Motion generationfor a rover on rough terrains

David Bonnafous,SimonLacroixandThierrySimeonLAAS/CNRS

7, Ave duColonelRocheF-31077TOULOUSECedex 4�

firstname.name@laas.fr�Abstract

Thisarticle presentsanalgorithmthatdeterminessafemo-tionsfor anarticulatedroveron roughterrains. It reliesontheevaluationof a setof elementarytrajectorieson a dig-ital elevation mapbuilt as therovermoves.Thealgorithmrelieson the explicit computationof geometricconstraintsontheroverchassis.It hasbeenintegratedwithin a contin-uouslyrunning navigationloop on board the robot Lama,andtestedundervariousterrain conditions.

1. Intr oductionAmongthevariousissuesraisedby autonomousrovernavi-gationin unstructuredenvironments,traversingroughareasis one of the mostchallenging. Indeed,suchareasbringforth variousdifficulties to eachof the perception,trajec-tory evaluationandtrajectoryexecutioncontrolfunctions:� To catchthesurfacegeometryof theareato traverse,a

finemodelof theenvironmentis required;� To selectfeasiblemotions,geometricandkinematicsconstraintsontheroverhaveto beexplicitly takenintoaccount;� Finally, ensuringthe properexecutionof the selectedmotionsis a muchmoredifficult issuethanonsmoothterrains.

This paperfocuseson the secondpoint: it presentsanalgorithmthat determinessafeandefficient motionsfor arover on roughterrains.Thealgorithmconsistsin evaluat-ing a setof elementarytrajectories(circle arcs)on a digi-tal elevationmapcontinuouslyupdatedastherover moves,taking into accountgeometricalconstraintson the robotchassis. The approachhas beensuccessfullyintegratedwithin a simpleautonomousnavigation loop on boardtherobot Lama: tensof experimentshave beenachieved, inwhich therobot is askedto reacha few tensmetersdistantgoalin aninitially unknown terrain(figure1).

Related work: Pioneerwork on planning motions onrough terrainsdatesback to the late 80’s, andhasessen-tially beenconsideredwithin the context of planetaryex-plorationrobotics. In [1], an algorithmthat plan minimal

Figure1: TherobotLamaduringanautonomousroughterraintraverse.Here,thedigital elevationmapbuilt during thetraverseis surimposedontheimage.

time pathson a surfacerepresentedby B-splinepatchesispresented:it insistson the considerationof thevehicledy-namics. Work presentedin [2, 3, 4] extendthis approach,by consideringanarticulatedchassismodeandexplicit ve-hicle/terraininteractions.In our lab,we alsocontributedtothe problem[5, 6], anddevelopeda plannerthat finds tra-jectoriesto reacha distantgoal for an articulatedchassis.Latestdevelopmentsincludedthe considerationof the ter-rain modelinguncertaintiesandthenecessityfor the roverto localizeitself [7]. To ourknowledge,all thesework haveonly beentestedin simulatedenvironments.

More recently, various simpler approacheshave beenpresentedand effectively demonstratedon board rovers.Most of theseapproachesrely on the segmentationof theterrain model into two or more terrain navigation classes(flat, obstacle,slope) [8], or on the estimateof the ter-rain traversabilityby fitting planesover terrainpatches[9],sometimesusingfuzzy rulesfor this segmentationandforelementarymotiongeneration[10]. In thesecases,demon-strationsonflat groundwith sparserocksarepresented.

Outline: Thispaperis articulatedasfollows: thenext sec-tion givesanoverview of thethreecomponentsinvolvedintheapproach,andpresentstheprincipleof themotiongen-

erationalgorithm. Section3 is dedicatedto thedetermina-tion of thechassisinternalconfigurationonagivenpositionontheterrainmodel.Section4 depictshow theoptimalcir-clearcis chosen,on thebasisof a risk definedby adiscretesetof configurationsevaluatedalongthearc,a of an inter-estrelatedto thegoalto reachposition.Someexperimentalresultsof thewholeapproacharepresentedin section5.

2 Overview of the approachThenavigationapproachto reachagivengoalis sketchedinfigure2. It is averysimpleinstanceof a“perceive- decide”paradigm(oftenappliedwhendealingwith rathereasyter-rains[11, 12]): from a pair of stereoimages,a 3D imageis computedusingapixel correlation-basedalgorithm.This3D imageis merged in a digital elevation map(DEM) ofthe terrain,andevery time this mapis updated,a setof el-ementarytrajectoriesis evaluated: the best trajectoryse-lecteddefinesthe motion commandsto sendto the rover,andtheprocessis re-iterateduntil thegoalis reached.

Stereovision

DEM update

Trajectory selection

Motion commands

Goal position

Figure2: Principleof thenavigationloop

Digital elevation map building: Digital elevation mapsarea popularway to representtheenvironmentof a rover:their structureis easyto manage,and they can representquitefaithfully theterrainsurfacegeometry. Themaindif-ficulty to updatesuchmapscomesfrom theuncertaintiesonthe3D input data;however, a realisticmodelcanbeeasilybuilt by computingthemeanelevationof thedatapointsontheDEM grid cells.

Oneof the problemswhendealingwith rough terrainsis the large numberof occlusionscausedby the terrainir-regularitiesandthedataresolutiondecreaseon the ground(figure3). To palliatethis,theDEM is continuouslyupdatedastherobotnavigates,which requirestheknowledgeof therobot3D position,with a precisionof theorderof thegridsize.Odometrybeingnot reliableon roughterrains,in oursystemthe3D positionestimateis providedby avisualmo-tion estimationtechnique[13], which is runningin parallel

of thenavigationloop.

Figure3: A digital elevationmapbuilt with a singlestereoimagepair:severalareasareunperceivedbecauseof theterrain irregularitiesandthedrasticdataresolutiondecreasewith thedistance.

Motion control: The six wheels of Lama being non-orientable, rotations are producedaccording to a skid-steeringscheme:eachof the threewheel of one side oftherobotaregiventhesamerotationspeedcommand,andthedifferenceof theleft andright speedcommandinducesa rotation(figure 4). Thanksto a preciseoptical encoderandto a powerful motor/gearset,six simplePD controllersensurea tight control of eachwheelrotationspeed,what-ever the terrain characteristicsare. Becauseof unpre-dictableground/wheelfrictions,theinformationreturnedbythewheelencodersdonotallow afaithful estimationof therotationspeed:for thatpurpose,a fiber-optic gyrometerisused.Thelocomotionlayeris thereforeabletohandlelinearandangularrover velocities ������� commands,by sendingthesix PDcontrollerscommandsat �� ���� .

Figure4: Motion control of Lama.A difference in the lateral wheelspeedsinducesan angular velocity,producinga circle trajectory with aradius � . Only the middleaxle con-tributes to the rotation. It can beshownthat the speedsto be appliedto the front and rear axles wheelsso that they do not opposetoo muchagainst this rotation are the same����������

and����� �"!#�

.

r

Vleftω

V Vright

Motion generation: Theheartof thesystemis themotiongenerationalgorithm: it consistsin evaluatingthe risk andthe interestof asetof elementarytrajectories(figure5), theonewith thesmallestrisk/interestratio beingselected.Theconsideredtrajectoriesarecirclearcs,asthey correspondtoa controleasilyhandledby thelocomotionlayer.

To evaluatea circle arc, a discretesetof configurationalongit areconsidered:a risk is definedfor eachconfigura-tion by checkingconstraintsontheinternalchassisconfigu-rationandon therobotattitude(section3). Theintegrationof theriskscomputedalonganarcandtheconsiderationofits interest,in termsof gettingcloserto the goal, are thenusedto selecttheoptimalone(section4).

Figure5: Thesetof circlearcsevaluatedat eachstepof theloop.

3 Chassisposeand configuration de-termination

Theability to predicttherobotposeandits chassisinternalconfigurationfor a givenposition ��$%��&���'( on thedigital el-evationmapis a key point in our algorithm,asit producesthebasicparametersthatwill beusedto selectfeasibleandsafemotions.WedescribeheretheplaceRobot function,thatfulfills this requirement.

3.1 Chassisgeometry

Lama1 is a Marsokhodarticulatedchassis[14]. Its lengthcan be actively controlledby modifying the distancebe-tweenthe axles(figure 3.1), thus enablingthe possibilityto move in a peristalticmode.However, for thealgorithmsandexperimentspresentedin this paper, the inter-axledis-tanceis maintainedfixed.

Figure 6: Geometryof Lamalocomotion structure. Depend-ing on the angular valuesof )+*and )(, , the lengthof the chassiscanbeadapted.In its ”nominal”configuration,thechassisoveralllengthis -/. 021 meter.

3 3 33 3 33 3 33 3 34 4 44 4 44 4 44 4 4 5 5 55 5 55 5 55 5 56 66 66 66 6(β1)l

(β2)l

β2

1.20m1.10m to 1.70m

0.45m

β1

Thechassisis alsopassively articulated,asshown in fig-ure7), which givestherobothigh obstacleclimbing skills.Themechanicalvariationsof thesethreeparameters,whosevaluesis providedto thelocomotioncontrollayerby angu-lar encoders,areboundedby thefollowingvalues:798�:<;>=@?BADC EF=@8<:�; (1)G<G ; =IHKJL=NM�8 ; (2)

Therobotattitudeis definedby theattitudeof its middleaxlewith respectto thevertical: thetwo pitchandroll angleOQP

and R Paremeasuredthanksto atwo-axisinclinometer.

3.2 Robot placementon the DEM

Givena position ��$%��&���'( on thedigital elevationmap,therobot placementfunctionplaceRobot providesthe five

1Thechassisof Lamais ownedby Alcatelandis lent to LAAS. All theequipmentshasbeenconceivedanddevelopedatLAAS.

α1

α2

β3

Figure7: Thethreepassivearticulationsof thechassis.

angularvalues( R P � O P � ?BA � ?SE � H J thatentirelydefinethechassisconfigurationparameters.

This functionrelieson thecomputationof a singleaxleplacement(functionplaceAxle), which itself makeiter-ative calls to theplaceWheel function(figure 8). Simi-larly, oncethe middle axle is placedon the DEM, severaliterative calls to theplaceAxle function arerequiredtoplacethefront andrearaxle,to finally obtainthefive con-figurationsangles.

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Figure8: Principle of theplaceAxle function: the axle orientationbeingsetto 0, twocallsto theplaceWheel functiondefinetheelevationof the wheelsfor this orientation(left). Thedistanced betweenthe twowheelsrotationaxesdefinea newaxleorientation(right), andtheprocessis reiterateduntil d stabilizesitself around0.

Theimplementationof thefunctionplaceWheel is ofcrucial importance,at it is calleda lot of timesto computethe robot five configurationsangles.For that purpose,wehave tabulatedthe elevationsof the conic wheelprofile ina rectangulararray, with a resolutiontwice as fine as theDEM resolution:theminimumdistancebetweenthis arrayelevationsandtheDEM elevationson theprojectedrectan-glegivestheelevationof thewheelon theDEM.

However, the placeAxle function is quite timeconsuming: not only it makes successive calls to theplaceWheel function,but alsoat eachiterationthe tab-ulatedwheelprofile valueshave to berotatedaccordingtothe currentaxle orientation. Table1 gives the numberofiterationsthat have beenrequiredfor more than 300,000callsto theplaceAxle function: asonecansee,in morethan d� <e of the cases,only oneiteration is required. Wethereforechooseto only executea single iteration in theplaceAxle functionfor eachof thethreeaxles:ona SunUltra 10 SparcStation,a call to the placeRobot func-tion, which determinesthe 5 robot configurationparame-ters,takeslessthan 8�fhg .

Nb iterations Nb placements1 2937802 156943 40244 15215 8676 5477 3828 2779 197

Table1: Statisticson the numberof iterationsrequiredby thefunctionplaceAxle.

3.3 Experimental validation

To checkthe validity of the robot placementfunction, wemadesomeexperimentaltrials,in whichtherobotwasman-ually drivenalonga straightline, roving over rocksof vari-oussizes(figure9).

Figure9: A predictedplacementof theroboton theDEM (left), andthecorrespondingplacementin reality (right).

Figure10 shows a comparisonbetweenthe robot con-figuration anglespredictedby the placementfunction onthecomputedDEM andtheanglesmeasuredon boardtherobot:nosignificantdifferencescanbenoticed.

4 Evaluation of the arcsEvery time theDEM is updated,our algorithmevaluatesasetof circlearcsto selectthe“optimal” one.In thissection,we explain how this evaluationis madeon thebasisof theplacementfunction,andthesearchstrategy thatselectsthearcto execute.

4.1 The ”danger” of a placement

Besidestheinternalchassisconfigurationconstraints1 and2 mentionedabove,weconsidertwo stabilityconstraintsoneachof thethreeaxles:

7 R PjiDk = Rml C P C nh= R Poipk(3)7 O Poipk = O l C P C nh= O PjiDk(4)

whereq , f and r respectively standsfor therear, middleandfront axles. The pitch androll angles

Oand R for the

-20

-15

-10

-5

0

5

10

15

20

0 1 2 3 4 5 6 7 8

alph

a_1s

Distance

MeasuredPredicted

-20

-15

-10

-5

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8

beta

_3t

Distance

MeasuredPredicted

-15

-10

-5

0

5

10

15

20

0 1 2 3 4 5 6 7 8ro

llu

Distance

MeasuredPredicted

Figure10: Comparisonbetweenthepredictedandmeasuredangles(indegrees),asa functionof thecurvilinearabscissaon a straighttrajectory.Fromtop to bottom: v *Dw�)(xywz�{}|�~ . Theimagesof figure9 were takenduringthistrajectory, whenthecorrespondingabscissawasapproximately1D� .

front andrearaxlesareeasilyderived from the five angu-lar valuesthatdefinethechassisconfiguration2. Soin total,a setof 9 boundingconstraintsareconsidered:any place-mentthatviolatesoneof theseconstraintsis consideredasnot valid. We considerthattheseconstraintsareall “equiv-alent”, in thesensethatnoneof themcanbeviolated,andthat thecloseris a valueto a bound,themoredangerousistherobotconfiguration.Theseconstraintsarethereforenor-malized,andweendupwith thefollowingconstraintset:����� 7 G�� =N�D�B= G<� �� ����� �/C�������C ���

An otherconstrainthasalso to be considered:indeed,therearealwayssomeunperceived areasin the DEM, es-pecially behind sharpobstacles(as one can see on fig-ure 9, just below the left rear wheel). To considerthis,

2Theconsiderationof a constrainton thepitchanglefor anaxlemightbesurprising,but onemustnot forget thatsomeequipmentsaremountedoneachof theaxles.

the placeWheel function returnsa value comprisedin� �� Gp�, which indicatestheproportionof unknown pixels in

theDEM in theareadefinedby theprojectionof thewheel.We decidedthat this valueshouldnot be greaterthan � : ,and the biggestof the 6 valuesreturnedby a call to theplaceRobot functiondefinesa tenthconstraint.

Now givena robotposition ��$Q�D&K�D'( on a circle arc, therobot placementfunction provides the five correspondingconfigurationangles,to which corresponda point in the9-dimensionalconstraintspaceafternormalization.Thedan-ger � of a givenposition ��$Q�D&K�D'( is expressedby:

��� k C �(C �D� � fh� $ ����� �/C�������C�A"��� ��� �D� � 4.2 The costof a motion

The costof an elementarymotion from the robot position��$ A ��& A �D' A to ��$ E ��& E �D' E integratesthenotionof “danger”(or risk) presentedabove in thefollowing way:� A"��E � � G<�  � �yA �¢¡ �yA"��E "£ g¤A"��E

where:� £ g(A"��E is thedistancebetweenthetwo consideredpo-sitions.� �yA is thecostassociatedto thedanger� A , computedasfollows:

� A �¦¥ if � A = � P �¨§G<� �©K� G�� 7 � A otherwise

Theintroductionof thethreshold� P �¨§ on � is to reducethe influenceof small irregularitiesof the terrain: in thecaseof a flat terrainfor instance,therobotis saidto bein arisk-lessflat configuration,andonly thegoalorientationisconsideredto selectthearcto execute.� and ¡ �yA"��E is a costassociatedto theinternalconfigu-rationchangebetweenpositions

Gand M :

¡ � A"��E �ª¥ if � � E 7 � A � = ¡ P �¨§� � EB7 � A � otherwise

Thisparameterfavorsthetrajectoriesin which therobotinternalconfigurationdoesnot changetoo much. Again,the introductionof a threshold¡ P �«§ underwhich it hasnoinfluenceis to getrid of thesmallterrainirregularities.

4.3 Search algorithm

OncetheDEM is updated,a setof circle arcsis generated,andeacharcis discretizedinto adiscretesetof robotconfig-urations��$%��&���'( , whichdefinesatreestructure.Configura-tionsareregularly spaced,andaredefinedup to a maximalcurvilinearabscissaon thearcs,which correspondapprox-imately to twice the distancethat the robot is supposedtotravel until theDEM is updatedagain: this givestherobot

akind of “look ahead”behavior, andavoidstheselectionoftrajectoriesthatgo too closeto obstacles.

Theoptimalcircle arcis determinedthanksto an ¬ ­ al-gorithm, in which the heuristicis the distanceof the Dub-bins path [15] to reachthe goal. The cost to go from thelastconfigurationona circlearcto thegoal is alsoequaltothe Dubbinsdistance.Thanksto the efficiency of the ¬ ­algorithm,only a smallnumberof configurationsalongthearcsareeffectively evaluated(practically, asetof 40circlesarcsis considered,andabout20 configurationsaredefinedon eacharcs: mostof the timesonly a third or a fourth ofthisconfigurationsetis evaluated).

5 ResultsThewholenavigationloophasbeenintegratedonboardtherobot Lama,within the LAAS Architecturefor Autonomy[16]. It proved its efficiency on variouskinds of terrains:figures11and12presenttwo trajectoriesexecutedby Lamausingthis navigation loop. The meantime requiredto se-lect an optimal arc at eachstepis approximately8 < f®g :therefore,wealsousethisalgorithmto find motionsoneasyterrains.

Figure11: Lamafoundits waytrougha narrowcorridor: 85 iterationsof the navigationloop havebeenexecuted,the trajectory is about ¯#°#�long. (Live demonstrationin the“Cit e del’espace”museumin Toulouse,Sept.2000).

6 Summary and discussionWe describedan algorithmthat generateselementarymo-tionson roughterrains,which explicitly takesinto accountthegeometricconstraintsonanarticulatedchassis.Theap-proachhasbeenintegratedon boardthe robot Lama,andis very oftendemonstratedin continuouslyrunningexper-iments,wherethe rover is able to autonomouslyreachafew tensmetersdistantgoal in initially unknown terrains.This functionality is integratedwithin a more global au-tonomouslong rangenavigation system,which manages

Figure12: Lamafoundapasstoclimba 2metershighhill: 50iterationsof the navigationloop havebeenexecuted,the trajectory is about ±#1D�long. (Trial in our experimentationsite).

several terrainmodels,motion modesand localizational-gorithms[17].

Among the open problemsthat still have to be tack-led, theconsiderationof realisticdynamicissuesis oneofthe most important. Theseissueshave beenmodeledandconsideredin pioneerwork relatedto roughterrainmotionplanning,but their considerationon boardreal rovers re-quiresadditionalwork andvalidation,asshown by recentpracticalcontributions[18, 19].

References

[1] Z. Shiller andY-R. Gwo. Dynamicmotion planningof au-tonomousvehicles.IEEE Transactionson RoboticsandAu-tomation, 7(2):241–249,April 1991.

[2] S. Jimenez,A.Luciani, andC. Laugier. Predictingthe dy-namicbehaviour of a planetaryrover vehicleusingphysicalmodeling. In InternationalWorkshopon IntelligentRobotsandSystems,Yokohama(Japan). INRIA-LIFIA, 1993.

[3] M. Cherif andC. Laugier. Motion planningof autonomousoff-road vehiclesunderphysicalinteractionconstraints.InIEEE Int. Conf. on Robotics and Automation, Nagoya(Japan), pages1687–1693,May 1995.

[4] M. Cherif. Motion planningfor all-terrainvehicles:aphysi-calmodelingapproachfor copingwith dynamicandcontactinteractionconstraints.IEEE Transactionson RoboticsandAutomation, 15(2):202–218,1999.

[5] T. SimeonandB. Dacre-Wright. A practicalmotion plan-nerfor all-terrainmobilerobots. In IEEE/RSJInternationalConferenceon Intelligent Robotsand Systems,Yokohama(Japon), pages26–30,July1993.

[6] A. Hait and T. Simeon. Motion planning on rough ter-rain for an articulatedvehicle in presenceof uncertainties.In IEEE/RSJInternationalConferenceon IntelligentRobotsandSystems,Osaka(Japan), pages1126–1133,Nov. 1996.

[7] A. Hait,T. Simeon,andM. Taix. Robustmotionplanningforroughterrainnavigation. In IEEE/RSJInternationalConfer-enceon Intelligent Robotsand Systems,Kyongju (Korea),pages11–16,Oct.1999.

[8] S. Laubachand J. Burdik. An autonomoussensor-basedpath-plannerfor planetarymicrorovers. In IEEE Interna-tional ConferenceOnRoboticsandAutomation.Detroit, MI(USA), May 1999.

[9] S. Singh, R. Simmons,M.F. Smith, A. Stentz,V. Verma,A. Yahja, and K. Schwehr. Recentprogressin local andglobal traversability for planetaryrovers. In IEEE Interna-tional Conferenceon Roboticsand Automation,SanFran-cisco,Ca (USA), 2000.

[10] A. Howard andH. Seraji. Real-timeassessmentof terraintraversabilityfor autonomousrovernavigation.In IEEE/RSJInternationalConferenceon IntelligentRobotsandsystems,pages58–63.JPL,Nov. 2000.

[11] D. Langer, J. Rosenblatt,and M. Hebert. A behavior-basedsystemfor off-roadnavigation. IEEETransactionsonRoboticsandAutomation, 10(6):776–782,Dec.1994.

[12] H. Haddad,M. Khatib,S. Lacroix,andR. Chatila. Reactivenavigationin outdoorenvironmentsusingpotentialfields. InInternationalConferenceon RoboticsandAutomation,Leu-ven(Belgium), pages1232–1237,May 1998.

[13] A. Mallet, S. Lacroix, and L. Gallo. Position estimationin outdoorenvironmentsusingpixel trackingandstereovi-sion. In IEEEInternationalConferenceonRoboticsandAu-tomation,SanFrancisco,Ca(USA), pages3519–3524,April2000.

[14] A. Kemurdjian,V. Gromov, V. Mishkinyuk, V. Kucherenko,andP. Sologub. Small marsokhodconfiguration. In IEEEInternationalConferenceon RoboticsandAutomation,Nice(France), pages165–168,May 1992.

[15] L.E. Dubbins.Oncurvesof minimal lengthwith aconstraintonoveragecurvatureandwith prescribedinitial andterminalpositionsand tagents. AmericanJournal of Mathematics,79:497–516,1957.

[16] R. Alami, R. Chatila,S.Fleury, M. Ghallab,andF. Ingrand.An architecturefor autonomy. SpecialIssueof the Interna-tional Journalof RoboticsResearch on IntegratedArchitec-turesfor RobotControl and Programming, 17(4):315–337,April 1998.RapportLAAS N. 97352,Septembre1997,46p.

[17] S. Lacroix, A. Mallet, D. Bonnafous,G. Bauzil, S. Fleury,M. Herrb,andR. Chatila˙Autonomousrover navigationonunknown terrains:Functionsandintegration.In 7th Interna-tional Symposiumon ExperimentalRobotics,Honolulu, HI(USA), Dec.2000.

[18] G. Andrade-Barosso,F. Ben-Amar, P. Bidaud, andR. Chatila. Modeling robot-soil interactionfor planetaryrover motion control. In 1998 IEEE/RSJInternationalConferenceon Intelligent Robotsaned Systems,Victoria(Canada), pages576–581,Oct.1998.

[19] S.Farritor, H. Hacot,andS.Dubowsky. Physics-basedplan-ning for planetaryexploration. In IEEE InternationalCon-ferenceOn Roboticsand Automation.Leuwen(Belgium),pages278–283,May 1998.