Automatic Steering Methods for Autonomous Automobile …

1 Automatic Steering Methods for AutonomousAutomobile Path TrackingJarrod M. SniderCMU-RI-TR-09-08 February 2009 Robotics InstituteCarnegie Mellon UniversityPittsburgh, Pennsylvaniac Carnegie Mellon UniversityAbstractThis research derives, implements, tunes and compares selected pathtracking Methods for controlling a car-likerobot along a predetermined path. The scope includes commonly used Methods found in practice as well as sometheoretical Methods found in various literature from other areas of research. This work reviews literature and identifiesimportant path tracking models and control algorithms from the vast background and resources.

2 This paper augmentsthe literature with a comprehensive collection of important path tracking ideas, a guide to their implementations and,most importantly, an independent and realistic comparison of the performance of these various approaches. Thisdocument does not catalog all of the work in vehicle modeling and control;only a selection that is perceived to beimportant ideas when considering practical system identification, ease ofimplementation/tuning and computationalefficiency. There are several other Methods that meet this criteria, however they are deemed similar to one or more ofthe approaches presented and are not included.

3 The performance results, analysis and comparison of tracking methodsultimately reveal that none of the approaches work well in all applications and that they have some complementarycharacteristics. These complementary characteristics lead to an idea thata combination of Methods may be useful formore general applications. Additionally, applications for which the methodsin this paper do not provide adequatesolutions are work would not have been possible without the support, motivation and encouragement of Dr. Chris Urmson,under whose supervision I chose this area of research.

4 I would like to acknowledge the advice and guidance of Red Whittaker, whom never ceases to amaze and inspire me. Special thanks go to Tugrul Galatali, whoseknowledge and assistance was instrumental in the success ofthis research and acknowledge Mechanical Simulation for their generous support and discount of CarSim. Without CarSim, qualityanalysis and comparison of tracking Methods may not have been would also like to thank the members of my family, especially my wife, Amy, and my son Xavier for supportingand encouraging me in everything I Design .. Change Course.

5 Eight Course .. Course ..52 Geometric Path Vehicle Model .. Pursuit .. the Pure Pursuit Controller .. Method .. the Stanley Controller ..153 Path Tracking Using a Kinematic Bicycle Model .. Coordinates .. Controller .. Form .. Time-Varying Feedback Control .. Scaling .. the Kinematic Controller ..254 Path Tracking Control Using a Dynamic Vehicle Model .. Dynamic Bicycle Model .. Coordinates .. Parameter Identification .. Control .. the Optimal Controller .. Control with Feed Forward Term .. the Optimal Controller with Feed Forward Term.

6 Preview Control .. the Optimal Preview Controller ..495 Performance Results ..616 Conclusions and Future Work65 VList of Figures1 Sandstorm ..12 Stanley ..13 Boss ..14 Screen shot from a CarSim animation ..35 Lane Change Course ..46 Figure Eight Course ..57 Road Course ..68 Velocity profiles used on theRoad Course..79 Geometric Bicycle Model ..810 Pure Pursuit geometry ..911 Pure Pursuit at multiple speeds and various gains on the lane change course ..1112 Pure Pursuit at multiple speeds and various gains on the figure eight course ..1213 Pure Pursuit at multiple velocity profiles and various gains on the road course.

7 1314 Stanley method geometry ..1415 Stanley controller at multiple speeds and various gains on the lane change course ..1516 Stanley controller at multiple speeds and various gains on the figure eight course ..1617 Stanley controller at multiple velocity profiles and various gains on the road course ..1718 Kinematic bicycle model ..1819 Kinematic bicycle model in path coordinates ..2120 Kinematic controller at multiple speeds and various gains on the lane change course ..2621 Kinematic controller at multiple speeds and various gains on the figure eight course.

8 2722 Kinematic controller at multiple velocity profiles and various gains on the road course ..2823 Dynamic Bicycle Model ..2924 Dynamic Bicycle Model in path coordinates ..3125 Example of lateral force tire data ..3426 Linear approximation of the lateral force tire data ..3427 LQR controller at multiple speeds and various gains on thelane change course ..3928 LQR controller at multiple speeds and various gains on thefigure eight course ..4029 LQR at multiple velocity profiles and various gains on the road course ..41VI30 LQR controller with feed forward term at multiple speeds and various gains on the lane change course4431 LQR controller with feed forward term at multiple speeds and various gains on the figure eight course4532 LQR controller with feed forward term at multiple velocity profiles and various gains on the road course 4633 Optimal preview controller with preview at multiplespeeds and various gains on the lane changecourse.

9 4934 Optimal preview controller with preview at multiplespeeds and various gains on the lane changecourse ..5035 Optimal preview controller with preview at multiplespeeds and various gains on the lane changecourse ..5136 Optimal preview controller with preview at multiplespeeds and various gains on the lane changecourse ..5237 Optimal preview controller with preview at multiplespeeds and various gains on the figure eightcourse ..5338 Optimal preview controller with preview at multiplespeeds and various gains on the figure eightcourse ..5439 Optimal preview controller with preview at multiplespeeds and various gains on the figure eightcourse.

10 5540 Optimal preview controller with preview at multiplespeeds and various gains on the figure eightcourse ..5641 Optimal preview controller with preview at multiplespeeds and various gains on the road course5742 Optimal preview controller with preview at multiplespeeds and various gains on the road course5843 Optimal preview controller with preview at multiplespeeds and various gains on the road course5944 Optimal preview controller with preview at multiplespeeds and various gains on the road course6045 Comparison of the tuned controllers on the lane change course.