Etude dynamique pour le as longitudinal

Dans le document en fr (Page 134-147)

A.2 T ransfert de harge Longitudinal

A.2.2 Etude dynamique pour le as longitudinal

Tout d'abord, nous alulons l'aélération du entre de gravité

G

du

véhiule,ela passe par le alul de sa vitesse.

Calul de la vitesse de G :

Pardénition, on a:

− →

V G/R 0 = d −→

OG dt

!

R 0

= d( −−→

OO + −−→

O G) dt

!

R 0

= −→

V O + d −−→

O G dt

!

R 0

(A.39)

CemOA : archive ouverte d'Irstea / Cemagref

Calulons lesdeux termesde l'équationA.39.

Calul de l'aélération de

G

:

Par dénition, ona:

Calulons lesdeux termesde l'équationA.42.

alulde

CemOA : archive ouverte d'Irstea / Cemagref

(b. θ. ¨ cos(ψ s ) − b. θ. ˙ ψ ˙ s . sin(ψ s )).~y 1 + ...

CemOA : archive ouverte d'Irstea / Cemagref

alul de

Finalement ,on obtient :

− →

Après avoir déterminé l'aélération du entre d'inertie du véhiule en

fontiondesparamètres

ψ s

et

θ

,nousdevonsdéterminerlemomentdynamique

en

G

du véhiule.

Calul du moment dynamique

Par dénition, lemoment dynamique en

G

est donné par :

− →

CemOA : archive ouverte d'Irstea / Cemagref

d'où, nous obtenons :

Seule la omposante du moment dynamique sur

~y 2

est néessaire pour

trouverles eorts normaux

F ~ r1

et

F ~ r2

et ona :

Il nous faut alulerles deux termes de

− →

A e moment de l'analyse, nous devons faire le bilan des fores exerées

CemOA : archive ouverte d'Irstea / Cemagref

Bilan des Fores

Nousavons trois fores qui sontexerées sur levéhiule,elles sont :

l'ationdu sol sur la roue arriére:

− →

Maintenant, alulons lesdiérents momentsappliqués aupoint

G

.

Bilan des Moments appliqué en

G

Lemomentdû àl'ationdu solsurlarouearrière

Lemomentdû à l'ationdu solsur laroue avant

− →

Nouspouvonsdorénavantutiliserleprinipefondamentaldeladynamique.

Equation des fores en

~x 2

− F t1 − F t2 − m.g. sin(ψ s ) = m. − a → G .~x 2

(A.65)

CemOA : archive ouverte d'Irstea / Cemagref

F t1 + F t2 = − m. h

˙

v + b.( ˙ ψ s 2 − θ ˙ 2 .cos 2 (ψ s )) + h.( ¨ ψ s + ˙ θ 2 . sin 2 (ψ s )) + g. sin(ψ s ) i

(A.66)

Equation des fores en

~z 2

F r1 + F r2 − m.g. cos(ψ s ) = m. − a → G .~z 2

(A.67)

F r1 + F r2 = m. h

v. ψ ˙ s − b.( ¨ ψ s + ( ˙ θ 2 − 2. ψ ˙ s 2 ). cos(ψ s ). sin(ψ s )) + h.( ˙ ψ s 2 − θ ˙ 2 . sin 2 (ψ s ) + g.

(A.68)

Equations des moments en

G

en

~y 2

b.F r1 − a.F r2 + (h + D

2 ).(F t1 + F t2 ) = I y . ψ ¨ s + (I x − I z ). θ ˙ 2 . cos(ψ s ). sin(ψ

(A.69)

s )

On suppose (

a = b

) le entre d'inertie est au entre du véhiule. On

ob-tient:

F r1 − F r2 = − I y . ψ ¨ s + (I x − I z ). θ ˙ 2 . cos(ψ s ). sin(ψ s ) − (h + D 2 ).(F t1 + F t2 ) a

(A.70)

Expression du transfert de harge Longitudinal (TCLon)

Pardénition, le transfertde harge longitudinal

T CLon

est déni par :

T CLon =

F r1 − F r2

F r1 + F r2

(A.71)

CemOA : archive ouverte d'Irstea / Cemagref

DansnotreasenutilisantleséquationsA.66,A.68etA.70,nousobtenons

nalement l'expression :

T CLon = 1 m.a .

I y . ψ ¨ s + (I x − I z ). θ ˙ 2 . cos(ψ s ). sin(ψ s )

v. ψ ˙ s − b.( ¨ ψ s + ( ˙ θ 2 − 2. ψ ˙ 2 s ). cos(ψ s ). sin(ψ s )) + h.( ˙ ψ 2 s − θ ˙ 2 .sin 2 (ψ s )) + g. cos(ψ s ) +m. (h + D 2 ). h

˙

v + b.( ˙ ψ 2 s − θ ˙ 2 .cos 2 (ψ s )) + h.( ¨ ψ s + ˙ θ 2 . sin 2 (ψ s )) + g. sin(ψ s ) i v. ψ ˙ s − b.( ¨ ψ s + ( ˙ θ 2 − 2. ψ ˙ s 2 ). cos(ψ s ).sin(ψ s )) + h.( ˙ ψ 2 s − θ ˙ 2 . sin 2 (ψ s )) + g. cos(ψ s )

(A.72)

CemOA : archive ouverte d'Irstea / Cemagref

[Berkemeier 2008℄ Matthew D. Berkemeier, Eri Poulson et Travis Groethe.

ElementaryMehanialAnalysis ofObstale Crossingfor Wheeled

Ve-hiles. InIEEEInternationalConfereneonRobotisandAutomation

(ICRA),pages 23192324, Pasadena, CA, USA, 19-23 May, 2008.

[Biesiadeki 2005℄ J. J. Biesiadeki, Baumgartner E., R. Bonitz, B. Cooper,

F. Hartman, C. Leger, M. Maimone, S. Maxwell, A. Trebi-Ollenu et

J. Wright. Mars Exploration Rover surfae operations : driving

op-portunity at Meridiani Planum. In IEEE International Conferene on

Systems,Manand Cybernetis, pages 18231830,Hawaii,USA, 10-12

Otober, 2005.

[Bouteldja 2004℄ M. Bouteldja, N. K.M'Sirdi, S. Glaser etV. Dolemasolo.

Stability Analysis andRolloverSenario Predition For Trator

Semi-Trailer. In International Conferene on Advanes in Vehile Control

etSafety, editeurs, AVCS04,Genova , Italy, 2004.

[Bouton 2009℄ Niolas Bouton. Stabilité dynamiquedes véhiules légers

tout-terrain. Nouvelles solutions. Appliation aux véhiules légers de type

quad.PhDthesis,UniversitéBlaisePasal-Clermont-FerrandII,2009.

[Bouton 2010℄ Niolas Bouton, Roland Lenain, Benoit Thuilot et Philippe

Martinet. A new devie dediated to autonomous mobile robot

dy-nami stability : Appliation to an o-road mobile robot. In IEEE

International Conferene onRobotis andAutomation(ICRA),pages

38133818,Anhorage, Alaska,3-8 May, 2010.

[Cremean 2006℄ Lars B. Cremean, Tully B. Foote, Jeremy H. Gillula,

George H. Hines, Dmitriy Kogan, Kristopher L. Kriehbaum,

Jef-frey C. Lamb, Jeremy Leibs, Laura Lindzey, Christopher E.

Ras-mussen,AlexanderD.Stewart,JoelW.BurdiketRihardM.Murray.

Alie : An information-rih autonomous vehile for high-speed desert

navigation. Journalof FieldRobotis, vol.23, pages777810,

Septem-ber, 2006.

[Cui 2010℄ Yan Cui et T.R. Kurfess. Inuene of Parameter Variations for

CemOA : archive ouverte d'Irstea / Cemagref

Conferene on Computer Engineering and Tehnology (ICCET),

vol-ume 5, pages 600604,Chengdu, China,16-18 April,2010.

[Debain 2010a℄ Christophe Debain, Pierre Delmas, Roland Lenain etRoland

Chapuis. Integrity of an autonomous agriultural vehile aording

the denition of trajetory traversability. In International Conferene

onAgriulturalEngineering(AgEng2010),Clermont-Ferrand,Frane,

06-08 September, 2010.

[Debain 2010b℄ Christophe Debain,FlorentMalartre,Pierre Delmas, Roland

Chapuis, Thierry Humbert et Mihel Berduat. Smart range nder

and amera fusion - Appliation to real-time dense digital elevation

map estimation. In International workshop of Mobile Robotis for

environment/agriulture (Robotis 2010), Clermont-Ferrand, Frane,

03-04 September, 2010.

[Delmas 2009℄ Pierre Delmas, Niolas Bouton, Christophe Debain et Roland

Chapuis. UGV in outdoor environment : A safe mobility approah

based on a Digital Elevation Model. In IEEE International

Confer-ene on Robotis and Biomimetis (ROBIO), Guilin, CHINA, 19-23

Deember, 2009.

[Diaz-Calderon 2006℄ Antonio Diaz-Calderon et Alonzo Kelly. Development

ofaTerrainAdaptiveStabilityPreditionSystemforMassArtiulating

Mobile Robots. Fieldand servie robots. Springer Verlag,2006.

[Fox 1997℄ DieterFox etWolframBurgard. The DynamiWindow Approah

to Collision Avoidane. Rapporttehnique, Février 191997.

[Fraihard 2004℄ Thierry Fraihard et Hajime Asama. Inevitable ollision

states-asteptowardssaferrobots?AdvanedRobotis,vol.18,no.10,

pages 10011024, 2004.

[Gong 2007℄ Jianwei Gong, Yulin Duan, Beijing Man et Guangming Xiong.

VPH+ : An Enhaned Vetor Polar Histogram Method for Mobile

Robot Obstale Avoidane. In IEEE International Conferene on

Mehatronis and Automation (ICMA), volume 6, pages 27842788,

Harbin, Heilongjiang,China,2007.

[Ha 2004℄ A. Ha, T. Brown et J. Martens. Detetion of Vehile Rollover.

In SAE Tehnial Paper Series, 2004-01-1757, SAE World Congress,

2004.

[Hardy 2006℄ MihaelHardy.CombinatorisofPartialDerivatives.Eletroni

Journal of Combinatoris, vol.13, pageR1, 2006.

[Hiroaki 1998℄ SadayukiTsugawaHiroaki,HiroakiMorietShinKato. A

Lat-CemOA : archive ouverte d'Irstea / Cemagref

in the Field of View. In IEEE International Conferene onIntelligent

Vehiles, pages 4145,Stuttgart, Germany, 1998.

[Howard 2008℄ ThomasM.Howard,ColinJ.Green,AlonzoKellyetDaveF

er-guson. State spae sampling of feasible motions for high-performane

mobilerobotnavigationinomplexenvironments.JournalFieldRobot,

vol. 25,pages 325345,June 2008.

[Imine 2008℄ H.Imine, J.DakhllalahetY.Sellami. Validation Expérimentale

de l'Identiation de laHauteur du Centre de Gravité du Poids Lourd

etde l'Estimationdu Risque de Renversement. In Conferene

Interna-tionaleFranophoneAutomatique, CIFA08,pages149154,Buarest,

Roumanie, 2008.

[Johansson 2004℄ B. Johansson et M. Gafvert. Untripped SUV rollover

de-tetion and prevention. In 43rd IEEE Conferene on Deision and

Control(CDC), volume 5,pages54615466,Atlantis,ParadiseIsland,

Bahamas,14-17 Deember 2004.

[Kelly1997a℄ Alonzo Kelly etAnthony Stentz. Analysis of Requirements for

High Speed Rough Terrain Autonomous Mobility.Part 1 : Throughput

and Response. In International Conferene onRobotis and

Automa-tion (ICRA), volume 4, pages 33183325, Albuquerque, NM, 20-25

April,1997.

[Kelly1997b℄ Alonzo Kellyet Anthony Stentz. Analysis of Requirements for

High Speed Rough Terrain Autonomous Mobility. Part 2 : Resolution

and Auray. In International Conferene on Robotis and

Automa-tion (ICRA), volume 4, pages 33263333, Albuquerque, NM, 20-25

April,1997.

[Khatib1980℄ OussamaKhatib.CommandeDynamiquedansl'Espae

Opéra-tionneldesRobotsManipulateursenPrésened'Obstales.PhDthesis,

EoleNationaleSupérieurde l'Aéronautique etde l'Espae,Toulouse,

1980.

[Khatib1986℄ Oussama Khatib. Real-Time obstale avoidane for

manipu-lators and mobile robots. International Journal of Robotis Researh,

vol. 5,no. Issue 1, pages 9098,Spring 1986.

[Koren 1991℄ Y. Koren et J. Borenstein. Potential Field Methods and Their

Inherent Limitations for Mobile Robot Navigation. In International

Conferene on Robotis and Automation (ICRA), volume 2, pages

13981404,Saramento,CA, 9-11 April,1991.

[Lau 2009℄ Boris Lau, Christoph Sprunk et Wolfram Burgard. Kinodynami

CemOA : archive ouverte d'Irstea / Cemagref

nationalonferene onIntelligentRObotsand Systems (IROS), pages

24272433, Pisataway, NJ, USA, 11-15 Otober, 2009.

[Lefebvre 2005℄ O.Lefebvre,F.LamirauxetD. Bonnafous. Fastomputation

of robot-obstale interations in nonholonomitrajetory deformation.

InInternationalConfereneonRobotisandAutomation(ICRA),

vol-ume 1-4, pages 46124617, Barelona,Spain, 18-22 April,2005.

[Leger 2005℄ Chris Leger, Ashitey Trebi-Ollennu, John Wright, Sott

Maxwell,BobBonitz, JeBiesiadeki,FrankHartman,BrianCooper,

EriBaumgartneretMark Maimone. Mars Exploration Roversurfae

operations:drivingspiritatGusevCrater. InIEEEInternational

Con-ferene on Systems, Man and Cybernetis, pages 18151822, Hawaii,

USA, 10-12 Otober, 2005.

[Lenain 2003℄ R. Lenain, B. Thuilot, C. Cariou et P. Martinet. Adaptative

ontrolforarlikevehilesguidanerelyingonRTKGPS:rejetionof

sliding eets in agriulturalappliations. In International Conferene

onRobotisandAutomation(ICRA),volume1,pages115120,Taipei,

TWN, 14-19September, 2003.

[Lu 2007℄ Baozhan Lu, Sihong Zu et Ying Zhang. Researh on Parameter

Mathing of Front Axle Suspension Vehile Based on MATLAB,

Au-gust 2007.

[Malartre 2009℄ Florent Malartre, Thomas Feraud, Christophe Debain et

Roland Chapuis. Digital Elevation Map Estimation by Vision-Lidar

fusion. InIEEE InternationalConferene onRobotis and

Biomimet-is(ROBIO),Guilin, China, 19-23Deember 2009.

[Malartre 2010℄ Florent Malartre, Pierre Delmas, Roland Chapuis et

Christophe Debain. Real-Time Dense Digital Elevation Map

esti-mation using lasersanner and amera SLAM proess. In 11th

In-ternational Conferene on Control, Automation, Robotis and Vision

(ICARCV), Singapour, 7-10 Deember 2010.

[Minguez 2000℄ J. Minguez et L. Montano. Nearness diagram navigation

(ND) : a new real Time Collision Avoidane Approah. In

Interna-tionalConfereneonIntelligentRobots andSystems, IROS, volume3,

pages 20942100, Takamatsu,Japan, 2000.

[Odenthal 1999℄ Dirk Odenthal, Tilman Bünte et Jürgen Akermann.

Non-linear Steering And Braking Control For Vehile Rollover Avoidane.

In inEuropean ControlConferene, 1999.

[Peters 2006℄ S.C. Peters et K Iagnemma. An analysis of rollover stability

CemOA : archive ouverte d'Irstea / Cemagref

ferene onRobotis and Automation(ICRA),pages 3711 3716,

Or-lando,Floride,15-19 May 2006.

[Quinlan1993℄ Sean Quinlanet Oussama Khatib. Elasti Bands :

Connet-ing Path Planning and Control. In IEEE International Conferene

onRobotis and Automation, pages 802807,Atlanta,Georgia, USA,

May 1993.

[Ryu 2004℄ J. Ryu et J. C. Gerdes. Estimation of vehile roll and road bank

angle. In Amerian Control Conferene, volume 3, pages 21102115,

Boston, Massahusetts, 30June,2 July 2004.

[Samson1995℄ C. Samson. Control of hained systems : appliation to path

followingandtime-varyingpointstabilizationofmobilerobots.InIEEE

Transationson AutomatiControl, volume 40,pages6477, January

1995.

[Sardain2004℄ P. Sardainet G. Bessonnet. Fores Ating on a Biped Robot.

Centerof Pressure-ZeroMoment Point. InIEEETransationson

Sys-tems,ManandCybernetis,PartA:SystemsandHumans,volume34,

pages 630637,2004.

[Shmitt 1993℄ Mihel Shmitt et Juliette Mattioli. Morphologie

mathéma-tique. Masson, 1993.

[Shoeld2006℄ B. Shoeld, T. Hagglund et A Rantzer. Vehile dynamis

ontrolandontrolleralloationforrolloverprevention.InIEEE

Inter-nationalConferene onControlAppliations,pages 149154,Munih,

Germany,Otober2006.

[Shiller 1999℄ Zvi Shiller. Motion Planning for Mars Rover. In First

Work-shoponRobotMotionand Control(RoMoCo), pages257262,Kiekrz,

Poland, 28-29 June, 1999.

[Simmons1996℄ ReidSimmons.TheCurvature-VeloityMethodforLoal

Ob-stale Avoidane. In International Conferene on Robotis and

Au-tomation(ICRA),volume4,pages33753382,Minneapolis,MN,22-28

April1996.

[Taylor 1999℄ Koseka Blasi Taylor, R. Blasi, C. J. Taylor et J. Malik. A

Comparative Study of Vision-Based LateralControlStrategiesfor

Au-tonomous Highway Driving. In International Journal of Robotis

Re-searh, volume 18, pages442453, 1999.

[Tessier 2007℄ Cédri Tessier. Système de loalisation basé sur une stratégie

de pereption ognitive appliqué à la navigation autonome d'un robot

mobile. PhD thesis, Université Blaise Pasal -Clermont II, November

CemOA : archive ouverte d'Irstea / Cemagref

[Thuilot 2002℄ B. Thuilot, C. Cariou, P. Martinet et M. Berduat.

Auto-mati Guidane of a Farm Trator Relying on a Single CP-DGPS.

Autonomous Robots, vol.13, pages 5371,July 2002.

[Thuilot 2004℄ B. Thuilot, J. Bom, F. Marmoiton et P. Martinet. Aurate

automati guidane of an urban vehile relying on a kinemati GPS

sensor. In Symposium on Intelligent Autonomous Vehiles IAV04,

2004.

[Ulrih1998℄ Iwan Ulrih et Johann Borenstein. VFH+ : Reliable

Obsta-le Avoidane for Fast Mobile Robots. In International Conferene on

Robotis and Automation (ICRA), volume 2, pages 15721577,

Leu-ven, Belgium, 16-20 May 1998.

[Ulrih2000℄ I.UlrihetJ.Borenstein.VFH* :LoalObstaleAvoidanewith

Look-Ahead Veriation. In International ConfereneonRobotis and

Automation(ICRA), volume 3, pages 25052511, San Franiso, CA,

24-28 April2000.

[Wilde 2009℄ Doran K. Wilde. Computing lothoid segments for

traje-tory generation. In IEEE/RSJ international onferene on

Intelli-gentRObotsandSystems,IROS'09,pages24402445,Pisataway,NJ,

USA, 2009.

[Ye 2004℄ Cang Ye et Johann Borenstein. Obstale Avoidane for the

Seg-way Roboti Mobility Platform. In 10th International Conferene on

RobotisandRemoteSystemsforHazarousEnvironments,Gainesville,

Florida,28-31 Marh2004.

CemOA : archive ouverte d'Irstea / Cemagref

Dans le document en fr (Page 134-147)

Documents relatifs