Dynamics and Control of Autonomous Underwater Vehicles with Internal Actuators

278 Pages·2016·7.21 MB·English

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
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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.
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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.
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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
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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
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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
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