Controlled Autonomous Vehicle Drift Maneuvering Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Mohamed Lamine Kaba, B.S. Graduate Program in Electrical and Computer Engineering The Ohio State University 2019 Thesis Committee: Dr. Wei Zhang, Advisor Dr. Lisa Fiorentini c Copyright by Mohamed Lamine Kaba 2019 Abstract Drifting is an extreme maneuver which brings a vehicle into a relatively unstable and often hard to control configuration. Yet, it is an often necessary maneuver completed by profes- sional race car drivers; or to a limited extent, regular drivers aiming to regain control of their vehicle during bad road/weather conditions (e.g. vehicle skidding during snow). The study of autonomous vehicles during drifting can give insights into how to improve standard safety systems for both modern automobiles, as well as future autonomous vehicles, which must self-maneuver through such "obstacles". As complex as vehicle drifting is to maneuver, it is as complex (from a mathematical stand- point) to design drift trajectories/sequences for autonomous vehicles to track. The dynamic behavior of a vehicle during drifting is highly nonlinear; and nonlinear systems in general are typically hard to control. In this work, a set of scheduled linear controllers are used to give a vehicle the ability to autonomously drift itself about a globally planned path made using clothoids. This allows for the use of control methods such as LQR (Linear Quadratic Regulation) and PID (Proportional Integral Derivative) control in designing drift controllers capable of drifting and path following. The autonomous vehicle drifting algorithms are sim- ulated using MATLAB R /Simulink R . They are also tested on a modified 1:28 scale car, where a motion capture system is used for location tracking. Lastly, vehicle dynamics' system identification is covered in this work as well. ii This thesis is dedicated to my loving family. iii Acknowledgments I would like to express my gratitude to Prof. Zhang for having been my advisor over the course of this research, and for his teachings. His State-Space controls course solidified my interest in controls, and his approach to teaching the course (and in general) has funda- mentally changed the way in which I learn new information. I would also like to thank Prof. Fiorentini for taking time out of her schedule during a very busy week to be part of my thesis committee. Her feedback gave me a lot to think about in regards to future applications of this work. I would also like to thank Hao Yan for his collaboration on this project while he was completing his master's project. I enjoyed having a like-minded person to swap ideas with. Finally my mom, Oumou, for her endless sacrifices over the years which have allowed me to get where I am today. And to the rest of my family for their endless support of my endeavors. iv Vita December 2016 . B.S., Electrical and Computer Engineering, Ohio State University, Columbus, Ohio February 2017 - January 2018 . .Systems Engineer, Tata Consultancy Services, Auburn Hills, Michigan June 2018 - August 2018 . Research Assistant, Ohio State University, Columbus, Ohio Fields of Study Major Field: Electrical and Computer Engineering v Table of Contents Page Abstract........................................... ii Dedication......................................... iii Acknowledgments..................................... iv Vita.............................................v List of Figures ...................................... viii List of Tables .......................................x List of Abbreviations ..................................x Chapters 1 Introduction1 1.1 Background on Autonomous Vehicles...................... 1 1.1.1 The Need for Autonomous Vehicles................... 1 1.1.2 Levels of Autonomy ........................... 2 1.2 Motivation .................................... 4 1.3 Consulted Literature and Objective....................... 6 1.4 Thesis Work.................................... 9 1.5 Thesis Overview ................................. 10 2 Background Theory 11 2.1 Systems and Modeling Theory ......................... 11 2.1.1 Systems Theory ............................. 11 2.1.2 Systems Modeling ............................ 13 2.2 Modeling of Dynamical Systems......................... 14 2.2.1 Discretization............................... 16 2.3 Linear Systems.................................. 17 3 Vehicle Model 24 3.1 Vehicle Modeling Overview and Assumptions................. 27 3.2 Nonlinear Single Track Model Dynamics.................... 29 3.3 Tire Modeling................................... 32 3.3.1 Dugoff Tire Model............................ 35 3.3.2 Modified Fiala Tire Model........................ 36 3.4 Linear Vehicle Model............................... 40 vi 4 Control Systems Planning and Design 42 4.1 Path Trajectory Creation ............................ 42 4.2 Vehicle Dynamics Equilibrium.......................... 46 4.2.1 Equilibrium Analysis Overview..................... 46 4.2.2 Phase Portrait .............................. 51 4.3 Controls Overview ................................ 56 4.3.1 Tracking and Regulation......................... 56 4.4 Deviation Definitions and Control ....................... 61 4.4.1 Deviation Definitions........................... 61 4.4.2 Vehicle Controller ............................ 66 5 System Architecture and Identification 70 5.1 Vehicle Specifications............................... 71 5.2 Vehicle Architecture ............................... 73 5.3 System Identification............................... 78 5.3.1 Physical Parameters Identification ................... 81 5.3.2 Tire and Road Parameters Identification................ 83 5.3.3 Steering and Force Identification.................... 88 6 Experimentation 99 6.1 Simulation Overview............................... 99 6.2 Steady State Drifting............................... 101 6.3 Transient Drifting ................................ 103 7 Conclusion and Future Work 107 Bibliography 108 vii List of Figures Figure Page 1.1 Example of vehicle during drifting (Courtesy of: Borna Bevanda on Un- splash). ...................................... 5 1.2 Mixed open and closed loop transient drift [41]................. 7 1.3 Minimum time cornering through friction-circle acceleration planning [20].. 8 1.4 Steady state drifting (courtesy of [38])...................... 9 3.1 Vehicle inertial frame. Dashed line is parallel to x-axis of coordinate. 25 3.2 Vehicle's body frame. .............................. 26 3.3 Vehicle's tire frame contact patch. ....................... 26 3.4 Friction circle of longitudinal/lateral force Coupling ............. 33 3.5 Rear tire Fiala lateral force as critical slip angle, αcr, is varied. αcr;mx corre- sponds to maximum critical slip e.g. when ξ = 1................ 38 4.1 Generic clothoid map adapted from [24]. (Left) Path in x-y plane starting from origin. (Right) Curvature, κ, of path as arc length, s, increases.. 44 4.2 r and β over a sweep of steering angles, at Vx = 1:05 m=s........... 48 f r 4.3 Fy and Fy over a sweep of steering angles, at Vx = 1:05 m=s. 48 4.4 Longitudinal force equilibria over a sweep of steering angles, at Vx = 1:05 m=s. 49 ◦ 4.5 r−β phase dynamic when vx = 1:1 and δ = 5 , with marked equilibria. Red: Cornering, Blue: Counterclockwise drift, Green: Clockwise drift . 53 4.6 r and β fo Vx = 0:3; 0:6; 0:9 and 1:1 m=s. ................... 55 4.7 Combined path error (ela) and its components: orientation error (∆ ) and position error (e).................................. 65 4.8 Arbitrary clothoid map from 3 types of curvatures (straight, spiral and arc) 67 4.9 Vehicle control architecture............................ 68 5.1 Project's scaled vehicle (Side view)........................ 71 5.2 Project architecture................................ 73 5.3 Motive screenshot of OptiTrack system during object selection. 75 5.4 Three of 6 of our OptiTrack system's cameras. ................ 76 5.5 Vehicle center of mass balancing......................... 82 5.6 Raw OptiTrack data of vehicle location during a sample ramp steer maneuver. 85 viii 5.7 Yaw rate (r) estimated from OptiTrack yaw ( ) data. Blue: Finite difference estimation. Brown: Kalman filter estimation (using former).......... 85 5.8 Identified absolute front/rear lateral forces overlaid with Modified Fiala Model (Yellow), and cornering stiffness line (Orange). ............ 87 5.9 Identified force coefficients over multiple wr runs. Vertical line correspond to trimmed average of a given coefficient...................... 92 5.10 Vehicle trajectories at fixed steering signals versus fitted radius of trajectory. 94 5.11 Radius fit for multiple input Arduino signals (hence steering angles) super- imposed....................................... 94 5.12 Fit of Arduino signal ws to steering angle (degrees) using piece-wise linear and quadratic fit, respectively........................... 95 5.13 Less accurate linear fit of Arduino signal ws to steering angle (degrees). 96 6.1 Vehicle dynamics simulation. .......................... 100 6.2 Vehicle dynamics inner control system overview. 100 6.3 Vehicle model started near drifting equilibrium at open loop. 101 6.4 Induced vehicle drift................................ 102 6.5 Project's clothoid testing map. ......................... 103 6.6 Resulting vehicle drift in simulation....................... 104 6.7 Drifting test on scaled vehicle..........................