Lateral Slip Prevention, Detection, and Recovery for High-Speed Autonomous Off-Road Driving Thesis by: Haomiao Huang In Partial Fulfillment of the Requirements For the Degree of Bachelor of Science California Institute of Technology Pasadena, California 2005 2 Acknowledgments I would like to thank Dr. Richard Murray for his patient guidance throughout this project, without which I would have been utterly lost. I would also like to thank Ole Balling of STI for providing me with the physics of how a car drives. I want to thank Lars Cremean for reading this thesis, and providing me with valuable feedback. I wish to thank the entire Caltech DARPA Grand Challenge team. Without their hard work on Alice and Bob, I would have no data to study and no research to do. Finally, I want to give a big shout out to Robbie Grogan, Laura Lindzey, and Jeff Lamb, who used their own precious spare time to see that I got to go out to the desert and take data, and then put up with my endless requests for “let’s do that one more time”. Thanks, guys! Haomiao Huang May 18th, 2005 3 Abstract Driving off paved roads presents many difficulties and challenges, and one of the chief among these is lateral wheel slip. Lateral slip is constantly present when driving off-road, but during sharp turns or over surfaces such as gravel or sand high slip can lead to sideways drift or even spinning the vehicle. Just as human drivers must be taught to handle sideslip, an autonomous controller for an off-road robot must also be designed with such conditions in mind. This paper presents an analysis of the conditions leading to high lateral slip and simulation results of a controller designed to minimize slip and prevent spinning out. Recorded data from an off-highway vehicle sliding under human control is also presented and analyzed. 4 Table of Contents 1 Introduction................................................................................................................. 7 1.1 Definition of Terms............................................................................................. 7 1.2 Slide Prevention.................................................................................................. 7 1.3 Detecting Lateral Slip and Sliding...................................................................... 8 1.4 Recovery from Sliding........................................................................................ 8 2 Background................................................................................................................. 9 2.1 Vehicle Dynamics & Modeling .......................................................................... 9 2.2 Sliding & Off-Road Driving ............................................................................. 14 3 Slide Detection.......................................................................................................... 17 3.1 Measurement of Wheel Slip Angles ................................................................. 17 3.2 Human Controlled Driving Data & Results...................................................... 17 3.2.1 Test Platform: Alice.................................................................................. 17 3.2.2 Test Data & Analysis................................................................................ 18 4 Slide Prevention........................................................................................................ 32 4.1 Trajectory Generation for Slip Prevention........................................................ 32 4.2 Throttle Control for Slip Prevention – Future Work ........................................ 34 5 Recovery from Sliding.............................................................................................. 35 5.1 PID Path Controller................................................................................................. 35 5.2 Simulation of a Skid Controller .............................................................................. 36 6 Conclusions & Future Work..................................................................................... 40 7 References...................................................................................................................... 41 5 Table of Figures Figure 1. Vehicle coordinate frame and variable definitions.............................................. 9 Figure 2. Vehicle dynamics diagram for dynamic bicycle model including tire forces... 10 Figure 5. Steering model verification on prior DGC Vehicle.......................................... 14 Figure 6. Simple slide during turn. .................................................................................. 14 Figure 7. Wheel velocity vectors demonstration. ............................................................ 15 Figure 8. Spinning or fishtail slide, coming out of turn................................................... 15 Figure 9. Maxing out friction circle................................................................................. 15 Figure 10. Alice ................................................................................................................ 18 Figure 11. Path of a single human driven turn used for data analysis .............................. 19 Figure 12. Rear slip angles of all sliding and non-sliding turns superimposed ............... 19 Figure 13. Slip angles and steering from a single sliding turn......................................... 20 Figure 14. Slip angles and steering from a single non-sliding turn ................................. 20 Figure 15. Body slip angles shown for a non-sliding turn............................................... 21 Figure 16. Body slip angles for a sliding turn.................................................................. 22 Figure 17. Rate of change of body slip angles for non-sliding turn. ............................... 23 Figure 18. Rate of change of body slip angles for a sliding turn.................................... 23 Figure 19. Yaw deviation of a non-sliding turn............................................................... 24 Figure 20. Yaw deviation of a sliding turn. ..................................................................... 25 Figure 21. Gaussian classifier.......................................................................................... 26 Figure 22. Gaussian representation of yaw deviation training data................................. 27 Figure 23. Selection criteria on yaw deviation. ............................................................... 28 Figure 24. Yaw deviation for a non-sliding turn.............................................................. 29 Figure 25. Yaw deviation and classification for a sliding turn........................................ 29 Figure 26. Another sliding turn........................................................................................ 30 Figure 27. Max sideslip angle for a range of lateral accelerations .................................. 32 Figure 28. Max sideslip for range of accelerations at lower friction............................... 33 Figure 29. Simulated run over a path at high speed......................................................... 33 Figure 30. Same path as previous, but at a lower speed to reduce lateral acceleration. .. 34 Figure 31. Lateral error of PID controller with vehicle running on asphalt .................... 36 Figure 32. Simulated turn without counter-steering controller........................................ 37 Figure 34. Simulated turn with counter-steering. ............................................................ 38 Figure 35. Errors for turn with counter steering. ............................................................. 39 6 1 Introduction Unwanted lateral motion is an important consideration when driving a car off road. Several kinds of conditions can occur, from a full 4-wheel slide (when the vehicle slides physically sideways) to over-steer-induced spinout, where the back wheels move sideways at a much higher speed than the front wheels, causing the vehicle to spin. Sliding occurs when the vehicle’s tires no longer grip the ground with sufficient force to prevent lateral motion. Such sliding usually occurs when high vehicle speeds are combined with a low surface coefficient of friction. A high frictional force is required to provide the lateral acceleration needed to corner at high speeds, and when tire forces are saturated the vehicle begins to slip sideways. The slide can also be caused by hitting a bump which lifts the vehicle’s tires off the ground, causing them to skid sideways. This can cause the vehicle to deviate substantially from a steered path or even spin out. These conditions can also give rise to high lateral velocities (at an angle perpendicular to the vehicle’s heading), causing tripped rollovers when the vehicle’s wheels hit an object such as a rock or a curb. These considerations are all common in off-road driving. Driving on dirt, gravel, and similar surfaces give a much lower coefficient of friction, thus reducing the amount of cornering force the tires can provide. There are bumps and dips in the road which can kick the wheels into a skid. Driving off-road also brings the vehicle in close proximity to rocks and other obstacles which can be avoided in normal driving but are highly dangerous if the vehicle spins or slides into them. The DARPA Grand Challenge, an off-road autonomous vehicle race, provides a unique opportunity to explore the problem of lateral slip.