MODELING, DESIGN AND CONTROL OF GLIDING ROBOTIC FISH By Feitian Zhang A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Electrical Engineering – Doctor of Philosophy 2014 ABSTRACT MODELING, DESIGN AND CONTROL OF GLIDING ROBOTIC FISH By Feitian Zhang Autonomous underwater robots have been studied by researchers for the past half century. In particular, for the past two decades, due to the increasing demand for environmental sustainability, significant attention has been paid to aquatic environmental monitoring using autonomous under- water robots. In this dissertation, a new type of underwater robots, gliding robotic fish, is proposed for mobile sensing in versatile aquatic environments. Such a robot combines buoyancy-driven gliding and fin-actuated swimming, inspired by underwater gliders and robotic fish, to realize both energy-efficient locomotion and high maneuverability. Two prototypes, a preliminary miniature underwater glider and a fully functioning gliding robotic fish, are presented. The actuation system and the sensing system are introduced. Dynamic model of a gliding robotic fish is derived by in- tegrating the dynamics of miniature underwater glider and the influence of an actively-controlled tail. Hydrodynamic model is established where hydrodynamic forces and moments are dependent on the angle of attack and the sideslip angle. Using the technique of computational fluid dynamics (CFD) water-tunnel simulation is carried out for evaluating the hydrodynamic coefficients. Scaling analysis is provided to shed light on the dimension design. Two operational modes of gliding robotic fish, steady gliding in the sagittal plane and tail- enabled spiraling in the three-dimensional space, are discussed. Steady-state equations for both motions are derived and solved numerically. In particular, for spiral motion, recursive Newton’s method is adopted and the region of convergence for this method is numerically examined. The local asymptotic stability of the computed equilibria is established through checking the Jacobian matrix, and the basins of attraction are further numerically explored. Simulation and experiments are conducted to validate steady-state models and calculated equilibria for both motions. Tail-enabled feedback control strategies are studied in both sagittal-plane glide stabilization and three-dimensional heading maintenance. A passivity-based controller and a sliding mode con- troller are designed and tested in experiments for those two problems, respectively. In sagittal- plane glide stabilization, a nonlinear observer is designed and implemented to estimate velocity- related states. A three-dimensional curve tracking problem is also discussed and a two-degree-of- freedom control scheme is proposed by integrating static inverse mapping and H∞ control tech- nique. The differential geometric features, such as the torsion and curvature, are explored for planning the trajectory. Finally, the field tests with the lab-developed prototype of gliding robotic fish are conducted in the Kalamazoo River, Michigan and the Wintergreen Lake, Michigan for detecting oil spill and sampling harmful algal blooms, respectively. Both gliding and spiraling motions are tested in the experiments as well as the fish-like swimming. The field test results are presented to show the effectiveness of the designed robot in environmental monitoring tasks. Dedicated to my wife Mi Zhou and our son Andrew Anbang Zhang with all my love. iv ACKNOWLEDGMENTS First, I would like to express my warmest gratitude to my advisor, the director of Smart Mi- crosystems Lab at Michigan State University, Prof. Xiaobo Tan. Five years ago, Prof. Tan provided me a valuable opportunity of starting my Ph.D. journey here in the field of underwater robotics, and now upon the completion of my Ph.D. training, with experience and knowledge gained during the past five years, I am excitedly looking forward to my postdoctoral research life at University of Maryland. I genuinely thank him for his advising in my research and mentoring in my career path. I want to thank my academic committee members, Prof. Hassan Khalil, Prof. Guoming Zhu and Prof. Mukherjee at Michigan State University, and our research collaborator, Prof. Fumin Zhang at Georgia Institute of Technology, for their insightful comments in the area of control and robotics. I also thank Prof. Elena Litchman at Michigan State University and Prof. Derek Paley at University of Maryland for their generosity and kindness in providing experimental facilities and testing fields for the project. In Smart Microsystems Lab, I owe many people a debt of gratitude. The research in gliding robotic fish needs diverse expertise and extensive collaboration. I want to thank John Thon and Cody Thon for their continuous contribution in mechanical design and robot manufacturing, and Jianxun Wang and Hong Lei for their help in circuit development, and Bin Tian, Osama En-Nasr, Scott O’Connor, Suriya Madhan, Tingyuan Zhang and Yujie Hao for their help in conducting experiments and collecting data. I would also like to thank the other students in Smart Microsystems Lab and the faculty, stu- dents and post-docs in my department, whose comments and discussions have helped my research. Thanks also to all of the administrators and staff members in the ECE department who have helped me over the years. v I also want to acknowledge the support from the funding agencies NSF (IIS 0916720, ECCS 1050236, IIS 1319602, IIP 1343413, CCF 1331852) that makes this work possible. Most of all, I want to thank my mother, Dongmei He, my father, Guangbo Zhang and my wife, Mi Zhou for their unconditional love in both good times and bad times. I could not have finished my Ph.D. program in the past five years without their understanding, support and encouragement. vi TABLE OF CONTENTS LIST OF TABLES ....................................... ix LIST OF FIGURES ...................................... x Chapter 1 Introduction .................................. 1 1.1 Technology in AquaticEnvironmentalMonitoring . ............ 1 1.2 GlidingRoboticFish .............................. ... 3 1.2.1 DesignConcept................................ 3 1.2.2 MotionandControl.............................. 6 1.3 OverviewofContributions . ..... 12 Chapter 2 Implementation of Gliding Robotic Fish .................. 14 2.1 ActuationSystem ................................. .. 14 2.2 GlidingRoboticFishComponents . ...... 16 2.3 MechanicalDesign ................................ .. 19 Chapter 3 Dynamic Model of Gliding Robotic Fish .................. 22 3.1 FullDynamicModel ................................ 22 3.2 HydrodynamicModel............................... .. 26 3.2.1 HydrodynamicEquations. .. 26 3.2.2 CFD-based Evaluation of Hydrodynamic Coefficients . .......... 27 Chapter 4 Steady Gliding in the Sagittal Plane ..................... 36 4.1 ReducedModelintheSagittalPlane . ....... 36 4.2 Computation of Steady Gliding Path in the Sagittal Plane .............. 37 4.3 ScalingAnalysis................................. ... 40 4.4 ExperimentalResultsandModelValidation . .......... 44 Chapter 5 Steady Spiral in Three-Dimensional Space ................. 55 5.1 Steady-StateSpiralingEquations . ......... 55 5.2 Computation of Spiral Path and Evaluation of Stability . .............. 58 5.2.1 Newton’s method for Solving the Steady-State SpiralingEquations. 58 5.2.2 RegionofConvergenceforNewton’sMethod . ...... 60 5.2.3 StabilityAnalysisofSpiralingMotion . ........ 63 5.2.4 Basinsof Attractionfor the SpiralingDynamics . .......... 64 5.3 ExperimentalResults . .. .. .. .. .. .. .. .. .... 67 Chapter 6 Passivity-based Stabilization with a Whale-type Tail ............ 71 6.1 Model of a Gliding Robotic Fish with a Whale-type Tail . ............ 71 vii 6.1.1 DynamicModelintheSagittalPlane. ..... 72 6.1.2 SystemReductionviaSingularPerturbation . ......... 75 6.2 Passivity-basedControllerDesign . ......... 78 6.2.1 Passivity-based Controller for the Approximated ReducedModel. 78 6.2.2 Stability Analysis for the Full Closed-loop System . ........... 81 6.2.3 SimulationResults . .. .. .. .. .. .. .. .. 85 6.3 ObserverDesign.................................. .. 89 6.4 ExperimentalResults . .. .. .. .. .. .. .. .. .... 97 6.4.1 FilterDesign ................................. 97 6.4.2 Open-loopExperiments. .. 98 6.4.3 Closed-loopExperiments. 101 Chapter 7 Yaw Stabilization Using Sliding Mode Control ............... 115 7.1 ProblemStatement ................................ 115 7.2 SlidingModeControlforYawStabilization . ..........116 7.3 Simulation...................................... 121 7.4 ExperimentalResults . .. .. .. .. .. .. .. .. .129 Chapter 8 Three-Dimensional Curve Tracking ..................... 133 8.1 Three-Dimensional Steady Spiral and Its Differential Geometry Features . 133 8.2 InfluenceofControlInputsonSpiralTrajectory . ............136 8.3 TwoDegree-of-FreedomControlDesign . ........143 8.3.1 Feedforward Control via Inverse Mapping of Steady SpiralMotion . 145 8.3.2 Linearized Model Around the Steady Spiral Trajectory ...........147 8.3.3 H∞ ControllerDesign. .148 8.4 SimulationResults ............................... 151 Chapter 9 Field Test Results for Environmental Monitoring ............. 159 9.1 KalamazooRiverTest.............................. 159 9.2 WintergreenLakeTest ............................. 162 Chapter 10 Conclusions and Future Work ........................ 169 10.1Conclusions .................................... 169 10.2FutureWork....................................