Morphing Aerospace Vehicles and Structures

List of Contributors xiii Foreword xv Series Preface xvii Acknowledgments xix 1 Introduction 1 John Valasek 1.1 Introduction 1 1.2 The Early Years: Bio-Inspiration 2 1.3 The Middle Years: Variable Geometry 5 1.4 The Later Years: A Return to Bio-Inspiration 9 1.5 Conclusion 10 References 10 Part I BIO-INSPIRATION 2 Wing Morphing in Insects, Birds and Bats: Mechanism and Function 13 Graham K. Taylor, Anna C. Carruthers, Tatjana Y. Hubel, and Simon M. Walker 2.1 Introduction 13 2.2 Insects 14 2.2.1 Wing Structure and Mechanism 15 2.2.2 Gross Wing Morphing 18 2.3 Birds 25 2.3.1 Wing Structure and Mechanism 25 2.3.2 Gross Wing Morphing 28 2.3.3 Local Feather Deflections 30 2.4 Bats 32 2.4.1 Wing Structure and Mechanism 33 2.4.2 Gross Wing Morphing 35 2.5 Conclusion 37 Acknowledgements 37 References 38 3 Bio-Inspiration of Morphing for Micro Air Vehicles 41 Gregg Abate and Wei Shyy 3.1 Micro Air Vehicles 41 3.2 MAV Design Concepts 43 3.3 Technical Challenges for MAVs 46 3.4 Flight Characteristics of MAVs and NAVs 47 3.5 Bio-Inspired Morphing Concepts for MAVs 48 3.5.1 Wing Planform 50 3.5.2 Airfoil Shape 50 3.5.3 Tail Modulation 50 3.5.4 CG Shifting 50 3.5.5 Flapping Modulation 51 3.6 Outlook for Morphing at the MAV/NAV scale 51 3.7 Future Challenges 51 3.8 Conclusion 53 References 53 Part II CONTROL AND DYNAMICS 4 Morphing Unmanned Air Vehicle Intelligent Shape and Flight Control 57 John Valasek, Kenton Kirkpatrick, and Amanda Lampton 4.1 Introduction 57 4.2 A-RLC Architecture Functionality 58 4.3 Learning Air Vehicle Shape Changes 59 4.3.1 Overview of Reinforcement Learning 59 4.3.2 Implementation of Shape Change Learning Agent 62 4.4 Mathematical Modeling of Morphing Air Vehicle 63 4.4.1 Aerodynamic Modeling 63 4.4.2 Constitutive Equations 64 4.4.3 Model Grid 67 4.4.4 Dynamical Modeling 68 4.4.5 Reference Trajectory 71 4.4.6 Shape Memory Alloy Actuator Dynamics 71 4.4.7 Control Effectors on Morphing Wing 73 4.5 Morphing Control Law 73 4.5.1 Structured Adaptive Model Inversion (SAMI) Control for Attitude Control 73 4.5.2 Update Laws 76 4.5.3 Stability Analysis 77 4.6 Numerical Examples 77 4.6.1 Purpose and Scope 77 4.6.2 Example 1: Learning New Major Goals 77 4.6.3 Example 2: Learning New Intermediate Goals 80 4.7 Conclusions 84 Acknowledgments 84 References 84 5 Modeling and Simulation of Morphing Wing Aircraft 87 Borna Obradovic and Kamesh Subbarao 5.1 Introduction 87 5.1.1 Gull-Wing Aircraft 87 5.2 Modeling of Aerodynamics with Morphing 88 5.2.1 Vortex-Lattice Aerodynamics for Morphing 90 5.2.2 Calculation of Forces and Moments 92 5.2.3 Effect of Gull-Wing Morphing on Aerodynamics 92 5.3 Modeling of Flight Dynamics with Morphing 93 5.3.1 Overview of Standard Approaches 93 5.3.2 Extended Rigid-Body Dynamics 97 5.3.3 Modeling of Morphing 100 5.4 Actuator Moments and Power 105 5.5 Open-Loop Maneuvers and Effects of Morphing 109 5.5.1 Longitudinal Maneuvers 109 5.5.2 Turn Maneuvers 114 5.6 Control of Gull-Wing Aircraft using Morphing 118 5.6.1 Power-Optimal Stability Augmentation System using Morphing 119 5.7 Conclusion 123 Appendix 123 References 124 6 Flight Dynamics Modeling of Avian-Inspired Aircraft 127 Jared Grauer and James Hubbard Jr 6.1 Introduction 127 6.2 Unique Characteristics of Flapping Flight 129 6.2.1 Experimental Research Flight Platform 129 6.2.2 Unsteady Aerodynamics 130 6.2.3 Configuration-Dependent Mass Distribution 131 6.2.4 Nonlinear Flight Motions 131 6.3 Vehicle Equations of Motion 134 6.3.1 Conventional Models for Aerospace Vehicles 134 6.3.2 Multibody Model Configuration 136 6.3.3 Kinematics 138 6.3.4 Dynamics 138 6.4 System Identification 140 6.4.1 Coupled Actuator Models 141 6.4.2 Tail Aerodynamics 143 6.4.3 Wing Aerodynamics 143 6.5 Simulation and Feedback Control 144 6.6 Conclusion 148 References 148 7 Flight Dynamics of Morphing Aircraft with Time-Varying Inertias 151 Daniel T. Grant, Stephen Sorley, Animesh Chakravarthy, and Rick Lind 7.1 Introduction 151 7.2 Aircraft 152 7.2.1 Design 152 7.2.2 Modeling 154 7.3 Equations of Motion 156 7.3.1 Body-Axis States 156 7.3.2 Influence of Time-Varying Inertias 157 7.3.3 Nonlinear Equations for Moment 157 7.3.4 Linearized Equations for Moment 159 7.3.5 Flight Dynamics 161 7.4 Time-Varying Poles 162 7.4.1 Definition 162 7.4.2 Discussion 164 7.4.3 Modal Interpretation 164 7.5 Flight Dynamics with Time-Varying Morphing 166 7.5.1 Morphing 166 7.5.2 Model 166 7.5.3 Poles 168 7.5.4 Modal Interpretation 171 References 174 8 Optimal Trajectory Control of Morphing Aircraft in Perching Maneuvers 177 Adam M. Wickenheiser and Ephrahim Garcia 8.1 Introduction 177 8.2 Aircraft Description 179 8.3 Vehicle Equations of Motion 181 8.4 Aerodynamics 185 8.5 Trajectory Optimization for Perching 191 8.6 Optimization Results 196 8.7 Conclusions 202 References 202 Part III SMART MATERIALS AND STRUCTURES 9 Morphing Smart Material Actuator Control Using Reinforcement Learning 207 Kenton Kirkpatrick and John Valasek 9.1 Introduction to Smart Materials 207 9.1.1 Piezoelectrics 208 9.1.2 Shape Memory Alloys 208 9.1.3 Challenges in Controlling Shape Memory Alloys 209 9.2 Introduction to Reinforcement Learning 210 9.2.1 The Reinforcement Learning Problem 210 9.2.2 Temporal-Difference Methods 211 9.2.3 Action Selection 213 9.2.4 Function Approximation 215 9.3 Smart Material Control as a Reinforcement Learning Problem 218 9.3.1 State-Spaces and Action-Spaces for Smart Material Actuators 218 9.3.2 Function Approximation Selection 220 9.3.3 Exploiting Action-Value Function for Control 220 9.4 Example 221 9.4.1 Simulation 222 9.4.2 Experimentation 225 9.5 Conclusion 228 References 229 10 Incorporation of Shape Memory Alloy Actuators into Morphing Aerostructures 231 Justin R. Schick, Darren J. Hartl and Dimitris C. Lagoudas 10.1 Introduction to Shape Memory Alloys 231 10.1.1 Underlying Mechanisms 232 10.1.2 Unique Engineering Effects 233 10.1.3 Alternate Shape Memory Alloy Options 237 10.2 Aerospace Applications of SMAs 238 10.2.1 Fixed-Wing Aircraft 239 10.2.2 Rotorcraft 245 10.2.3 Spacecraft 246 10.3 Characterization of SMA Actuators and Analysis of Actuator Systems 247 10.3.1 Experimental Techniques and Considerations 248 10.3.2 Established Analysis Tools 252 10.4 Conclusion 256 References 256 11 Hierarchical Control and Planning for Advanced Morphing Systems 261 Mrinal Kumar and Suman Chakravorty 11.1 Introduction 261 11.1.1 Hierarchical Control Philosophy 262 11.2 Morphing Dynamics and Performance Maps 264 11.2.1 Discretization of Performance Maps via Graphs 265 11.2.2 Planning on Morphing Graphs 270 11.3 Application to Advanced Morphing Structures 271 11.3.1 Morphing Graph Construction 273 11.3.2 Introduction to the Kagom´e Truss 275 11.3.3 Examples of Morphing with the Kagom´e Truss 277 11.4 Conclusion 279 References 279 12 A Collective Assessment 281 John Valasek 12.1 Looking Around: State-of-the-Art 281 12.1.1 Bio-Inspiration 281 12.1.2 Aerodynamics 281 12.1.3 Structures 282 12.1.4 Automatic Control 282 12.2 Looking Ahead: The Way Forward 282 12.2.1 Materials 282 12.2.2 Propulsion 283 12.3 Conclusion 283 Index 285