Trajectory control in curves, towards the Perceptive-ESC, through a Piecewise Affine approach

228 Pages·2012·3.44 MB·English

Universit´e d’E´vry-Val-d’Essonne E´cole doctorale Sitevry
Num´ero d’ordre ...
Trajectory control in curves, towards
the Perceptive-ESC, through a
Piecewise Affine approach
`
THESE
pr´esent´ee et soutenue publiquement le 15 Novembre 2011
pour l’obtention du
´
Doctorat de l’Universit´e d’Evry-Val-d’Essonne
(sp´ecialit´e Automatique, Syst`emes Productiques et Robotique)
par
Andr´e Benine-Neto
Composition du jury
Pr´esident : Carlos Canudas-de-Wit Directeur de Recherche au CNRS-GIPSA-LAB
Rapporteurs : Didier Dumur Professeur `a Sup´elec
Dominique Meizel Professeur `a l’ENSIL
Brigitte d’Andr´ea Novel Professeur `a l’Ecole de Mines ParisTech
Dimitri Peaucelle Charg´e de Recherche au LAAS-CNRS
Andreas Eidehall Ing´enieur Volvo Car Corporation
Nicoleta Minoiu-Enache Ing´enieur chez Renault S.A.
Directeur : Sa¨ıd Mammar Professeur `a l’Universit´e d’E´vry-Val-d’Essonne
Laboratoire sur les Interactions V´ehicules-Infrastructure-Conducteurs
IFSTTAR. 14, route de la Mini`ere 78000 Versailles-Satory

Acknowledgments
First of all, I would like to thank my advisor Sa¨ıd Mammar, professor at Universit´e d’Evry, for
his theoretical support, solve-problems ideas and promptness throughout the entire research. I
am very grateful for this cooperation which has resulted in two submitted journals and several
conference papers. It has been a great pleasure to work with him.
IthankDidierDumurandDominiqueMeizelfortheirinterestinmywork,foracceptingbeing
the main reporters of the thesis and for their constructive feedback about the work. Equally,
I appreciate the efforts of Brigitte d’Andr´ea-Novel, Dimitri Peaucelle, Andreas Eidehall and
Nicoleta Minoui-Enache for being part of the board of inspection.
Also with important cooperation, I would like to express my appreciation to Stefano Scalzi
for his continuous collaboration during the PhD program. I am very grateful for our technical
discussions.
Benoit Lusetti has made available his support in a number of ways which certainly enriched
the content of this thesis, specially concerning the practical implementation of the driver as-
sistance systems on the prototype vehicle, for which I extend the acknowledgements also to
Jean-Marie Chevreau and Micha¨el Messias.
It is a pleasure to thank Neil Atinkson for his royal English reviews of the thesis and articles
as well as our friendship over the years.
I would like to thank Mariana Netto, for the support during the first two years of the Phd
program, for the indications of pertinent seminars for the development of my thesis and mainly,
with Jacques Erlich, director of LIVIC, for trusting my capacity and giving me the opportunity
to became part of the research group at LIVIC with the funding from LCPC in the framework
of program K.
I’d like to show my gratitude to the discussions with Sorin Olaru, William Pasillas-Lepine
and Nicoleta Minoiu Enache. Their suggestions and contributions have not only contributed for
this work but also to broaden my knowledge on piecewise affine systems, vehicle dynamics and
driver assistance systems.
Severalcontributionshavebeenprovidedbythecolleagues fromLIVICwhomIthankforthe
good working environment and conviviality. S´everine Somma, Isni´e Rusani, Jacques Erlich and
Didier Aubert mainly for administrative issues. Benoit Vanholme, Romain Gallen, Guillaume
Saint Pierre, Aur´elien Cord, Dominique Gruyer, Steve Pechberti, Jerome Perignon, Evange-
line Pollard, Lydie Nouveli`ere, Francis Dupin, S´ebastien Glaser and Hong-Tu-Luu, for several
discussionsthat helped menot only technically, butalso personally, to make this thesis possible.
Severalpeople encouraged meto take partin thePhd program. I wouldlike to thank profes-
sor Maria Helena Robert from UNICAMP (Universidade Estadual de Campinas) for providing
a reference letter. Breno Hulle da Silveira and Volker Heumann, my former supervisors for sup-
portingthedecisionofleavingtheindustrytostartaPhD.Gilberto Gouvˆea, formercolleague at
industry, for transmitting his passion and knowledge about vehicle dynamics. Mariana Moretti
not only for informing and encouraging me to apply for the phD position, but also for hosting
me during a conference. Mohammed El Katter for his excellent teaching skills that provided
good knowledgeof Frenchlanguage whichcertainly helped toquickly adaptto thelifein France.
I also thank my family and friends for the support during this 3 years of PhD program.
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A` Francesca et Ozzy,
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”Essentially, all models are wrong, but some are useful”,
George E. P. Box
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Contents
List of Figures xi
List of Tables xvii
Nomenclature xix
1 Mathematical symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
2 Nomenclature for piecewise affine systems . . . . . . . . . . . . . . . . . . . . xix
3 Vehicle nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx
4 Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Resum´e xxiii
Part I Introduction 1
Chapter 1 Motivations and Methodology 3
1.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Goals and contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Document organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter 2 State of the art 9
2.1 Intelligent transportation systems . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Research projects on ITS . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Trends for research on safety related issues of ITS . . . . . . . . . . . 18
2.2 ADAS for vehicle lateral stability . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Yaw stability control . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Lane departure warning systems . . . . . . . . . . . . . . . . . . . . . 24
2.2.3 Lane keeping assistance . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.4 Control strategies for lane keeping . . . . . . . . . . . . . . . . . . . . 26
2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
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Contents
Part II Lyapunov based system control theory and vehicle model 31
Chapter 3 Theoretical background for system control 33
3.1 Continuous dynamic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Lyapunov Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Quadratic Lyapunov function. . . . . . . . . . . . . . . . . . . . . . . 36
3.2.2 Invariant sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Linear and Bilinear matrix inequalities . . . . . . . . . . . . . . . . . . . . . 38
3.3.1 Convexity notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 Convex optimisation problem . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.3 Convex optimisation problem involving LMI . . . . . . . . . . . . . . 40
3.3.4 Optimisation problem involving BMI . . . . . . . . . . . . . . . . . . 42
3.4 Hybrid systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.1 An introduction to hybrid systems . . . . . . . . . . . . . . . . . . . . 42
3.4.2 Piecewise affine systems . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 Tools for analysis and control of piecewise affine systems . . . . . . . . . . . 47
3.5.1 Previous work on Piecewise affine systems . . . . . . . . . . . . . . . 47
3.5.2 Lyapunov stability of piecewise affine systems . . . . . . . . . . . . . 50
3.5.3 State feedback control for piecewise affine systems . . . . . . . . . . . 54
3.5.4 Output feedback control for piecewise affine systems . . . . . . . . . . 58
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Chapter 4 Vehicle model 61
4.1 Vehicle Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1.1 2-DOF nonlinear vehicle model . . . . . . . . . . . . . . . . . . . . . . 62
4.1.2 Tyre forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1.3 Nonlinear model analysis . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 Piecewise affine vehicle model . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.1 Analysis of PWA vehicle model . . . . . . . . . . . . . . . . . . . . . 71
4.2.2 Assumptions for PWA vehicle model for formal analysis and control
synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3 Road Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4 Additional dynamics for lane keeping . . . . . . . . . . . . . . . . . . . . . . 78
4.5 Electrically assisted steering column . . . . . . . . . . . . . . . . . . . . . . . 80
4.6 Simulation environment and practical implementation . . . . . . . . . . . . . 82
4.6.1 CarSim simulation environment . . . . . . . . . . . . . . . . . . . . . 82
4.6.2 Practical Implementation on prototype vehicle CARLLA . . . . . . . 82
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