October 19, Probabilistic Modeling III
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Transcript of October 19, Probabilistic Modeling III
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Mul$‐RobotSystemsProbabilis$cModelingIII
CSCI7000‐006Monday,October19,2009
NikolausCorrell
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Sofar
• Probabilis$cmodelsforreac$veanddelibera$vesystems
• Parametercalibra$onusing– Controlparameters– Geometricproper$es
• Systemiden$fica$onforreac$veswarms
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Today
• Modelingofdelibera$vesystemswithlargestatespace– Probabilis$cmodelsforsub‐systems– DiscreteEventSystemsimula$on
• Examples– Coverage– Taskalloca$on
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Review:Probabilis$cModeling
• Enumerateallpossiblestatesofasystem• Calculateallstatetransi$onprobabili$es• Writedownrateequa$onsfortheprobabilityofthesystemtobeainacertainstate
• Solveequa$onsanaly$cally/numerically
• Problem:Whataboutsystemswithlargestatespaces
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Modelingoflargestatespaces
• Iden$fykeysourcesofuncertaintyinasystem– Actua$on– Sensing– Communica$on
• Measure/approximateprobabilitydensityfunc$on
• Samplefromthesedistribu$onswhensimula$ngthealgorithmS.Ru$shauser,N.Correll,andA.Mar$noli.Collabora$veCoverageusingaSwarmofNetworkedMiniatureRobots.Robo$cs&AutonomousSystems,57(5):517‐525,2009.
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Example:coverage
• Algorithm– Buildaminimalspanning‐treeon‐line
– Movefrombladetobladereac$vely
– Localiza$onbycoun$ngblades
– Start‐overwhenlost• Uncertainty– Naviga$on
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BasicNaviga$onBehaviors
9/20/2007 NikolausCorrell 7
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Quan$fyingSensor&ActuatorNoise
Timeforcoveringoneblade Probabilityofnonaviga$onerror(geometricdistribu$on)
6000experimentsinWebots,10%wheel‐slip
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DiscreteEventSystemSimula$on
AllBladesinspected?
Determinenextnodentovisit
Chooserobot(closestnextevent$me),addevent$meforrobot
Algorithm
Failureprobabilites
Naviga$onSuccess?
MoveRobotton
MoveRobotsomewhereelse
NoYes
No
Yes
Webots‐GeneratedEventTimeData
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DESvs.Webots:Naviga$onuncertainty
50%slip.
10%slip
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DiscreteEventSystemSimula$on
• Simula$ngthealgorithmgeneratessampletrajectoriesinstatespace
• Previousexample:limitedtonaviga$onuncertainty
• Simula$oncanmodelarbitrarylevelofdetail,includingcommunica$on
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DESvs.Webots:Communica$on
10%wheelslip
NoComm.
Comm.
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Example:DistributedRobotGarden
• Mo$va$on:PrecisionAgriculture
• Robotswaterandforagetomatoplants
• Potsmonitorhumiditylevelandcoordinaterobo$csystem
• Robotsinventoryeachplantandstoreitintoitspot’sdatabase
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Sub‐tasks/Sourcesofuncertainty
• Visualrecogni$onofripeandgreentomatoes• Visualservoingwithmonocularvision
• Manipula$onwith4‐DOFarm
• Coordina$on/taskalloca$onofheterogeneoussystemoverwirelessnetwork
• Mul$‐robotnaviga$onin$ghtenvironments
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Robo$cPlaeorm
Localiza(onHagisonicStargazer
Computa(onDellLa$tudeD620
WateringSystemHargrave
Differen(alWheelsiRobotCreate
Manipula(onCrustcrawler4‐DOF
VisionLogitechQuickCam
UbuntuLinux,WillowGarageROS,USB
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Plant
Infra‐redBeaconiRobotRoombabase
WirelessrouterTemperature@lert
HumiditySensorVegetronix
OpenWRTLinux,Atheroschipsets
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Filter‐basedobjectrecogni$on
• Filterimage– Sobel– Houghtransform– Color– Spectralhighlights
– Sizeandshape• Weightedsumoffiltershighlightsobjectloca$on
Sobel Hough Color SpectralHighlights
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Inventory
• Challenges– Percep$on– Notpossiblefromsingleperspec$ve
• Algorithm- Fetchfruitinventoryfrompot(JSON)- Objectrecogni$onfrom6non‐overlappingperspec$ves
- Mergeobserva$onwithinventory• Confidencegrowswitheverymeasurement
• Inventorydura$on:45s
1
2
3
6
5
4
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VisualServoing/Grasping
• Challenges– Percep$on(fruits+stem)– LimitedDOF/workspace
• Algorithm- Selectfruitwiththestrongestconfidence
- Servotoini$alposi$on- ServotofruitusingimageJacobian
- Relyonradiuses$matefordepth
- Closegripper/retractarmwhenarrived
2
F.ChaumeleandS.Hutchinson,“Visualservocontrolparti:Basicapproaches,”Robo$cs&Automa$onMagazine,vol.13,no.4,pp.82–90
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Results:VisualServoing/Grasping
• Percep$on– 75%correctlydetected
• VisualServo– 75%correctgrasps(10trials)
– 28.3s+/‐10spergrasp
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TaskAlloca$on
• Challenges– Unreliablechannel(ad‐
hocwifi)– Uncertaintyin
naviga$onandtaskexecu$on
• Robotsreplywiththeirdistance+lengthoftaskqueue(approx.$me)
• Plantselects“best”robot
• Alloca$onrepeatedperiodically
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Naviga$on• Challenges
– Narrowpassages– Deadlocks(mul$‐robot)– Communica$on
• Localiza$on– Sensorfusion:odometry+passive
infraredbeacons– Broadcastposi$onat1Hz
• Mo$onplanning– Grid‐mapoftheenvironment:sta$c
obstacles+otherrobots– Wavefrontalgorithm(Latombe)– Reac$vebehaviorforavoiding
bumps– Reac$vebehaviorfordocking
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Modelthedistributedgarden
• Measureaverage$meandsuccessrateof– Naviga$onfromAtoB– Watering
– Communica$on– Harves$ng
• Compare– Differenttaskalloca$onschemes– Distribu$onofsensing,actua$on,andcomputa$on(ex:humiditysensingontheplantvs.robot)
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Possiblemodel
T1:Harvestrequest
T2:Robotreceivestask
T3:Robotreachesplant
x*73s+/‐15s
(p|Naviga$onfailure)x
T4:Robotgrasps
28.3s+/‐10s25%
Assump$ons
‐ Notaskalloca$on(singlerobot)‐ Infinitenumberofgraspingtrial
Nextstep
‐simulatetaskalloca$onbasedoncommunica$onmodel‐finitenumberoffruitsperplant
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Openresearchques$ons
• Whataboutrareevents?– Howotendowehavetotryeachsub‐system?
– Howotendoweneedtosimulatetheen$resystem?
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Summary
• Complexdelibera$vesystemscanbemodeledbystudyingsampletrajectoriesthroughstatespace
• Openproblems– Genera$ngsufficientnumberofsamples
– Rareevents