Robust Estimation of Road Friction Coefficient for Vehicle Active Safety Systems by Chang Sun Ahn A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical Engineering) in The University of Michigan 2011 Doctoral Committee: Professor Huei Peng, Chair Professor Timothy J. Gordon Professor Jeffrey L. Stein Assistant Professor Ryan M. Eustice © Chang Sun Ahn 2011 ACKNOWLEDGEMENTS First and foremost I would like to express my gratitude to my advisor, Huei Peng, for his guidance, support, and motivation throughout my doctoral study. Without his encouragement, this dissertation and my doctoral study would not have been possible. I would also like to thank my committee members: Professor Timothy J. Gordon, Professor Jeffrey L. Stein, and Professor Ryan M. Eustice. Their advice and comments were greatly helpful to complete this dissertation. I gratefully acknowledge the support from Ford Motor Company through the Ford-University of Michigan Innovation Alliance Project program. Particularly, my gratitude goes to Dr. H. Eric Tseng for his guidance, insights into vehicle dynamics, and care for my personal development. In addition, I would like to thank Mitch McConnell at Ford Motor Company for his assistance in the vehicle winter test. My colleagues at the University of Michigan’s Vehicle Dynamics Lab (VDL) have been crucial part of my life at Ann Arbor. Many thanks for the unforgettable years to my friends: Chiao-Ting Li, Sean Yang, Jongwha Yoon, Youseok Kou, William Smith, Shenbo Li, Byung-Joo Kim, and Tianyou Guo. Finally, I would like to express my loving appreciation to my wife, Yeon Kim, and my mother. Their sustained love and support made this work possible. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS ................................................................................................ ii LIST OF FIGURES ........................................................................................................... vi LIST OF TABLES ........................................................................................................... xiii LIST OF SYMBOLS ....................................................................................................... xiv ABSTRACT ..................................................................................................................... xvi CHAPTER 1 Introduction................................................................................................... 1 1.1 Motivation ................................................................................................................ 1 1.2 Problem Description ................................................................................................ 2 1.3 Literature Review ..................................................................................................... 3 1.3.1 Vision/Temperature Based Methods ............................................................... 4 1.3.2 Tire Tread Based Methods .............................................................................. 5 1.3.3 Wheel Dynamics Based Methods ................................................................... 5 1.3.4 Vehicle Dynamics Based Methods ................................................................. 6 1.3.5 Tire Self-Aligning Moment Based Methods ................................................... 7 1.3.6 Summary ......................................................................................................... 7 1.4 Objective, Approaches, and Scope of Study ............................................................ 8 1.5 Contributions ............................................................................................................ 9 CHAPTER 2 System Models............................................................................................ 11 2.1 Vehicle Lateral Dynamics Model .......................................................................... 11 2.1.1 Vehicle Model on a Level Road.................................................................... 11 2.1.2 Vehicle Model on a Banked Road ................................................................ 13 2.1.3 Load Transfer Model..................................................................................... 14 2.2 Vehicle Longitudinal Dynamics Model ................................................................. 15 2.3 Tire Model .............................................................................................................. 16 2.4 Steering System Model .......................................................................................... 22 2.4.1 Tire Self-Aligning Moment Observer ........................................................... 24 iii CHAPTER 3 Lateral Dynamics Based Estimation ........................................................... 26 3.1 Estimation Algorithm for Large Lateral Excitation ............................................... 26 3.1.1 Maximum Self-Aligning Moment Detection ................................................ 26 3.1.2 Simulation Results ........................................................................................ 27 3.2 Estimation Algorithm for Medium Lateral Excitation ........................................... 29 3.2.1 Nonlinear Least Squares Method .................................................................. 30 3.2.2 Dynamic Approach ....................................................................................... 40 3.3 Summary ................................................................................................................ 67 CHAPTER 4 Longitudinal Dynamics Based Estimation ................................................. 69 4.1 Phenomena in the Tire Contact Patch .................................................................... 72 4.1.1 Tire Longitudinal Force in the Linear Range ................................................ 72 4.1.2 Phenomena in the Tire Contact Patch ........................................................... 74 4.1.3 Modeling of Stress/Deformation Distribution in the Contact Patch ............. 77 4.1.4 Factors Affecting Longitudinal Force Generation ........................................ 82 4.2 Estimation of Friction Coefficient in the Linear Range (0-2%) ............................ 86 4.2.1 Algorithm ...................................................................................................... 86 4.2.2 Simulations .................................................................................................... 89 4.3 Estimation of Friction Coefficient in the Saturation Range (30~100%) ................ 91 4.3.1 Algorithm ...................................................................................................... 91 4.3.2 Simulations .................................................................................................... 93 4.4 Summary ................................................................................................................ 95 CHAPTER 5 Integrated Friction Estimation Algorithm .................................................. 96 5.1 Increasing Coverage of the Lateral Dynamics Based Methods ............................. 97 5.2 Integration of the Estimators ................................................................................ 103 5.3 Simulations ........................................................................................................... 108 CHAPTER 6 Experimental Validation ........................................................................... 115 6.1 Experimental Vehicle ........................................................................................... 115 6.2 Model Identification and Validation .................................................................... 118 6.2.1 Vehicle and Tire Parameter Identification .................................................. 118 6.2.2 Steering System Parameter Identification ................................................... 120 6.3 Validation of the Lateral Dynamics Based Algorithm ......................................... 123 iv 6.3.1 Observer with King-pin Moment Measurement ......................................... 123 6.3.2 Experimental Validation ............................................................................. 124 6.4 Validation of the Longitudinal Dynamics Based Algorithm ............................... 128 6.5 Validation of the Integrated Algorithm ................................................................ 131 CHAPTER 7 Conclusion and Direction for Future Research ........................................ 135 7.1 Conclusion ........................................................................................................... 135 7.2 Directions for Future Research ............................................................................ 136 APPENDICES ................................................................................................................ 138 BIBLIIOGRAPHY ......................................................................................................... 140 v LIST OF FIGURES Figure 1.1 Friction circle of a tire [2].......................................................................... 2 Figure 1.2 Tire force/moment characteristics [5]........................................................ 3 Figure 1.3 Classification of friction coefficient estimation algorithms ...................... 4 Figure 2.1 Vehicle bicycle model ............................................................................