Mul$‐RobotSystemsProbabilis$cModelingIII

CSCI7000‐006Monday,October19,2009

NikolausCorrell

Sofar

•  Probabilis$cmodelsforreac$veanddelibera$vesystems

•  Parametercalibra$onusing– Controlparameters– Geometricproper$es

•  Systemiden$fica$onforreac$veswarms

Today

•  Modelingofdelibera$vesystemswithlargestatespace– Probabilis$cmodelsforsub‐systems– DiscreteEventSystemsimula$on

•  Examples– Coverage– Taskalloca$on

Review:Probabilis$cModeling

•  Enumerateallpossiblestatesofasystem•  Calculateallstatetransi$onprobabili$es•  Writedownrateequa$onsfortheprobabilityofthesystemtobeainacertainstate

•  Solveequa$onsanaly$cally/numerically

•  Problem:Whataboutsystemswithlargestatespaces

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.

Example:coverage

•  Algorithm–  Buildaminimalspanning‐treeon‐line

– Movefrombladetobladereac$vely

–  Localiza$onbycoun$ngblades

–  Start‐overwhenlost•  Uncertainty– Naviga$on

BasicNaviga$onBehaviors

9/20/2007 NikolausCorrell 7

Quan$fyingSensor&ActuatorNoise

Timeforcoveringoneblade Probabilityofnonaviga$onerror(geometricdistribu$on)

6000experimentsinWebots,10%wheel‐slip

DiscreteEventSystemSimula$on

AllBladesinspected?

Determinenextnodentovisit

Chooserobot(closestnextevent$me),addevent$meforrobot

Algorithm

Failureprobabilites

Naviga$onSuccess?

MoveRobotton

MoveRobotsomewhereelse

NoYes

No

Yes

Webots‐GeneratedEventTimeData

DESvs.Webots:Naviga$onuncertainty

50%slip.

10%slip

DiscreteEventSystemSimula$on

•  Simula$ngthealgorithmgeneratessampletrajectoriesinstatespace

•  Previousexample:limitedtonaviga$onuncertainty

•  Simula$oncanmodelarbitrarylevelofdetail,includingcommunica$on

DESvs.Webots:Communica$on

10%wheelslip

NoComm.

Comm.

Example:DistributedRobotGarden

•  Mo$va$on:PrecisionAgriculture

•  Robotswaterandforagetomatoplants

•  Potsmonitorhumiditylevelandcoordinaterobo$csystem

•  Robotsinventoryeachplantandstoreitintoitspot’sdatabase

Sub‐tasks/Sourcesofuncertainty

•  Visualrecogni$onofripeandgreentomatoes•  Visualservoingwithmonocularvision

•  Manipula$onwith4‐DOFarm

•  Coordina$on/taskalloca$onofheterogeneoussystemoverwirelessnetwork

•  Mul$‐robotnaviga$onin$ghtenvironments

Robo$cPlaeorm

Localiza(onHagisonicStargazer

Computa(onDellLa$tudeD620

WateringSystemHargrave

Differen(alWheelsiRobotCreate

Manipula(onCrustcrawler4‐DOF

VisionLogitechQuickCam

UbuntuLinux,WillowGarageROS,USB

Plant

Infra‐redBeaconiRobotRoombabase

WirelessrouterTemperature@lert

HumiditySensorVegetronix

OpenWRTLinux,Atheroschipsets

Filter‐basedobjectrecogni$on

•  Filterimage–  Sobel– Houghtransform–  Color–  Spectralhighlights

–  Sizeandshape•  Weightedsumoffiltershighlightsobjectloca$on

Sobel Hough Color SpectralHighlights

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

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

Results:VisualServoing/Grasping

•  Percep$on– 75%correctlydetected

•  VisualServo– 75%correctgrasps(10trials)

– 28.3s+/‐10spergrasp

TaskAlloca$on

•  Challenges–  Unreliablechannel(ad‐

hocwifi)–  Uncertaintyin

naviga$onandtaskexecu$on

•  Robotsreplywiththeirdistance+lengthoftaskqueue(approx.$me)

•  Plantselects“best”robot

•  Alloca$onrepeatedperiodically

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

Modelthedistributedgarden

•  Measureaverage$meandsuccessrateof– Naviga$onfromAtoB– Watering

–  Communica$on– Harves$ng

•  Compare– Differenttaskalloca$onschemes– Distribu$onofsensing,actua$on,andcomputa$on(ex:humiditysensingontheplantvs.robot)

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

Openresearchques$ons

•  Whataboutrareevents?– Howotendowehavetotryeachsub‐system?

– Howotendoweneedtosimulatetheen$resystem?

Summary

•  Complexdelibera$vesystemscanbemodeledbystudyingsampletrajectoriesthroughstatespace

•  Openproblems– Genera$ngsufficientnumberofsamples

– Rareevents