effects of a roll torque and a moving mass on the horizontal-plane motion are studied. The results illustrate that both the position and number of equilibrium points of the dynamical system are prone to the magnitude of the roll torque and the lateral position of the moving mass. We propose the design of using an internal moving mass to stabilize the horizontal-plane motion of the REMUS 100 AUV. A linear quadratic regulator (LQR) is designed to take advantage of both the linear momentum and lateral po- sition of the internal moving mass to stabilize the heading angle of the vehicle. Al- ternatively, we introduce a tunnel thruster to the design, and use backstepping and Lyapunov redesign techniques to derive a nonlinear feedback control law to achieve autopilot. The coupling effects between the closed-loop horizontal-plane and vertical-plane motions are also analyzed. vi To my parents, for always loving and supporting me. DYNAMICS AND CONTROL OF AUTONOMOUS UNDERWATER VEHICLES WITH INTERNAL ACTUATORS List of Tables ..................................................................... xi List of Figures.................................................................... xii 1 Introduction .................................................................. 1 1.1 Motivation....................................................................1 1.2 Dissertation Overview.......................................................6 2 Rigid Body Dynamics ....................................................... 8 2.1 Definition of Coordinates....................................................8 2.2 Transformations between Reference Frames...............................9 2.2.1 Transformation of Rotational Motion..............................9 2.2.2 Transformation of Rigid Motion.................................... 12 2.3 6-DOF Rigid-Body Equations of Motion................................... 14 3 Body-Fluid Dynamical System in an Ideal Fluid....................... 18 3.1 Kinetic Energy of a Body-Fluid Dynamical System....................... 18 3.1.1 Stationary Flow with a Moving Body.............................. 18 3.1.2 Unsteady Spatially Uniform Flow with a Moving Body.......... 24 3.1.3 Steady Spatially Non-uniform Flow with a Moving Body........ 27 3.2 Equations of Motion in a Stationary Flow................................. 27 3.2.1 Boltzmann-Hamel Equations....................................... 27 3.2.2 Lie-Poisson Description............................................. 28 3.3 Equations of Motion in a Uniform Flow................................... 30 viii 3.4 Equations of Motion in a Non-uniform Flow.............................. 33 3.5 Hydrostatics.................................................................. 37 3.6 Summary..................................................................... 41 4 Body-Fluid Dynamical System in a Real Fluid......................... 45 4.1 CFD Methods to Predict Viscous Forces on AUVs....................... 45 4.1.1 Axial Drag........................................................... 46 4.1.2 Cross-Flow Drag..................................................... 49 4.1.3 Body Lift............................................................. 59 4.1.4 Fin Lift............................................................... 66 4.2 Viscous Drag Terms in the Equations of Motion.......................... 70 4.3 Summary..................................................................... 73 5 Stability of an Underwater Vehicle in Ocean Currents ............... 75 5.1 Stability of an Underwater Vehicle in a Stationary Flow................. 77 5.1.1 Special Case in an Ideal Fluid...................................... 77 5.1.2 Stability of the Horizontal-Plane Motion.......................... 88 5.1.3 Effect of Roll Torque on the Horizontal-Plane Motion............ 105 5.1.4 Effect of A Moving Mass on the Horizontal-Plane Motion....... 118 5.2 Stability of an Underwater Vehicle in a Steady and Uniform Flow...... 121 5.2.1 Special Case in an Ideal Fluid...................................... 121 5.2.2 Stability of a Vehicle in a Real Fluid............................... 129 5.3 Effect of Unsteadiness and Non-uniformity................................ 136 6 Control of an Underwater Vehicle Using Internal Actuators ........ 139 6.1 Control of an Underactuated Vehicle....................................... 139 6.2 Kinetics of Underwater Vehicles with an Internal Actuator.............. 141 6.2.1 Internal Rotor........................................................ 141 6.2.2 Internal Moving Mass............................................... 146 ix 6.2.3 Equations of Motion on a Horizontal Plane ....................... 150 6.3 Heading Autopilot for an Underwater Vehicle ............................. 155 6.3.1 Linear Control Design ............................................... 155 6.3.2 Nonlinear Control Design ........................................... 177 6.3.3 Nonlinear Control Design with Tunnel Thrusters ................. 184 6.3.4 Coupling with the Vertical-Plane Motion .......................... 212 7 Conclusions ................................................................... 222 Appendices . .. 224 A Derivation of Body-Fluid Dynamical System Based on Newton-Euler Formulation .................................................................. 225 A.1 Mathematical Preliminaries......................................... 225 A.2 Hydrodynamic Loads in a Stationary Flow ........................ 232 A.3 Hydrodynamic Loads in a Spatially Uniform Unsteady Flow .... 240 A.4 Hydrodynamic Loads in a Spatially Non-uniform Flow........... 246 Bibliography ...................................................................... 252 x LIST OF TABLES 4.1 Main Geometric Parameters of the REMUS AUV ............................ 46 4.2 Principal Parameters in Numerical Modeling.................................. 47 4.3 Principal Parameters in Numerical Modeling.................................. 50 4.4 Drag Coefficients from Numerical Simulations ................................ 52 4.5 Mesh Size in Mesh Independent Study......................................... 56 4.6 Principal Parameters in Numerical Modeling.................................. 56 4.7 Principal Parameters in Numerical Modeling.................................. 59 4.8 Mesh Size in
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