The Interactions of Stance Width and Feedback Control Gain: A Modeling Study of Bipedal Postural Control A Dissertation Presented to The Academic Faculty by Jevin Eugene Scrivens In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Interdisciplinary Bioengineering Program School of Mechanical Engineering Georgia Institute of Technology August 2007 Copyright © 2007 by Jevin Eugene Scrivens The Interactions of Stance Width and Feedback Control Gain: A Modeling Study of Bipedal Postural Control Approved by: Dr. Stephen P. DeWeerth, Co-Advisor Dr. Young-Hui Chang Department of Biomedical Engineering School of Applied Physiology Georgia Institute of Technology Georgia Institute of Technology Dr. Lena H. Ting, Co-Advisor Dr. T. Richard Nichols Department of Biomedical Engineering School of Physiology Emory University and Georgia Institute of Emory University Technology Dr. Wayne J. Book School of Mechanical Engineering Georgia Institute of Technology Date Approved: June 28, 2007 ACKNOWLEDGMENTS I would like to thank a number of people who have supported me throughout my doctorial work. Thanks to my advisors Steve DeWeerth and Lena Ting, for encouraging me and helping me to form my research ideas. To my committee, Dr. Wayne Book, Dr. Young-Hui Chang, and Dr. Richard Nichols, whose direction and input was indispensable. I have also had the pleasure of working with many wonderful people in the Neuro Lab who have provided me with camaraderie, assistance, and advice: Kartik Sundar, Carrie Williams, Jim Ross, Shane Migliore, Richard Blum, Kate Williams, Gelsy Torres-Oviedo, Torrence Welch, Lucas McKay, Nate Bunderson, Amanda Pryor, Murat Sekerli, and Ivan Rikov. Thanks to Kunal Gosrani and Hugh Kinsel, for your many hours of labor, running thousands of robot trials. I would particularly like to thank Edgar Brown, Stefan Clemens, and Stacie Chevatal for being technical sounding boards and providing the critical support that I needed as I prepared this document. Special thanks to Malaika Kamunanwire, Aimee Lui-Thomas, Holly Neal, and Cherie Pimento, for helping to keep me sane with encouragement, motivation, laughs, and empathy. Thanks to my family, Mom, Dad, Jay, Janelle, Ted, Ann, and Kerry, whose support has been absolutely critical to my success. Most importantly, I would like to thank my wife, Diane, and my sons, Jevin and Justin, for being ……EVERYTHNG to me. TABLE OF CONTENTS Page ACKNOWLEDGMENTS ........................................................................................... iv LIST OF TABLES..................................................................................................... viii LIST OF FIGURES..................................................................................................... ix LIST OF SYMBOLS AND ABBREVIATIONS........................................................ xii SUMMARY ............................................................................................................... xiii CHAPTER 1: INTRODUCTION .................................................................................1 1.1 Background and Motivation.............................................................................2 1.1.1 Models of Standing Posture..........................................................................2 1.1.2 Models of Biological Control .......................................................................3 1.1.3 Observations of Biological Control of Posture..............................................5 1.1.4 Robot Control...............................................................................................7 1.2 Investigation Approach...................................................................................12 CHAPTER 2: MODEL SYSTEM DESIGN...............................................................15 2.1 System Design..................................................................................................15 2.1.1 Mechanical Component Design ..................................................................16 2.1.2 Controller Design.......................................................................................22 2.1.3 Simulation..................................................................................................24 2.1.4 Platform .....................................................................................................25 2.2 System Tuning and Calibration......................................................................25 2.2.1 Gain Tuning ...............................................................................................26 2.2.2 Compensation Tuning ................................................................................27 2.2.3 Simulation/Robot Comparison....................................................................28 2.3 System Validation ...........................................................................................30 2.3.1 Procedures..................................................................................................30 2.3.2 Analysis .....................................................................................................31 v 2.4 Results .............................................................................................................32 2.4.1 Mimicking the Cat Response......................................................................32 2.4.2 Effects of Stance Width Variation ..............................................................35 2.4.3 Effects of Feedback Gain Variation............................................................36 2.4.4 Effects of Feedback Delay Change.............................................................39 2.5 Summary and Discussion................................................................................40 CHAPTER 3: ACTIVE CONTROL WITH STANCE WIDTH VARIATIONS ......44 3.1 Dynamic Effects of Stance Width Variations.................................................44 3.1.1 Identification of Stabilizing Gain Regions ..................................................45 3.1.2 Analysis of Dynamic Responses.................................................................50 3.1.3 Evaluation of Performance Variation..........................................................55 3.2 Mechanics of Stance Width Variations ..........................................................58 3.2.1 Effective Inertia:.........................................................................................59 3.2.2 Displacement Ratio: ...................................................................................60 3.3 Effects of Stance Mechanics on the Active Dynamic Response.....................61 3.3.1 Resultant Mechanics of Stance Variation....................................................61 3.3.2 Delay Effects..............................................................................................63 3.4 Predictive Response Scaling ...........................................................................67 3.4.1 SWAG Factor.............................................................................................67 3.4.2 SWAG Implementation..............................................................................69 3.4.3 Mechanical Transfer Impedance.................................................................71 3.5 Summary and Discussion................................................................................78 CHAPTER 4: INTRINSIC STIFFNESS EFFECTS..................................................81 4.1 Stability Effects ...............................................................................................82 4.2 Dynamic Effects ..............................................................................................86 4.2.1 Addition of intrinsic stiffness......................................................................88 4.2.2 Replacement of active gain with intrinsic stiffness......................................94 4.3 Intrinsic with SWAG ......................................................................................98 vi 4.4 Discussion ......................................................................................................101 CHAPTER 5: DISCUSSION ....................................................................................103 5.1 Conclusions....................................................................................................103 5.1.1 Stability Range.........................................................................................103 5.1.2 Dynamic Response Variation ...................................................................104 5.1.3 Mechanical Leverage ...............................................................................104 5.1.4 Intrinsic Effects........................................................................................105 5.1.5 SWAG Function.......................................................................................105 5.2 Future Research Directions ..........................................................................106 5.3 Implications...................................................................................................107 5.3.1 Human/Animal Posture ............................................................................107 5.3.2 Robot Posture...........................................................................................108 APPENDIX A: AUTOLEV MODEL........................................................................110