Thiết kế, Mô hình hóa và Tối ưu Robot Mềm Sinh Học Tạo Lực Đẩy & Bơm Chất Lỏng

UNLV Theses, Dissertations, Professional Papers, and Capstones May 2018 The Design, Modeling, and Optimization of a Biomimetic Soft Robot for Fluid Pumping and Thrust Generation Using Electroactive Polymer Actuators Zakai Jedidiah Olsen Follow this and additional works at: https://digitalscholarship.edu/thesesdissertations Part of the Mechanical Engineering Commons Repository Citation Olsen, Zakai Jedidiah, "The Design, Modeling, and Optimization of a Biomimetic Soft Robot for Fluid Pumping and Thrust Generation Using Electroactive Polymer Actuators" (2018). UNLV Theses, Dissertations, Professional Papers, and Capstones.34917/13568638 This Thesis is protected by copyright and/or related rights. It has been brought to you by Digital Scholarship@UNLV with permission from the rights-holder(s). You are free to use this Thesis in any way that is permitted by the copyright and related rights legislation that applies to your use.

For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself. This Thesis has been accepted for inclusion in UNLV Theses, Dissertations, Professional Papers, and Capstones by an authorized administrator of Digital Scholarship@UNLV. For more information, please contact digitalscholarship@unlv. THE DESIGN, MODELING, AND OPTIMIZATION OF A BIOMIMETIC SOFT ROBOT FOR FLUID PUMPING AND THRUST GENERATION USING ELECTROACTIVE POLYMER ACTUATORS By Zakai J.

Olsen Bachelor of Science in Engineering – Mechanical Engineering University of Nevada, Las Vegas 2016 A thesis submitted in partial fulfillment of the requirements for the Master of Science in Engineering – Mechanical Engineering Department of Mechanical Engineering Howard R. Hughes College of Engineering The Graduate College University of Nevada, Las Vegas May 2018 Thesis Approval The Graduate College The University of Nevada, Las Vegas April 13, 2018 This thesis prepared by Zakai J. Olsen entitled The Design, Modeling, and Optimization of a Biomimetic Soft Robot for Fluid Pumping and Thrust Generation Using Electroactive Polymer Actuators is approved in partial fulfillment of the requirements for the degree of Master of Science in Engineering – Mechanical Engineering Department of Mechanical Engineering Kwang Kim, Ph. Kathryn Hausbeck Korgan, Ph.

Examination Committee Chair Graduate College Interim Dean Mohamed Trabia, Ph. Examination Committee Member Woosoon Yim, Ph. Examination Committee Member Rebecca Martin, Ph. Graduate College Faculty Representative ii Abstract Nature is a constant source of inspiration for engineers and scientists through its simple, effective, and elegant solutions to many complex problems.

Smart materials and soft robotics have been seen to be particularly well suited for developing biomimetic devices and are active fields of research. In this study, the design, modeling, and optimization of a new biomimetic soft robot is described. Preliminary work was made in the modeling of a biomimetic robot based on the locomotion and kinematics of jellyfish. Modifications were made to the governing equations for jellyfish locomotion that accounted for geometric differences between biology and the robotic design.

Particularly, the capability of the model to account for the mass and geometry of the robot design. A simple geometrically defined model is developed and used to show the feasibility of a proposed biomimetic robot. With the concept verified, a more robust physics- based model is developed. In this model, linear beam theory is coupled to an equivalent circuit model to actuate the robot with ionic polymer-metal composite (IPMC) actuators.

The circuit model is verified using a robust, Multiphysics finite element model of the IPMC actuator. The newly created physics-based model of the soft robot is compared to that of the geometric model as well as biological jellyfish swimming to highlight its improved efficiency. The design is then optimized using a sequential quadratic programming algorithm for nonlinear multivariable optimization. Standard deviations of the optimized values are used to verify their accuracy, and the propulsion efficiency of the unoptimized and optimized model are compared to verify the improvement in efficiency and overall performance.

Scale effects on the optimal design are also examined as an initial form of dimensional analysis. The optimized design shows clear improvement over the unoptimized counterpart, and the modularity of the modeling approach allows for more complex models that include nonlinearities to be easily added. iii Acknowledgements I would like to thank my advisor, Dr. Kwang Kim, for his immense support and advice throughout my undergraduate and graduate studies.

His mentorship, teaching, financial support, research guidance, and amazing travel opportunities given to me have greatly shaped my career as an engineer and researcher. I am profoundly grateful for Dr. Kim’s generosity and interest invested in these many areas of my life, all of which have helped lead me to graduating at this time. I would also like to thank committee members, Dr.

Mohamed Trabia, Dr. Woosoon Yim, and Dr. Rebecca Martin for their teaching and advice during my career at UNLV. I truly appreciate their time and interest spent on my studies and development as a researcher.

All of the faculty and staff who have had such a positive impact on me throughout my time at UNLV are very much appreciated and my sincere thanks go to each of them. The incredible professors I have studied under have given me the education necessary to pursue a graduate career, and beyond. I would like to specifically thank Joan Conway for all her incredible assistance, encouragement, and support. All my colleagues in the AMSL lab who helped me throughout my graduate studies are well-deserving of my thanks.

Their advice and support are greatly appreciated, equally as much as their friendship. I also thank the National Science Foundation PIRE program and the Nevada NASA Space Grant Consortium for the funding and support for my graduate research. Finally, an acknowledgement of warmhearted gratitude for my friends and family. Their continual support of my academic and professional endeavors has helped me stay focused and level-headed.

I particularly give special thanks to my younger brother, Luke Olsen, for always being there to give his advice and perspective whenever I needed it. iv Table of Contents Abstract. iv List of Tables. vii List of Figures.

Kinematics of Swimming Jellyfish. Derivation of Governing Equations. Modeling of Jellyfish Locomotion. Design Principle of a Biomimetic Jellyfish.

Electromechanical Modeling of Ionic Polymer-Metal Composite Actuators. Physics-Based Modeling. Governing Partial Differential Equations. Multi-Physics Modeling in COMSOL.

Equivalent Circuit Modeling. RCW Circuit Model. Comparison and Utility of Modeling Approaches. Modeling of a Biomimetic Soft Robot.

Governing Equation and Model Inputs. Geometry Based Modeling. Description of Robot Body as Geometric Surface. Derivation of Model Parameters.

Comparison to Biological Jellyfish. Physics-Based Modeling. Beam Theory Approach. Derivation of Model Parameters.

Addition of IPMC Electromechanical Effects. Evaluation and Comparison to Previous Model. Sequential Quadratic Programming Optimization. Selection of Design Variables.

Optimization of Design Variables. Comparison of Unoptimized and Optimized Design. Scale Effects on Optimal Parameter Values. Fabrication of Prototype.

Structure of Future Experimental Study. Additions to Physics-Based Model. 88 Appendix A: Additional Figures of COMSOL Domains and Mesh. 89 Appendix B: Coefficients for Volume and Cross-Sectional Area in Physics-Based Model.

105 vi List of Tables Table 3.1 Model parameters for 2D vs 1D PNP Comparison.2 Metrics for 1D vs 2D PNP Comparison .3 Metrics for 1D vs Refined 1D PNP Comparison.4 Parameters and Dimensions of IPMC Used for Experimental Comparison .5 Parameter Values for Equivalent Circuit Model.1 Direction Cosine Angles for Inlet and Outlet During Different Swimming Modes .2 Beam Geometry and Loading for COMSOL Comparison .3 Physics-Based Model Comparison Parameters .1 Simulation Parameters for IPMC Length Optimization .2 Simulation Parameters for Pairwise Optimization.3 Parameter Values for Unoptimized and Expected Optimal Designs .4 Parameters for SQP Optimization of Design Variables.5 Results of SQP Optimization .6 Propulsion Efficiency for Unoptimized and Optimized Models .7 Results of Optimization with Scaled Shell Radius. 77 vii List of Figures Figure 2.1 Illustration of Jet Propulsion Mechanism Found in Biological Jellyfish .2 Illustration of Jellyfish Body Structure .3 Free Body Diagram of Swimming Jellyfish .4 Position, Velocity, and Acceleration of Biological Jellyfish .5 Illustrative Cross-Section of Proposed Soft Robot Design .1 Cantilever IPMC Diagram for COMSOL Multiphysics Modeling .2 COMSOL Domain for 1D PNP FEM .3 Domain for 2D Solid Mechanics in COMSOL.4 Comparison of 1D and 2D PNP Models .5 Differences in 1D Domain Structures Used in COMSOL .6 Comparison of 1D and Refined 1D PNP Models .7 Unconstrained IPMC Deformation Under External Stress Loading.8 Comparison Between Refined 1D COMSOL Model and Experimental Data .9 Circuit Diagram Used for Equivalent Circuit IPMC Model .10 Comparison Between RCW Circuit Model and Experimental Data .11 Comparison of FEM, Equivalent Circuit, and Experimental IPMC Deflection .1 Illustration of Direction Cosine for Inlet and Outlet Valves.2 Representative Waveforms Generated with Fourier Series Square Wave.3 Geometric Description of Robot Body as an Ellipsoid.4 Drag Coefficient as a Function of Reynold’s Number .5 Input Half-Axis Dimension for Geometric Model, 1000th Partial Sum Input .6 Simulation of Geometric Model with Various Inputs and Swimming Modes .7 Thrust Profile for Geometric Model in Both Swimming Modes .8 Diagram of Physics-Based Description of Robot Body .9 Illustrative Cross-Section of Proposed Physics-Based Model .10 Comparison of Beam Theory to FEM Implementation .11 Error of Straight Beam Assumption .12 RCW Model Charge Response for Fourier Series Input .13 Comparison of Physics-Based Model to Geometric and Jellyfish Models.14 Thrust Profile for Physics-Based Model .15 Mass Flux for Physics-Based Model .16 Velocity Profiles for Fluid Pump Operation .1 Distance vs IPMC Length .2 Surface Plot of Distance vs Length and Contraction Time.3 Surface Plot of Distance vs Length and Time Ratio .4 Surface Plot of Distance vs Time Ratio and Contraction Time .5 Probability Density Function: IPMC Length .6 Probability Density Function: Time Ratio .7 Probability Density Function: Contraction Time.8 Comparison of Unoptimized and Optimized Models: Distance Traveled .9 Velocity Profiles for Efficiency Calculation.10 Optimized IPMC Length Versus Radius of Shell .11 Optimized Time Ratio Versus Radius of Shell .12 Optimized Contraction Time Versus Radius of Shell.1 Engineering Sketch of Prototype Mold Design .2 Second Mold Design CAD Image .3 First 3D Printed Mold .4 Second 3D Printed Mold.5 Current Status of Elastomer Prototype Body .1 Finite Element Mesh for 2D PNP Domain .2 Enhanced View of Figure A.3 Finite Element Mesh of 2D Solid Mechanics Domain .4 Enhanced View of Figure A.5 Finite Element Mesh of 1D PNP Domain.6 Enhanced View of Figure A.5, Electrode-Polymer Interface .7 Enhanced View of Figure A.5, Membrane-Membrane Interface .8 Finite Element Mesh of 2D Solid Mechanics Domain for 1D PNP Modeling.9 Enhanced View of Figure A. 91 x Nomenclature 𝐴𝐴𝑣𝑣 Velar / valve aperture area (m2) 𝐺𝐺 Acceleration reaction (N) 𝛼𝛼ℎ Hydrofilicity coefficient ℎ Bell height (m) (N-m/mol) ℎ𝑡𝑡 Integrator time step (s) 𝛼𝛼𝐴𝐴𝐴𝐴 Added mass coefficient 𝐼𝐼 Moment of inertia (m4) 𝛼𝛼𝑅𝑅𝑅𝑅𝑅𝑅 Hydrofilicity coefficient for 𝐽𝐽 Cation flux (mol/m3-s) circuit model (N/m-C) 𝜅𝜅 Bending strain (1/m) 𝛼𝛼𝑐𝑐 Hydrofilicity coefficient in 𝐿𝐿𝑐𝑐 Characteristic length (m) COMSOL (N/C) 𝑚𝑚 Mass of jellyfish / robot (kg) 𝛼𝛼 Starting polar angle 𝜇𝜇 Cation mobility (s-mol/kg) 𝛽𝛽ℎ Hydrofilicity coefficient 𝑁𝑁𝑤𝑤 Number of shape functions (N-m4/mol2) 𝑵𝑵𝒔𝒔 Vector of shape functions 𝛽𝛽 Ending polar angle 𝑵𝑵𝜻𝜻 Vector of nondimensional shape 𝐶𝐶𝑑𝑑 Drag coefficient functions 𝑐𝑐0 Anion concentraction (mol/m3) 𝜈𝜈 Kinematic viscosity of water 𝐶𝐶 Stiffness tensor (Pa) (m2/s) 𝑐𝑐 Cation concentration (mol/m3) 𝑂𝑂𝐺𝐺 Order of gauss quadrature 𝐷𝐷𝑒𝑒 Electric displacement (C/m2) 𝑃𝑃𝑤𝑤 Transverse loading (N/m) 𝐷𝐷𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 Drag force of jellyfish / robot 𝜙𝜙 Electric potential (V) (N) 𝑄𝑄 Charge in IPMC (C) 𝛿𝛿𝑖𝑖 Perturbation of ith SQP variable 𝜌𝜌𝑤𝑤 Density of water (kg/m2) 𝛿𝛿𝑡𝑡 Time ratio 𝜌𝜌𝑐𝑐 Charge density (C/m3) 𝐷𝐷 Cation diffusivity (m2/s) 𝜌𝜌𝑚𝑚 Material density (kg/m3) 𝑑𝑑𝑑𝑑 Volume change for jellyfish 𝑅𝑅𝑅𝑅 Reynold’s number swimming model (m3) 𝑟𝑟 Instantaneous bell radius (m) 𝐸𝐸�⃗ Electric field strength (N/C) 𝜌𝜌 Radius of curvature (m) 𝜀𝜀0 Dielectric constant in vacuum 𝑆𝑆0 Initial cross-sectional area (m2) (F/m) 𝑆𝑆𝐴𝐴 Cross-sectional area w.