TRAJECTORY PLANNING AND CONTROL FOR AN A
TRAJECTORY PLANNING AND CONTROL FOR ANAUTONOMOUS RACE VEHICLEA DISSERTATIONSUBMITTED TO THE DEPARTMENT OF MECHANICALENGINEERINGAND THE COMMITTEE ON GRADUATE STUDIESOF STANFORD UNIVERSITYIN PARTIAL FULFILLMENT OF THE REQUIREMENTSFOR THE DEGREE OFDOCTOR OF PHILOSOPHYNitin R. KapaniaMarch 2016
2016 by Nitin Rakesh Kapania. All Rights Reserved.Re-distributed by Stanford University under license with the author.This work is licensed under a Creative Commons AttributionNoncommercial 3.0 United States 3.0/us/This dissertation is online at: http://purl.stanford.edu/gp933pt4922ii
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.J Gerdes, Primary AdviserI certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.Mykel KochenderferI certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.Allison OkamuraApproved for the Stanford University Committee on Graduate Studies.Patricia J. Gumport, Vice Provost for Graduate EducationThis signature page was generated electronically upon submission of this dissertation inelectronic format. An original signed hard copy of the signature page is on file inUniversity Archives.iii
For my dad.iv
AbstractAutonomous vehicle technologies offer potential to eliminate the number of trafficaccidents that occur every year, not only saving numerous lives but mitigating thecostly economic and social impact of automobile related accidents. The premise behind this dissertation is that autonomous cars of the near future can only achieve thisambitious goal by obtaining the capability to successfully maneuver in friction-limitedsituations. With automobile racing as an inspiration, this dissertation presents andexperimentally validates three vital components for driving at the limits of tire friction. The first contribution is a feedback-feedforward steering algorithm that enablesan autonomous vehicle to accurately follow a specified trajectory at the friction limits while preserving robust stability margins. The second contribution is a trajectorygeneration algorithm that leverages the computational speed of convex optimizationto rapidly generate both a longitudinal speed profile and lateral curvature profile forthe autonomous vehicle to follow. While the algorithm is applicable to a wide varietyof driving objectives, the work presented is for the specific case of vehicle racing,and generating minimum-time profiles is therefore the chosen application. The finalcontribution is a set of iterative learning control and search algorithms that enableautonomous vehicles to drive more effectively by learning from previous driving maneuvers. These contributions enable an autonomous Audi TTS test vehicle to drivearound a race circuit at a level of performance comparable to a professional humandriver. The dissertation concludes with a discussion of how the algorithms presentedcan be translated into automotive safety systems in the near future.v
AcknowledgmentMy dad has been my biggest role model for as long as I can remember, dating backto when I was three or four and liked to copy everything he did. There’s a picture wehave back home where my dad is shaving before work, and there I am standing next tohim with shaving cream all over my face, trying to imitate him with a (hopefully) fakerazor my mom gave me. I think it was in middle school when I first comprehendedhow smart my dad was, just based on the kinds of books he had in his office at workand home. I would sometimes open one up just to see the fancy math symbols, whichwere like a beautiful foreign language to me. Wanting to be like him is probably thenumber one reason I went to an engineering school for undergrad and definitely amajor reason why I decided to do a PhD. But he’s a statics guy, dealing primarilywith structures that really should not move too much. Sorry dad, but I’ve alwaysfound dynamics a little more exciting, and cars are just more beautiful than planes ;)The rest of my family is pretty awesome too. My younger sister Esha has anenormous heart and in her words, is the “glue” that holds our family together. WhileI would like her to spend a little less time studying in med school and more time outand about in Chicago, I always look forward to catching up with her. My youngestsister Rhea has been gifted with a sense of humor very similar to mine, and eventhough she is eight years younger than me, we have a blast playing video games,quoting Mean Girls, and constantly teasing Esha. Finally, my mom has been thebest mom a son could have, and has supported me even though she was very sadwhen her “bestest” decided to move across the country to California. Whenever Ivisit home, I always get to pick what the family eats for dinner and I always get fedfirst, much to my sisters’ dismay.vi
Academically and professionally, I owe a lot to my advisor Chris Gerdes. Dedicating an entire lab to automotive research is very difficult given the cyclical natureof the automotive industry. Nevertheless, he has established one of the strongestautomotive research labs in the country, and it has been amazing to be a part ofhis program’s growth over the last five years. My favorite interactions with Chriscame during our research trips to the Thunderhill race course. At the race track,he was always eager sit in the car with me while I tested my research ideas, offeringinsights and perspectives that he has developed over 25 years working with cars. Inthe evening, it was great to relax after a long day of data collection and brainstormideas to try for the next day. I occasionally had the chance to drive home with Chris,and I always enjoyed our conversations about everything from the stock market toStanford football. It was during these conversations that I realized Chris’ passion forautomobiles is exceeded only by his dedication to his family, and that has had a bigimpact on me.I also owe Chris for choosing a great bunch of people for me to work with. TheDynamic Design Lab is a diverse collection of highly intelligent people from all overthe place, both geographically and personally. Some of my closest connections atStanford have been with members of the DDL, and I will always remember our happyhours, celebrations, and send-off parties as some of the best times I have had here.One thing I’ve learned while here is that members of our lab form a small but outsized network of close friends and future colleagues that remains in place long aftergraduation. In addition to being great friends and colleagues, members of the DDLare great sources of knowledge, and the ideas that are generated in the lab every dayprovide a great headwind for doing amazing research.There are a few people I have worked with that I would like to acknowledgepersonally. John Subosits, Vincent Laurense, Paul Theodosis, Joe Funke and KrisadaKritiyakirana have all been great colleagues on the Audi-Stanford racing project,and have spent many hours of their own time helping me with the significant datacollection effort required for this dissertation. Additionally, I am grateful to havehad the help of Samuel Schacher and John Pedersen during the summers of 2014and 2015. I would also like to thank members of the Audi Electronics Researchvii
Laboratory, especially Rob Simpson and Vadim Butakov, for being great resourceswith our experimental Audi TTS testbed. In my time here, we have managed tobreak what seems like every component of the car at least once and went through amajor overhaul of the control electronics and firmware. Rob and Vadim were thereevery time we needed them, and we never had to miss a testing a trip due to a repairthat was not performed on time. Finally, it takes a lot of staff working behind thescenes to do great research, and I would like to thank Erina and Jo for the great jobthey have done over the last two years.I also would like to thank Dr. Mykel Kochenderfer and Dr. Allison Okamura forhelping me strengthen this dissertation. Allison started at Stanford in 2011 just as Idid, and I’ve always felt that I could go to her for anything I needed help with. I alsobecame friends with many of her students in the CHARM lab, and it was great to relaxwith them during design group happy hours. Dr. Kochenderfer arrived at Stanfordduring my fourth year, and has not only helped me structure my thesis contributionsclearly and concisely, but has become a welcome addition to the autonomous vehicleprogram at Stanford.And finally, where would I be without my lovely girlfriend Margaret? I met Margaret during my first year as a graduate student, and she has been a great companionover the last four years as we have explored graduate life and the Bay Area together.Margaret likes to say that she followed me into doing a PhD, but the truth is that Ihave been following her for a lot longer. Margaret is a true believer in enjoying theeveryday beauty of life, and has showed me me how to enjoy things as simple as goingon a hike, relaxing with her newly adopted cat, or more recently, eating at the sameburger joint every single Saturday night ;) I’m not sure what my life will be like afterI leave Stanford, but I know Margaret will be a significant part of it, and that makesme feel A-OK.viii
ContentsAbstractvAcknowledgmentvi1 Introduction1.11Driving at the Handling Limits . . . . . . . . . . . . . . . . . . . . .1.1.1Exceeding the Friction Limits: Understeer andOversteer . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.21.31.424Race Car Driving as Inspiration forAutonomous Safety Systems . . . . . . . . . . . . . . . . . . . . . . .5State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71.3.1Autonomous Race Vehicles . . . . . . . . . . . . . . . . . . . .71.3.2Automated Steering at the Limits of Handling . . . . . . . . .81.3.3Time-Optimal Trajectory Planning . . . . . . . . . . . . . . .91.3.4Iteration-Based Learning . . . . . . . . . . . . . . . . . . . . .11Research Contributions and Outline . . . . . . . . . . . . . . . . . . .122 Feedforward-Feedback Steering Controller162.1Path Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . .192.2Controller Architecture . . . . . . . . . . . . . . . . . . . . . . . . . .202.2.1Feedforward Steering Design . . . . . . . . . . . . . . . . . . .202.2.2Feedback Steering Design . . . . . . . . . . . . . . . . . . . .26Predicted Steady-State Path Tracking Error . . . . . . . . . . . . . .272.3ix
2.4Incorporating Sideslip-Path Tangency intoSteering Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.52.62.731Incorporating Sideslip Information IntoSteering Feedforward . . . . . . . . . . . . . . . . . . . . . . . . . . .35Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . .372.6.137Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . .Experimental Testing of Sideslip FeedbackController . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .412.8Experimental Data from Racetrack . . . . . . . . . . . . . . . . . . .432.9Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .483 Fast Generation Path Planning493.1Path Description and Vehicle Model . . . . . . . . . . . . . . . . . . .3.2Velocity Profile Generation Given Fixed3.33.453Reference Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55Updating Path Given Fixed Velocity Profile . . . . . . . . . . . . . .583.3.1Overall Approach and Minimum Curvature Heuristic . . . . .583.3.2Convex Problem Formulation . . . . . . . . . . . . . . . . . .59Algorithm Implementation and SimulatedResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .633.4.1Algorithm Implementation . . . . . . . . . . . . . . . . . . . .633.4.2Algorithm Validation . . . . . . . . . . . . . . . . . . . . . . .653.4.3Comparison with Other Methods . . . . . . . . . . . . . . . .653.4.4Lap Time Convergence and Predicted Lap Time . . . . . . . .693.5Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . .733.6Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . .743.7Incorporating the Effect of Distance Traveled . . . . . . . . . . . . . .773.7.1Balancing Minimum Distance and Curvature . . . . . . . . . .783.7.2Using Human Driver Data to Obtain Optimization3.7.3Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80Combined Cost Function and Simulated Results . . . . . . . .82x
3.8Discussion and Future Work . . . . . . . . . . . . . . . . . . . . . . .853.9Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .874 Iterative Learning Control884.1Dynamic System Model . . . . . . . . . . . . . . . . . . . . . . . . .4.2Lifted Domain Representation and ILCProblem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . .92984.3Proportional-Derivative Controller . . . . . . . . . . . . . . . . . . . . 1004.4Quadratically Optimal Controller . . . . . . . . . . . . . . . . . . . . 1034.5Simulated Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.6Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.7Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145 Learning the Optimal Speed Profile1155.1Effect of Tire Slip Norm on Lap Time . . . . . . . . . . . . . . . . . . 1175.2Naive Method: Greedy Algorithm . . . . . . . . . . . . . . . . . . . . 1215.3Framing Trajectory Learning as SearchProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.4A* Search Algorithm and Heuristic . . . . . . . . . . . . . . . . . . . 1285.5A* Implementation and Results . . . . . . . . . . . . . . . . . . . . . 1295.6Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . 1335.7Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1365.8Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376 Conclusion1386.1Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.2Applications for Future Automotive SafetySystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Bibliography145xi
List of Tables2.1Bicyle Model Definitions . . . . . . . . . . . . . . . . . . . . . . . . .212.2Vehicle Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . .383.1Optimization Parameters . . . . . . . . . . . . . . . . . . . . . . . . .653.2Lap Times in Seconds . . . . . . . . . . . . . . . . . . . . . . . . . .753.3Iteration Computation Time . . . . . . . . . . . . . . . . . . . . . . .854.1Vehicle Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.1Uk (µ) and Zk (µ) for k 191 . . . . . . . . . . . . . . . . . . . . . . . 1235.2Search Algorithm Information . . . . . . . . . . . . . . . . . . . . . . 1295.3Lap Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131xii
List of Figures1.1Driving at the limits . . . . . . . . . . . . . . . . . . . . . . . . . . .31.2Understeer and Oversteer . . . . . . . . . . . . . . . . . . . . . . . .41.3Audi’s autonomous RS7 . . . . . . . . . . . . . . . . . . . . . . . . .82.1Path coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . .192.2Block diagram of feedback-feedforward steering controller. . . . . . .202.3Schematic of planar bicycle model . . . . . . . . . . . . . . . . . . . .222.4Projection of lateral error at distance xp in front of the center of gravity. 242.5Nonlinear tire curves for FFW steering. . . . . . . . . . . . . . . . . .262.6Schematic of planar bicycle model showing projected lookahead error.272.7Steady-state path tracking error e, sideslip β and heading deviation Ψ as a function of vehicle speed. . . . . . . . . . . . . . . . . . . . .2.8Steady-state cornering where vehicle has lateral error but no lookaheaderror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.92930Zero steady-state lateral deviation requires vehicle velocity vector tobe tangent to path. . . . . . . . . . . . . . . . . . . . . . . . . . . . .312.10 Steady-state simulation results with sideslip added to feedback control322.11 Closed-loop pole locations for steering system as vehicle speed is variedfrom 5 to 25 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . .332.12 Maximum speed for closed-loop stability for the original lookaheadfeedback and the modified feedback with sideslip tracking. . . . . . .342.13 Effect of incorporating sideslip behavior into feedforward steering command δFFW , as a function of vehicle speed and desired path curvature.362.14 Audi TTS used for experimental validation. . . . . . . . . . . . . . .37xiii
2.15 Diagram showing controller setup. . . . . . . . . . . . . . . . . . . . .382.16 Curvature and velocity profile inputs for steering controller as a function of distance along racing line. . . . . . . . . . . . . . . . . . . . .392.17 Desired path for steering controller to follow. . . . . . . . . . . . . . .402.18 Parking lot test for constant radius turning at 10 m/s and 13 m/s. . .422.19 Experimental data with combined acceleration magnitude 8 m/s2 overa 3 km stretch of Thunderhill Raceway Park. Results are shown forboth the baseline FB-FFW controller and the modified controller withsideslip tracking in the feedforward loop. . . . . . . . . . . . . . . . .442.20 Histogram of path tracking error for six laps around the track. . . . .452.21 Experimental data with combined acceleration magnitude 9.5 m/s2over a 3 km stretch of Thunderhill Raceway Park. . . . . . . . . . . .473.1View of sample reference path and road boundaries . . . . . . . . . .543.2Velocity profile generation illustration . . . . . . . . . . . . . . . . . .573.3Nonlinear tire force curve given by Fiala model, along with affine tiremodel linearized at α α̃. . . . . . . . . . . . . . . . . . . . . . .603.4Path update for an example turn. . . . . . . . . . . . . . . . . . . . .623.5Iterative algorithm for fast generation of vehicle trajectories. . . . . .643.6Overhead view of Thunderhill Raceway park along with generated pathfrom algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.7Lateral path deviation of racing line from track centerline as a functionof distance along the centerline. . . . . . . . . . . . . . . . . . . . . .3.86667Racing lines from the two-step fast generation approach, nonlinear gradient descent algorithm, and experimental data taken from professionaldriver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.968Racing lines from the two-step fast generation approach, nonlinear gradient descent algorithm, and experimental data taken from professionaldriver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .693.10 Lap time as a function of iteration for the two-step fast trajectorygeneration method. . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiv70
3.11 Simulation results of fast generation algorithm . . . . . . . . . . . . .723.12 Diagram of controller setup. . . . . . . . . . . . . . . . . . . . . . . .743.13 Experimental data for an autonomous vehicle driving the trajectoriesprovided by the two-step fast generation and gradient descent algorithms. 763.14 Minimum distance path around Thunder Hill . . . . . . . . . . . . . .783.15 A family of racing lines generated from linear combinations of minimum distance and minimum curvature racing lines, with weightingparameter η. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .793.16 Ten laps of professional human driver data overlaid over the minimumdistance and minimum curv
tion. The rst contribution is a feedback-feedforward steering algorithm that enables an autonomous vehicle to accurately follow a speci ed trajectory at the friction lim-its while preserving robust stability margins. The second contribution is a trajectory generation algorithm that
Bruksanvisning för bilstereo . Bruksanvisning for bilstereo . Instrukcja obsługi samochodowego odtwarzacza stereo . Operating Instructions for Car Stereo . 610-104 . SV . Bruksanvisning i original
(like hiking and dining) or different transportation modes, such as walking and driving. We show examples of trajectory classification in Section 7. Trajectory Outlier Detection: Different from trajectory patterns that frequently occur in trajectory data, trajectory ou
10 tips och tricks för att lyckas med ert sap-projekt 20 SAPSANYTT 2/2015 De flesta projektledare känner säkert till Cobb’s paradox. Martin Cobb verkade som CIO för sekretariatet för Treasury Board of Canada 1995 då han ställde frågan
service i Norge och Finland drivs inom ramen för ett enskilt företag (NRK. 1 och Yleisradio), fin ns det i Sverige tre: Ett för tv (Sveriges Television , SVT ), ett för radio (Sveriges Radio , SR ) och ett för utbildnings program (Sveriges Utbildningsradio, UR, vilket till följd av sin begränsade storlek inte återfinns bland de 25 största
Hotell För hotell anges de tre klasserna A/B, C och D. Det betyder att den "normala" standarden C är acceptabel men att motiven för en högre standard är starka. Ljudklass C motsvarar de tidigare normkraven för hotell, ljudklass A/B motsvarar kraven för moderna hotell med hög standard och ljudklass D kan användas vid
LÄS NOGGRANT FÖLJANDE VILLKOR FÖR APPLE DEVELOPER PROGRAM LICENCE . Apple Developer Program License Agreement Syfte Du vill använda Apple-mjukvara (enligt definitionen nedan) för att utveckla en eller flera Applikationer (enligt definitionen nedan) för Apple-märkta produkter. . Applikationer som utvecklas för iOS-produkter, Apple .
St-Toolkit: A Framework for Trajectory Data Warehousing 3 Our contributions are twofold: a semantic model for trajectory data warehouse and a middleware for loading, designing and querying a spatio-temporal data warehouse. The model is based on the conceptual view on trajectories introduced by Spaccapietra et al. 2007. A trajectory is a segment
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