Robotics - Artificial Intelligence: A Modern Approach

1 RoboticsChapter25 Chapter251 OutlineRobots,E ectors,andSensorsLocalizationandMappingM otionPlanningMotor ControlChapter252 MobileRobotsChapter253 ManipulatorsRRRPRRCon gurationof robot speci edby 6 numbers)6degreesof freedom(DOF)6 is theminimumnumber requiredto positionend-e ector dynamicalsystems,addvelocity for (x, y) A car hasmore DOF(3)thancontrols(2),so isnon-holonomic;cannotgenerallytransitio nbetweentwo in nitesimallyclosecon gurationsChapter255 SensorsRange nders: sonar (land,underwater),laserrange nder,radar (aircraft),tactilesensors,GPSI magingsensors: cameras(visual,infrared)Proprioceptivese nsors: shaftdecoders(joints,wheels),inertialsen sors,forcesensors,torquesensorsChapter25 6 Localization|WhereAmI?Computecurrentloca tionandorientation(pose) givenobservations:Xt+1 XtAt 2At 1 AtZt 1Xt 1 ZtZt+ , yivt tt tt+1xt+1h(xt)xt t Z1Z2Z3Z4 AssumeGaussiannoisein motionprediction,sensor lteringto produceapproximatepositionestimateRobot positionRobot positionRobot lterfor simplecases:robotlandmarkAssumesthatland marksareidenti able|otherwise,posterior is multimodalChapter2510 MappingLocalization:givenmapandobservedl andmarks,updateposedistributionMapping:g ivenposeandobservedlandmarks,updatemapdi stributionSLAM:givenobservedlandmarks,up dateposeandmapdistributionProbabilisticf ormulationof SLAM:addlandmark locationsL1.

2 Lkto thestatevector,proceedas for :planincon gurationspacede nedby therobot'sDOFsconf-3conf-1conf-2conf-3co nf-2conf-1wwelbshouSolutionis a pointtrajectory in freeC-spaceChapter2514 Con gurationspaceplanningBasicproblem:1dstat es!Convertto :divideupspaceintosimplecells,eachof whichcanbe traversed\easily"( ,convex)Skeletonization:identify nitenumber of easilyconnectedpoints/linesthatforma graphsuchthatanytwo pointsare connectedby a pathonthegraphChapter2515 Celldecompositionexamplestartgoalstartgo alProblem:may be nopathin purefreespacecellsSolution:recursivedeco mpositionof mixed(free+obstacle)cellsChapter2516 Skeletonization:VoronoidiagramVoronoidia gram:locusof pointsequidistantfromobstaclesProblem:do esn'tscalewell to higherdimensionsChapter2517 Skeletonization:ProbabilisticRoadmapA probabilisticroadmapis generatedby generatingrandompointsin C-spaceandkeepingthosein freespace.

3 Creategraphby joiningpairsby straightlinesProblem:needto generateenoughpointsto ensurethateverystart/goalpairis connectedthroughthegraphChapter2518 MotorcontrolCanviewthemotor controlproblemas a searchproblemin thedynamicratherthankinematicstatespace: { statespacede nedbyx1; x2; : : : ;_x1;_x2; : : :{ continuous,high-dimensional(Sarcoshumano id:162dimensions)Deterministiccontrol:ma nyproblemsare linear, low-dimensional,exactlyknown,observableS impleregulatory controllawsare e ectivefor speci edmotionsStochasticoptimalcontrol: veryfewproblemsexactlysolvable)approxima te/adaptivemethodsChapter2519 BiologicalmotorcontrolMotor controlsystemsare characterizedby massiveredundancyIn ,3-linkarmmovingin planethrowingat a targetsimple12-parametercontroller,onede greeof freedomat target11-dimensionalcontinuousspaceof optimalcontrollersIdea:if thearmis noisy, only\one"optimalpolicyminimizeserror at ,noise-tolerancemightexplainactualmotor behaviourHarris& Wolpert(Nature, 1998).}}

4 Signal-dependentnoiseexplainseye saccadevelocity pro leperfectlyChapter2520 SetupSupposea controllerhas\intended"controlparameters 0whichare corruptedby noise,giving drawnfromP 0 Output( ,distancefromtarget)y=F( );yChapter2521 Simplelearningalgorithm:Stochasticgradie ntMinimizeE [y2]by gradientdescent:r 0E [y2] =r 0ZP 0( )F( )2d =Zr 0P 0( )P 0( )F( )2P 0( )d =E [r 0P 0( )P 0( )y2]Givensamples( j; yj),j= 1; : : : ; N, we have^r 0E [y2] =1 NNXj=1r 0P 0( j)P 0( j)y2jFor Gaussiannoisewithcovariance , ,P 0( ) =N( 0; ), we obtain^r 0E [y2] =1 NNXj=1 1( j 0)y2jChapter2522 Whatthealgorithmis doingxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxChapter2523 Resultsfor2{ vAngle phiChapter2524 Resultsfor2{ vAngle phiChapter2525 Resultsfor2{ (y^2)StepChapter2526 SummaryTherubber hitstheroadMobilerobotsandmanipulatorsDe greesof freedomto de nerobot con gurationLocalizationandmappingas probabilisticinferenceproblems(requirego od sensor andmotionmodels)Motionplanningin con gurationspacerequiressomemethod for nitizationChapter2527}}}